# International Journal of Heat and Mass Transfer (v.53, #9-10)

Turbulent collision rates of arbitrary-density particles by Leonid I. Zaichik; Olivier Simonin; Vladimir M. Alipchenkov

*(1613-1620)*. The paper deals with collisions resulting from the interaction between particles (droplets, bubbles) and turbulent eddies of the continuous fluid medium (gas or liquid). A statistical model is developed for predicting the collision rate. This model is valid for arbitrary values of the particle-to-fluid density, the particle inertia parameter, and the ratio between the particle size and the fluid turbulent lengthscale.

**Keywords:**Collision rate; Turbulence; Particles; Bubbles;

Unstably stratified Darcy flow with impressed horizontal temperature gradient, viscous dissipation and asymmetric thermal boundary conditions by A. Barletta; M. Celli; D.A. Nield

*(1621-1627)*. The free convection flow in a horizontal porous layer with an adiabatic bottom boundary and a top boundary with a stationary and non-uniform temperature distribution is investigated. The top boundary temperature distribution is assumed to have a constant gradient and the effect of viscous dissipation is taken into account. A basic parallel buoyant flow develops in the horizontal direction where the top boundary temperature changes. The governing parameters are the Gebhart number and the horizontal Rayleigh number associated with the gradient of the prescribed boundary temperature distribution. In fact, the system experiences a more and more intense effect of the frictional heating as the Gebhart number increases. A linear stability analysis of the basic buoyant flow is carried out. Oblique roll disturbances in any arbitrary horizontal direction are studied and the critical values of the horizontal Rayleigh number are evaluated numerically. It is shown that, for realistic values of the Gebhart number, the longitudinal rolls are the most unstable. Moreover, it is proved that the viscous dissipation yields a destabilising effect.

**Keywords:**Linear stability; Horizontal temperature gradient; Viscous dissipation; Porous layer; Darcy’s law; Rayleigh number;

Solidification and melting behaviors and characteristics of molten salt in cold filling pipe by Jianfeng Lu; Jing Ding; Jianping Yang

*(1628-1635)*. The solidification and melting phenomena and performances of molten salt during cold filling process in a straight pipe are numerically investigated using volume of fluid model. As the molten salt is filled into a cold pipe, the molten salt adjacent to the cold wall is rapidly cooled, and the solidification phenomena appears. After the whole pipe is filled, the solidification layer begins to melt by high temperature fluid heating. Because of the solidification layer, the flow section obviously shrinks, and the pressure loss remarkably increases. During the solidification and melting processes, the fluid temperature in the region with phase change only varies near the freezing point, and it quickly rises after the melting process. Because of the absorption or release of latent heat, the boundary heat flux of molten salt is increased in the solidification region, while it will be decreased in the melting region. As the inlet temperature rises, the pressure loss apparently decreases with the thickness of solidification layer decreasing. However, when the inlet flow velocity increases, the thickness of solidification layer decreases, but the flow resistance without phase change increases, so the pressure loss has a maximum at moderate flow velocity.

**Keywords:**Molten salt; Filling process; Solidification; Melting; Volume of fluid model;

Thermal models of railroad wheels and bearings by K.D. Cole; C.M. Tarawneh; A.A. Fuentes; B.M. Wilson; L. Navarro

*(1636-1645)*. The rolling surface for railroad wheels can be a heat source that may have an impact on the performance of the wheel bearing. In this study, experimental data from an electrically-heated railroad wheel set is analyzed by constructing thermal models of the wheel set. A steady finite-element model, a steady-analytical model, and a transient lumped-parameter model are discussed. Model parameters are determined from careful comparisons with the experimental data. The lumped-parameter model given here is intended as a simple predictive tool for determining when wheel heating caused by rail operations will have an impact on bearing temperature. The model parameters found in this study will also be useful as experimentally-validated boundary conditions in ongoing finite-element studies of heated wheels.

**Keywords:**Annular fin; Heat transfer coefficient; Parameter estimation; Contact conductance;

Fluid–structure interaction analysis of flow and heat transfer characteristics around a flexible microcantilever in a fluidic cell by Khalil Khanafer; Abdalla Alamiri; Ioan Pop

*(1646-1653)*. This study analyzes the effect of the flow conditions and the geometric variation of the microcantilever’s bluff body on the microcantilever detection capabilities within a fluidic using a finite element fluid–structure interaction (FSI) model. Periodic steady-state results of the current investigation show that the magnitude of the inlet fluid velocity, elasticity of the microcantilever, random noise, and the height of the bluff body has respective profound effect on deflection of the microcantilever. Low inlet fluid velocity condition exhibits no vortices around the microcantilever. However, the introduction of a random noise in the fluidic cell may cause the microcantilever to oscillate in a harmonic mode at low velocity. The results of this study show that microcantilevers excite earlier for large height compared with smaller heights of the bluff body at high inlet fluid velocity. This work paves the road for researchers in the area microcantilever to design efficient microcantilevers that display least errors in the measurements.

**Keywords:**Fluid-structure interaction; Fluidic cell; Heat transfer; Microcantilever;

Local and average heat transfer in the thermally developing region of an asymmetrically heated channel by Ramjee Repaka; V.V. Satyamurty

*(1654-1665)*. Forced convection heat transfer between parallel plates kept at unequal wall temperatures has been studied assuming laminar, incompressible, steady flow of a Newtonian fluid of constant thermophysical properties. Unequal wall temperatures have been characterized by an asymmetry parameter. It has been shown that the heat transferred from the walls monotonically varies with the axial distance even though the Nusselt number (at one of the walls) does not vary continuously due to asymmetry. It has been found that a modified Nusselt number varies continuously with the asymmetry parameter. Plots to obtain heat transferred from each wall have been presented which serve the purpose of mean Nusselt number. Non-dimensional heat transferred from the two walls is independent of the asymmetry parameter. The down stream boundary condition applicable for the thermal field when the walls are kept at unequal temperatures has been brought out which becomes necessary when solving elliptic form of conservation of thermal energy equation, say, when axial conduction is included.

**Keywords:**Forced convection; Asymmetric heating; Modified Nusselt number; Heat transfer continuity; Wall heat transfer;

Free convective visco-elastic flow with heat and mass transfer through a porous medium with periodic permeability by Rita Choudhury; Debasish Dey

*(1666-1672)*. The problem of three dimensional free convective flow with heat and mass transfer of a visco-elastic fluid through a highly porous medium with periodic permeability has been investigated. The porous medium is bounded by an infinite vertical porous plate with constant suction. The free stream velocity is supposed to be uniform. The analytical expressions for dimensionless skin-friction, the rate of heat transfer, the rate of mass transfer have been obtained and these results have been presented graphically for different values of the flow parameters involved in the solution.

**Keywords:**Visco-elastic; Heat transfer; Mass transfer; Prandtl number; Sherwood number; Nusselt number; Schmidt number;

Preparation and pool boiling characteristics of copper nanofluids over a flat plate heater by R. Kathiravan; Ravi Kumar; Akhilesh Gupta; Ramesh Chandra

*(1673-1681)*. The copper nanoparticles of average size of 10 nm have been prepared by the sputtering method and characterized through atomic force microscopy (AFM), X-ray diffraction (XRD) and transmission electron microscopy (TEM). The pool boiling heat transfer characteristics of 0.25%, 0.5% and 1.0% by weight concentrations of copper nanoparticles has been studied. Different copper based nanofluids were prepared in both, distilled water and distilled water with 9.0 wt% of sodium lauryl sulphate anionic surfactant (SDS). The pool boiling heat transfer data were acquired for the boiling of nanofluids over a 30 mm square and 0.44 mm thick stainless steel plate heater. The experimental results show that for the critical heat flux of pure water is 80% higher than that of water–surfactant fluid. Also, it was found that the critical heat flux for 0.25%, 0.5% and 1.0% concentrations of copper nanoparticles in copper–water nanofluids are 25%, 40% and 48% higher than that of pure water. But in the case of copper–water with surfactant nanofluids comparing with pure water, the CHF decreases to 75%, 68%, and 62% for respective concentrations of copper nanoparticles. The heat transfer coefficient decreases with increase of nanoparticles concentration in both water–copper and water–copper with surfactant nanofluids.

**Keywords:**Nanofluids; Copper nanoparticles; Critical heat flux; Sputtering; Boiling;

Heat and fluid flow characteristics of liquid sodium flowing past a nuclear fuel element with non-uniform energy generation by M.K. Ramis; G. Jilani

*(1682-1690)*. The prime objective of the present study is to analyze numerically the steady state fluid flow and heat transfer characteristics of liquid sodium as a coolant flowing past over a rectangular nuclear fuel element having non-uniform volumetric energy generation. Accordingly, employing stream function-vorticity formulation and using finite difference schemes, the equations governing the flow and thermal fields in the coolant are solved simultaneously with energy equation for the fuel element by satisfying the conditions of continuity of temperature and heat flux at the solid–fluid interface. Keeping Prandtl number

*Pr*= 0.005 for liquid sodium as constant, numerical results are presented and discussed for a wide range of aspect ratio*A*_{r}, conduction–convection parameter*N*_{cc}, total energy generation parameter*Q*_{t}and Reynolds number Re_{H}. It is concluded that the rate of heat dissipation from the fuel element to the coolant is independent of*A*_{r},*N*_{cc}and*Q*_{t}, whereas it increases in proportion to the increase in Re_{H}. It is also found that for a given material of the fuel element, there is an upper limiting value of*N*_{cc}and Re_{H}beyond which decrease in coolant temperature is negligibly small.**Keywords:**Nuclear fuel element; Conjugate heat transfer; Finite difference schemes; Conduction–convection parameter; Non-uniform energy generation;

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity by Yasin Varol; Hakan F. Oztop; Moghtada Mobedi; Ioan Pop

*(1691-1698)*. A numerical study on natural convection heat transfer of cold water near 4 °C in a thick bottom walled cavity filled with a porous medium has been performed. It is assumed that the cavity is isothermally heated from the outside of the thick bottom wall and cooled from ceiling. The finite-difference method has been used to solve the governing partial differential equations of heat and fluid flow. Effects of thermal conductivity ratio, Rayleigh number and bottom wall thickness on heat transfer from the bottom to the ceiling have been studied. The heatline visualization technique has been used to demonstrate the path of heat transport through the enclosure. Moreover, streamlines and isotherms have been used to present fluid flow and temperature distributions. The obtained results show that multiple circulation cells are formed in the cavity and the local Nusselt numbers at the bottom wall and solid–fluid interface are highly affected by formed cells. The increase of Rayleigh number and thermal conductivity ratio increases heat transfer through the cavity. However, the increase of thickness of the bottom wall reduces the mean Nusselt number. Almost one-dimensional conduction heat transfer is observed in the solid bottom wall of the cavity.

**Keywords:**Heatline; Maximum density; Conjugate; Natural convection;

Theoretical study of conjugate heat transfer effects on temperature profiles in parallel flow with embedded heat sources by Ananthanarayanan Veeraragavan; Christopher Cadou

*(1699-1711)*. A two-dimensional model for heat transfer in a “simulated flame” modeled as an embedded heat source is developed along with an analytical solution that relates the temperature field in the channel to the flow Pe number. The solution is derived from first principles by modeling the flame as a volumetric heat source and by applying “jump conditions” across the heat release zone. The model explores the role of heat recirculation via the structure of the device by accounting for the thermal coupling between the structure and the gas. The unique aspect of the model is that it solves for the two-dimensional temperature fields in both the structure and the gas simultaneously. The solution is obtained using separation of variables in the streamwise (

*x*) and the transverse (*y*) directions. Thermal coupling between the structure and gas is achieved by requiring that the temperatures and heat fluxes match at the interface. The outer structure boundary can be either adiabatic or have a convective heat loss based on Newton’s law of cooling. The resulting solution is a Fourier series (for both structure and gas temperature fields) which depends on the flow Pe and the outer structure boundary condition. This simple model and the resulting analytical solution provide an extremely computationally efficient tool for exploring the effects of varying channel height and gas velocity on the temperature distribution associated with reacting (combusting) flow in a channel. Understanding these tradeoffs is important for developing miniaturized, combustion-based power sources.**Keywords:**Micro/mesoscale combustion; Parallel plate; Conjugate heat transfer; Heat recirculation;

Development of a new simulation model of spin coating process and its application to optimize the 450 mm wafer coating process by Jung-Yeul Jung; Yong Tae Kang; Junemo Koo

*(1712-1717)*. A new one-dimensional simulation model to predict the surface coverage and average thickness of coating films obtained from spin coating processes is developed adopting moving mesh technique. The effects of initial profile, dispensed volume, solvent vapor pressure, relative humidity and initial viscosity on the coating film geometry are investigated numerically. The initially dispensed volume, solvent vapor pressure, initial viscosity and wafer rotation speed are found to be effective parameters to control the surface coverage and average film thickness. The relations between spin coating process parameters and the film geometry parameters, surface coverage and average film thickness, are derived from the new model. It is found that the photoresist solution consumption per a given size of chips could be reduced by optimizing the operation parameters.

**Keywords:**Spin coating; Photoresist; Photoresist consumption minimization; Wafer enlargement;

A fully coupled, transient double-diffusive convective model for salt-gradient solar ponds by Francisco Suárez; Scott W. Tyler; Amy E. Childress

*(1718-1730)*. A fully coupled two-dimensional, numerical model that evaluates, for the first time, the effects of double-diffusive convection in the thermal performance and stability of a salt-gradient solar pond is presented. The inclusion of circulation in the upper and lower convective zone clearly shows that erosion of the non-convective zone occurs. Model results show that in a two-week period, the temperature in the bottom of the solar pond increased from 20 °C to approximately 52 °C and, even though the insulating layer is being eroded by double-diffusive convection, the solar pond remained stable. Results from previous models that neglect the effect of double-diffusive convection are shown to over-estimate the temperatures in the bottom of the solar pond. Incorporation of convective mixing is shown to have profound impacts on the overall stability of a solar pond, and demonstrates the need to actively manage the mixing and heat transfer to maintain stability and an insulating non-convective zone.

**Keywords:**Solar pond; Convection; Double-diffusive convection; Stability; Radiation absorption; Transient model;

System instability of evaporative micro-channels by Hee Joon Lee; Shi-chune Yao

*(1731-1739)*. In parallel evaporative micro-channels, system instability may occur in terms of cyclical fluctuations at a long period. This is due to the co-existence of the liquid phase flow at high mass flux and the two-phase flow at a lower mass flux among different parallel channels under the same total pressure drop. For a system at constant flow rate pumping, with a pressure regulating tank and a constant heating pre-heater, alternations between these two states of boiling and non-boiling could happen with a period of minutes. This cyclical system instability has been modeled, where the liquid phase flow occurs at conditions of high inlet subcooling and low surface heat flux that the boiling inception is hard to initiate. The system instability criteria are established in terms of a system binary states parameter,

*S*, and a non-dimensional surface heat flux. This model has been validated experimentally.**Keywords:**System; Instability; Evaporation; Parallel micro-channels; Incipient boiling;

Flow instability of evaporative micro-channels by Hee Joon Lee; Dong Yao Liu; Shi-chune Yao

*(1740-1749)*. When boiling occurs in a micro-channel, the growing bubbles could be confined. They expand both upstream and downstream and cause flow instability in the form of flow fluctuations. The instability occurs frequently when the Bond number of the fluid in the micro-channel is less than unity. To reduce the flow instability, installation of an inlet orifice at the upstream or the micro-channel expanding at the downstream are found to be effective. A generalized instability model for micro-channels was established, which includes the effects of both inlet orifice and channel expansion. Experiments of evaporating water in 48 parallel micro-channels with 353 μm hydraulic diameter were conducted, and the generalized instability criterion was validated.

**Keywords:**Instability; Evaporation; Micro-channel; Inlet orifice; Expanding channel; Cross-cutting;

Modeling fluid spread in thin fibrous sheets: Effects of fiber orientation by A. Ashari; T.M. Bucher; H. Vahedi Tafreshi; M.A. Tahir; M.S.A. Rahman

*(1750-1758)*. In this paper, a dual-scale model is developed to simulate the radial spreading of liquids in thin fibrous sheets. Using 3-D microscale simulations, the required constitutive equations, capillary pressure and relative permeability, have been determined at each saturation level and used in a macroscale model developed based on the Richards’ equation of two-phase flow in porous media. The dual-scale approach allowed us to include the partially-saturated region of a porous medium in calculations. Simulating different fibrous sheets with identical parameters but different in-plane fiber orientations, it is revealed that the rate of fluid spread increases with increasing the in-plane alignment of the fibers. Our simulations are discussed with respect to existing studies in the literature.

**Keywords:**Fibrous porous media; Two-phase flows; Anisotropic permeability; Fiber orientation; Absorbency; CFD simulation;

Laminar natural convection in an air-filled square cavity with partitions on the top wall by W. Wu; C.Y. Ching

*(1759-1772)*. The laminar natural convection in an air-filled square cavity with a partition on the top wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number

*Gr*_{H}of approximately 1.3 × 10^{8}) and non-dimensional top wall temperatures*θ*_{T}of 0.56 (insulated) to 2.3. Experiments were performed with an aluminum partition with non-dimensional height*H*_{P}/*H*of 0.0625 and 0.125 attached to the top wall at*x*/*H*= 0.1, 0.2, 0.4 and 0.6. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields, but were mainly limited to the vicinity of the partition. The partition on the heated top wall resulted in a recirculating flow between the partition and the heated vertical wall. For a given partition height, the structure of this recirculating flow was dependent on the partition location and*θ*_{T}. A thermal boundary layer developed along the rear surface of the partition due to the thermal effect of the partition. The ambient temperature outside the boundary layer and*Nu*near the corner region was affected by the partition height due to the change in the recirculating flow and due to the thermal effect on the rear surface of the partition.**Keywords:**Laminar natural convection; Square cavity; Partition height and location;

Nucleate boiling heat transfer enhancement for water and FC-72 on titanium oxide and silicon oxide surfaces by W. Wu; H. Bostanci; L.C. Chow; Y. Hong; M. Su; J.P. Kizito

*(1773-1777)*. An experimental study was performed to investigate the nucleate boiling and critical heat flux (CHF) of water and FC-72 dielectric liquid on hydrophilic titanium oxide (TiO

_{2}) nanoparticle modified surface. A 1 cm^{2}copper heater with 1 μm thick TiO_{2}coating was utilized in saturated pool boiling tests with water and highly-wetting FC-72, and its performance was compared to that of a smooth surface. Results showed that TiO_{2}coated surface increased CHF by 50.4% and 38.2% for water and FC-72, respectively, and therefore indicated that boiling performance enhancement depends on the level of wettability improvement. A silicon oxide (SiO_{2}) coated surface, exhibiting similar surface topology, was tested to isolate the roughness related enhancement from the overall enhancement. Data confirmed that hydrophilicity of TiO_{2}coated surface provides an additional mechanism for boiling enhancement.**Keywords:**Boiling enhancement; Titanium oxide; Silicon oxide; Hydrophilic;

A general correlation for evaporative heat transfer in micro/mini-channels by Wei Li; Zan Wu

*(1778-1787)*. Experimental results of the saturated-flow boiling heat transfer in micro/mini-channels for both multi- and single-channel configurations were obtained from the literature. The collected database contains more than 3700 data points, covering a wide range of working fluids, operational conditions, and different micro-channel dimensions. The whole database was analyzed by using various existing correlations to verify their respective accuracies. However, none of the existing correlations could predict the data sets precisely. Using the boiling number, Bond number and Reynolds number, a general correlation for evaporative heat transfer in micro/mini-channels was established. In addition, the Bond number in predicting heat-transfer coefficients can be used as a criterion to classify a flow path as a micro-channel or as a conventional macro-channel.

**Keywords:**Micro-channel; Saturated-flow boiling; Heat transfer; Bond number; Reynolds number;

Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink by M. Subhas Abel; Mahantesh M. Nandeppanavar; Sharanagouda B. Malipatil

*(1788-1795)*. In the present article an analysis is carried out to study the boundary layer flow and heat transfer characteristics of a second grade, non-Newtonian fluid through a porous medium. The stretching sheet is assumed to be permeable so that suction effects come into play. The effects of viscous dissipation, non-uniform heat source/sink on heat transfer are addressed. The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. Analytical solutions are obtained for the resulting boundary value problems. The effects of viscous dissipation and non-uniform heat source/sink, Prandtl number, Eckert number and suction/injection on heat transfer are shown in several plots for two different heating processes (CST and PST cases). Dimensionless surface temperature gradient is tabulated for various values of the governing the parameters.

**Keywords:**Stretching sheet; Second grade fluid; Porous medium; Non-uniform heat source/sink; Suction/injection;

Heat flow choking in carbon nanotubes by Hai-Dong Wang; Bing-Yang Cao; Zeng-Yuan Guo

*(1796-1800)*. Based on Einstein’s mass–energy relation, the equivalent mass of thermal energy or heat is identified and referred to as thermomass. Hence, heat conduction in carbon nanotubes (CNTs) can be regarded as the motion of the weighty phonon gas governed by its mass and momentum conservation equations. The momentum conservation equation of phonon gas is a damped wave equation, which is essentially the general heat conduction law since it reduces to Fourier’s heat conduction law as the heat flux is not very high and the consequent inertial force of phonon gas is negligible. The ratio of the phonon gas velocity to the thermal sound speed (the propagation speed of thermal wave) can be defined as the thermal Mach number. For a CNT electrically heated by high-bias current flows, the phonon gas velocity increases along the heat flow direction, just like the gas flow in a converging nozzle. The heat flow in the CNT is governed by the electrode temperature until the thermal Mach numbers of phonon gas at the tube ends reach unity, and the further reduction of the electrode temperature has no effect on the heat flow in the CNT. Under this condition, the heat flow is said to be choked and temperature jumps will be observed at the tube ends. In this case the predicted temperature profile of the CNT based on Fourier’s law is much lower than that based on the general heat conduction law. The thermal conductivity which is determined by the measured heat flux over the temperature gradient of the CNT will be underestimated, and this thermal conductivity is actually the apparent thermal conductivity. In addition, the heat flow choking should be avoided in engineering situations to prevent the thermal failure of materials.

**Keywords:**Thermal wave; Choking; Thermal inertia; Carbon nanotube;

A study of the influence of initial liquid volume on the capillary flow in an interior corner under microgravity by Cai-Xia Wang; Sheng-Hua Xu; Zhi-Wei Sun; Wen-Rui Hu

*(1801-1807)*. In this work the influence of initial liquid volume on the capillary flow in an interior corner is studied systematically by microgravity experiments using the drop tower, under three different conditions: the Concus–Finn condition is satisfied, close to and dissatisfied. The capillary flow is studied by discussing the movement of tip of the meniscus in the corner. Experimental results show that with the increase of initial liquid volume the tip location increases for a given microgravity time, the achievable maximum tip velocity increases and the flow reaches its maximum tip velocity earlier. However, the results for the three different conditions show some difference.

**Keywords:**Capillary flow; Concus–Finn condition; Critical contact angle;

Use of infrared thermography for the study of evaporation in a square capillary tube by F. Chauvet; S. Cazin; P. Duru; M. Prat

*(1808-1818)*. In this paper we report experimental results on evaporation of a volatile wetting liquid in a capillary tube of square internal cross section, when conditions are such that liquid films develop along the tube internal corners under the effect of capillary forces, as the bulk meniscus recedes inside the tube. Combining an infrared thermography technique with visualizations by ombroscopy makes it possible to determine the time-space evolution of the temperature minimum on the capillary outer surface together with the bulk meniscus position within the tube. When the tube is held horizontal, the temperature minimum stays at the tube entrance and the evaporation rate reaches a stationary value. In contrast with the horizontal case, the position of the temperature minimum changes when the bulk meniscus has sufficiently receded inside the tube when the tube is vertical and opened at the top. The rate of evaporation then decreases significantly. This is explained by the thinning of the corner films in the vertical tube entrance region, under the conjugated effects of gravity and viscous forces up to the depinning of the films from the tube entrance. When the tube is held horizontal, the capillary effects are dominant and the film thickness remains essentially constant in the tube entrance region. This analysis is supported by a simple model of liquid flow within the corner films.

**Keywords:**Evaporation; Capillary tube; Liquid film; Corner flow; Infrared thermography;

Analysis of mixed convection in a lid-driven porous square cavity with linearly heated side wall(s) by Tanmay Basak; S. Roy; Sandeep Kumar Singh; I. Pop

*(1819-1840)*. Mixed convection flows in a lid-driven square cavity filled with porous medium are studied numerically using penalty finite element analysis for uniformly heated bottom wall, linearly heated side walls or cooled right wall. The top wall is well insulated and set with uniform velocity. The relevant parameters in the present study are Darcy number ( Da = 10 - 5 – 10 - 3 ) , Grashof number ( Gr = 10 3 – 10 5 ) , Prandtl number (

*Pr*= 0.015–10) and Reynolds number (*Re*= 1–10^{2}). The isotherms are generally symmetric at smaller*Pr*irrespective of*Da*and*Re*at*Gr*= 10^{5}for linearly heated side walls. The isotherms are also almost symmetric at small*Re*with higher*Gr*( Gr = 10 5 ) and*Da*( Da = 10 - 3 ) and natural convection is found to be dominant whereas the isotherms are compressed near the left and bottom walls at higher*Re*for linearly heated side walls. Compression of isotherms and dominance of forced convection is also observed at*Re*= 10^{2}for linearly heated left wall and cooled right wall. The local Nusselt number of the bottom wall ( Nu b ) for low*Da*is almost constant whereas*Nu*_{b}for higher*Da*and*Pr*shows non-monotonic variation at*Re*= 10 and an overall decreasing trend is observed at*Re*= 10^{2}for linearly heated side walls. The local Nusselt numbers of left and right walls ( Nu l and Nu r ) increase for*Da*= 10^{−3}and*Pr*= 0.7 whereas oscillatory trend is observed at*Re*= 10–10^{2}and*Pr*= 10. For linearly heated left wall and cooled right wall,*Nu*_{b}increases from the left edge towards the right edge of the bottom wall for both cases*Re*= 10 and 10^{2}irrespective to*Pr*and*Da*. It is also observed that*Nu*_{r}for higher*Pr*and*Da*is found to increase monotonically at both Re = 10 and 10 2 and Nu l show non-monotonic trend for higher*Pr*and*Da*at*Re*= 10 whereas for Re = 10 2 ,*Nu*_{l}increases monotonically. Average Nusselt numbers Nu b ¯ , Nu l ¯ , Nu r ¯ are found almost invariant with*Gr*for low*Pr*with all*Da*for linearly heated side walls or cooled right wall. On the other hand, Nu b ¯ is found to vary exponentially at higher*Pr*and*Da*and oscillations in Nu l ¯ and Nu r ¯ are observed for*Re*= 10 whereas increasing trend is observed for Nu l ¯ and Nu r ¯ for*Re*= 10^{2}for both linearly heated side walls or cooled right wall.**Keywords:**Mixed convection; Square cavity; Porous medium; Uniform and non-uniform heating; Penalty finite element method;

CuS/Cu

_{2}S nanofluids: Synthesis and thermal conductivity by Xiaohao Wei; Tiantian Kong; Haitao Zhu; Liqiu Wang*(1841-1843)*. We apply the chemical solution method to synthesize CuS/Cu

_{2}S nanofluids and experimentally measure their thermal conductivity. The measured thermal conductivity shows that the presence of nanoparticles can either upgrade or downgrade fluid conductivity, a phenomenon predicted by the recent thermal-wave theory of nanofluids.**Keywords:**Thermal-waves; Nanofluids; CuS/Cu

_{2}S nanoparticles; Chemical solution method; Thermal conductivity; Conductivity enhancement;

Blood flow velocity and ultra-filtration velocity measured by CT imaging system inside a densely bundled hollow fiber dialyzer by Junfeng Lu; Wen-Qiang Lu

*(1844-1850)*. Hollow fiber dialyzer is a device used for years in the therapy of hemodialysis treating people with severe kidney problems. In the design of such a device, the measurement of the blood flow velocity and the ultra-filtration velocity inside the dialyzer are very important. And non-invasive measurement solutions are highly desired during experiment. This paper presents a novel non-invasive measurement method to handle this work. The method adopts a CT (Computed Tomography) system to acquire blood motion data inside a densely bundled hollow fiber dialyzer, and then, by adopting a series of image processing methods, the blood flow velocity as well as the ultra-filtration velocity is measured.

**Keywords:**Blood flow velocity measurement; Ultra-filtration velocity measurement; Densely bundled hollow fiber dialyzer; CT imaging technology; Dialyzer design;

Influence of initial heat generation on dynamic characteristics of transient boiling crisis of water by V.I. Deev; K.V. Kutsenko; A.A. Lavrukhin; V.S. Kharitonov

*(1851-1855)*. The dynamic characteristics of transient boiling crisis were measured in the experiments with saturated water in a pool at atmospheric pressure. It was shown that initial heat generation in a heater strongly affects the process of transition from nucleate to film boiling under conditions of fast increase of heating power. A technique of calculation of critical heat flux, temperature drop and critical time interval is presented.

**Keywords:**Power transients; Water pool boiling; Critical heat flux; Physical models;

Convective diffusion from strip-like micro-probes into colloidal suspensions by Ondřej Wein

*(1856-1867)*. Full equations of convective diffusion are solved numerically for a strip-like (2D) electrodiffusion friction probe in a stream of microdisperse liquid, assuming a non-linear near-to-wall velocity profile ranging from simple shear flow (

*p*= 1) to ideal slip (*p*= 0). The range of generalized Peclet number*H*from*H*= 0.01 (almost pure spatial diffusion) to*H*= 100 (diffusion layer with negligible longitudinal diffusion) covers all cases of possible experimental relevance. The main result is expressed as a relative deviation of actual total diffusion flux*N*from its diffusion-layer approximation*N*_{DLA},*Ψ*=*N*/*N*_{DLA}− 1.**Keywords:**Electrodiffusion friction probes; Microdisperse fluid flow; Longitudinal diffusion;

Convective diffusion from convex microprobes into colloidal suspensions: The edge effects by Ondřej Wein

*(1868-1873)*. Electrochemically driven steady convective diffusion is analyzed for electrodiffusion friction probes of arbitrary convex shape in a stream of microdisperse liquid, assuming non-linear velocity profiles ranging from simple shear flow (

*p*= 1) to ideal slip motion (*p*= 0). Correction on the edge effects due to spatial diffusion at medium Peclet numbers is given, using the recent numerical data about the strip-like probes by Wein Simple correction formulas are presented for the disk-like probes.**Keywords:**Electrodiffusion diagnostics of flow; Microdisperse liquids; Spatial diffusion; Edge effects;

Autocalibration of electrodiffusion friction probes in microdispersion liquids by Ondřej Wein

*(1874-1881)*. Voltage-step transient problem, useful in electrodiffusion diagnostics of the near-to-wall flow kinematics, is solved for microdispersion liquids that manifest non-linear velocity profile close to the wall. The known solution of this problem for circular probes in a diffusion-layer approximation (DLA), assuming a power-law representation of the velocity profiles, Wein and Kovalevskaya , is corrected on the edge effects, important at low Peclet number, i.e. for the small probes and slow flows. A model of the transient process, controlled by convective diffusion at finite Peclet number, is developed here as a generalization of the approach by Wein et al. . The model is applied for treating primary voltage-step transient data of several aqueous high-molecular polysaccharide solutions, displaying strongly non-linear velocity profiles close to the wall.

**Keywords:**Electrodiffusion friction probes; Voltage-step transient; Edge effects; Microdispersion liquids; Non-linear velocity profiles;

Explicit full field analytic solutions for two-dimensional heat conduction problems with finite dimensions by Ru-Li Lin

*(1882-1892)*. This study presents explicit analytical solutions of heat conduction problems for isotropic media with finite dimensions. The geometry configurations considered in this study include composite layer, wedge and circular media. The boundary conditions are assumed to be either thermal isolation or isothermal. The full field analytical solutions of temperature and heat fluxes for the composite layered media subjected to an embedded heat source are derived first by Fourier transform technique in conjunction with the image method. The corresponding problems of composite wedge and circular media are constructed by conformal mapping and the solutions of composite layer media. The explicit full field solutions are expressed in simple closed-forms which can be easily used in engineering applications. The numerical calculations of the temperature and heat fluxes distributions are provided in full field configuration base on the available analytic solutions.

**Keywords:**Green’s function; Conformal mapping; Image method; Heat conduction;

The effect of cycle boundary conditions and adsorbent grain size on the water sorption dynamics in adsorption chillers by I.S. Glaznev; Yu.I. Aristov

*(1893-1898)*. The aim of this work was an experimental study of the temporal evolution of isobaric adsorption uptake (release) for simplest configuration of an adsorbent-heat exchanger unit, namely, a monolayer of loose adsorbent grains located on a metal plate. The study was performed by a large temperature jump method at four various boundary conditions of an adsorptive heat transformation cycle typical for air-conditioning application driven by low temperature heat:

*T*_{e}= 5 and 10 °C,*T*_{c}= 30 and 35 °C and*T*_{HS}= 80 °C. The size of the Fuji silica grains was varied from 0.2 to 1.8 mm to investigate its effect on water sorption dynamics. For each boundary set and grain size the experimental kinetic curve could be described by an exponential function up to 80–90% of the equilibrium conversion. Desorption runs are found to be faster than appropriate adsorption runs by a factor of 2.2–3.5, hence, for optimal durations of the isobaric ad- and desorption phases of the chilling cycle should be selected accordingly. The size*R*of the adsorbent grains was found to be a powerful tool to manage the dynamics of isobaric water ad-/desorption. For large grains the characteristic time was strongly dependent on the grain size and proportional to*R*^{2}. Much less important appeared to be an impact of the boundary conditions which variation just weakly affected the dimensionless kinetic curves for the four tested cycles. The maximal specific cooling/heating power was proportional to the maximal temperature difference Δ*T*and the contact area*S*between the layer and the metal plate, and can exceed 10 kW/kg. The heat transfer coefficient*α*estimated from this power was as large as 100–250 W/(m^{2}K) that much exceeds the value commonly used to describe the cycle dynamics.**Keywords:**Heat and mass transfer; Adsorption kinetics; Adsorbent; Transport processes; Adsorption chillers; Large temperature jump method;

Heat transfer characteristics of premixed flame impinging upwards to plane surfaces inclined with the flame jet axis by G.K. Agrawal; Suman Chakraborty; S.K. Som

*(1899-1907)*. A theoretical model of premixed turbulent flames impinging obliquely on a flat surface has been developed to predict the influences of jet Reynolds number, ratio of plate separation distance to nozzle diameter, plate inclination angle and equivalence ratio on the heat transfer characteristics. The model is based on numerical solution of the coupled governing differential equations for conservation of mass, momentum and energy. Methane and air have been considered as fuel and oxidizer respectively. Global two-step irreversible reaction kinetics has been employed for the oxidization of methane. The RNG

*k*–*ε*model has been used to compute the turbulence, and the Discrete Ordinates model has been used for radiative transfer in the flame. It has been observed that the heat flux distribution for an inclined plate is asymmetric about the transverse axis of tilt that divides the plate into uphill and downhill part. The heat flux in the uphill part is higher as compared to that at corresponding locations in downhill part. The local heat flux in the downhill part of the plate increases with a decrease in the plate inclination angle, while in the uphill part, the local heat flux at locations away from the plate centre is almost independent of the plate inclination angle. The local heat flux decreases with an increase in heating height. A fuel rich mixture increases the plate heat flux. The average Nusselt number, Nu ¯ , increases with an increase in jet Reynolds number, Re, and a decrease in the plate inclination angle. The increase in Nu ¯ is profound at higher values of Re and for a decrease in plate inclination angle from 10° to 0°.**Keywords:**Flame impingement; Heat transfer; Premixed flame;

Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method by Liang Hao; Ping Cheng

*(1908-1913)*. Pore-scale simulations of two phase flows in a packed-sphere bed and in a carbon paper gas diffusion layer (GDL) are carried out using the free energy multiphase lattice Boltzmann method (LBM). The simulations are performed based on the detailed microstructure of the porous media under periodic boundary conditions such that the average phase saturations in the porous medium remain constant. A comparison of the simulated and measured relative permeabilities for the packed sphere bed as a function of non-wetting phase saturation is performed, and effects of the wettability and the anisotropic characteristics of relative permeabilities of the GDL are investigated.

**Keywords:**Pore-scale; Relative permeability; Porous media; Lattice Boltzmann method;

Influence of carbon nanotube suspension on the thermal performance of a miniature thermosyphon by Zhen-hua Liu; Xue-fei Yang; Guo-san Wang; Guang-liang Guo

*(1914-1920)*. An experimental study was carried out to understand the heat transfer performance of a miniature thermosyphon using water-based carbon nanotube (CNT) suspensions as the working fluid. The suspensions consisted of deionized water and multi-wall carbon nanotubes with an average diameter of 15 nm and a length range of 5–15 μm. Experiments were performed under three steady operation pressures of 7.4 kPa, 13.2 kPa and 20 kPa, respectively. Effects of the CNT mass concentration and the operation pressure on the average evaporation and condensation heat transfer coefficients, the critical heat flux and the total heat resistance of the thermosyphon were investigated and discussed. Experimental results show that CNT suspensions can apparently improve the thermal performance of the thermosyphon and there is an optimal CNT mass concentration (about 2.0%) to achieve the maximum heat transfer enhancement. The operation pressure has a significant influence on the enhancement of the evaporation heat transfer coefficient, and slight influences on the enhancement of the critical heat flux. The enhanced heat transfer effect is weak at low heat fluxes while it is increased gradually with increasing the heat flux. The present experiment confirms that the thermal performance of a miniature thermosyphon can be strengthened evidently by using CNT suspensions.

**Keywords:**Nanoparticle; Carbon nanotube; Nanofluid; Heat pipe; Boiling heat transfer;

The theoretical simulation of the effect of solid–liquid contact angle on the critical heat flux of saturated water jet boiling on stagnation zone by Yu-hao Qiu; Zhen-hua Liu

*(1921-1926)*. A theoretical simulation was carried out for predicting the critical heat flux (CHF) of convective boiling for a round saturated water jet impingement on the stagnation zone of a hot surface. The study was focused on the effect of the solid–liquid contact angle on the CHF. A theoretical model based on the Long wave instability was applied to calculate the maximum liquid sub-film thickness under boiling bubbles and finally a semi-empirical and semi-theoretical correlation was proposed by combining the simulated calculation and the experimental data from the common metal heating surface. The correlation revealed the comprehensive effects of solid–liquid contact angles, jet velocity and jet diameter on the CHF and agreed well with the experimental data proposed by authors in the previous study.

**Keywords:**Jet; Boiling; Critical heat flux; Solid–liquid contact angle; Simulation;

Convective heat transfer over a heated square porous cylinder in a channel by Horng-Wen Wu; Ren-Hung Wang

*(1927-1937)*. A numerical study is made of the unsteady flow and convection heat transfer for a heated square porous cylinder in a channel. The general Darcy–Brinkman–Forchheimer model is adopted for the porous region. The parameters studies including porosity, Darcy number, and Reynolds number on heat transfer performance have been explored in detail. The results indicate that the average local Nusselt number is augmented as the Darcy number increases. The average local Nusselt number increases as Reynolds number increases; in particular, the increase is more obvious at a higher Darcy number. In contrast, the porosity has slight influence on heat transfer.

**Keywords:**Unsteady flow; Square porous cylinder; Convection heat transfer;

An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system by S.C. Wu; G.R. Liu; X.Y. Cui; T.T. Nguyen; G.Y. Zhang

*(1938-1950)*. This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for analyzing 2D and 3D transient heat transfer problems with mixed boundary conditions and complicated geometries. In the ES-PIM, shape functions are constructed using the polynomial PIM with the Delta function property for easy treatment of essential boundary conditions. A generalized smoothing technique is used to reconstruct the temperature gradient field within the edge-based smoothing domains. The generalized smoothed Galerkin weak form is then used to establish the discretized system equations. Our results show that the ES-PIM can provide more close-to-exact stiffness compared with the “overly-stiff” finite element method (FEM) and the “overly-soft” node-based smoothed point interpolation method (NS-PIM). Owing to this important property, the present ES-PIM provides more accurate solutions than standard FEM using the same mesh. As an example, a practical cooling system of the rapid direct plasma deposition dieless manufacturing is studied in detail using the present ES-PIM, and a set of “optional” processing parameters of fluid velocity and temperature are found.

**Keywords:**Numerical methods; Meshfree method; Transient heat transfer; Gradient smoothing; Point interpolation method; Rapid plasma deposition dieless manufacturing;

Water transport characteristics in a passive liquid-feed DMFC by Chao Xu; Amir Faghri

*(1951-1966)*. A two-dimensional, two-phase, non-isothermal model was developed to investigate the water transport characteristics in a passive liquid-feed direct methanol fuel cell (DMFC). The liquid–gas two-phase mass transport in the porous anode and cathode was formulated based on multi-fluid model in porous media, and water and methanol crossover through the membrane were considered with the effect of diffusion, electro-osmotic drag, and convection. The model enabled numerical investigation of the effects of various operating parameters, such as current density, methanol concentration, and air humidity, as well as the effect of the cathode hydrophobic air filter layer, on the water transport and cell performance. The results showed that for the free-breathing cathode, gas species concentration and temperature showed evident differences between the cell and the ambient air. The use of a hydrophobic air filter layer at the cathode helped to achieve water recovery from the cathode to the anode, although the oxygen transport resistance was increased to some extent. It was further revealed that the water transport can be influenced by the ambient relative humidity.

**Keywords:**Passive DMFC; Water transport; Two phase model; Air filter layer;

A general criterion for evaporative heat transfer in micro/mini-channels by Wei Li; Zan Wu

*(1967-1976)*. This paper presents a general criterion to classify a channel as micro-channel or macro-channel. Experimental results of saturated-flow boiling heat transfer in micro/mini-channels for both multi- and single-channel configurations were obtained from the literature. The collected database contains 4228 data points, covering a wide range of working fluids, operational conditions, and different micro-channel dimensions. Seven existing correlations were evaluated against the database to verify their respective accuracies. A combined non-dimensional number Bo ∗ Re l 0.5 = 200 was introduced as the new conventional-to-micro/mini-channel criterion. In addition, a generalized prediction method was proposed based on the new criterion, with accurate predictive capability.

**Keywords:**Micro-channel; Saturated-flow boiling; Heat transfer; Bond number; Reynolds number;

An analytical model for a liquid plug moving in curved microchannels by Zhizhao Che; Teck Neng Wong; Nam-Trung Nguyen

*(1977-1985)*. Droplet-based microfluidics has wide applications and triggers numerous researchers’ interest. It is significant to study the flow field inside a droplet moving in microchannels. This paper presents an analytical method to investigate the flow field inside a confined droplet (a plug) moving in curved microchannels with high aspect ratio. The flow field is compared against a one-dimensional solution and the published experimental data. The effects of the plug length and the curvature on the flow pattern and the flow resistance are studied. The results suggest that the vortex pattern of the plug can be controlled by designing the channel geometry.

**Keywords:**Curved microchannel; Plug flow; Analytical model; Vortex; Flow resistance;

A comprehensive numerical model for melting with natural convection by Shimin Wang; Amir Faghri; Theodore L. Bergman

*(1986-2000)*. A comprehensive and efficient numerical model for melting with natural convection is developed. The model is based on the finite volume approach and temperature transforming model. A new method for solid velocity correction with an explicit update for melting front and buoyancy force (the governing equations are otherwise discretized in fully implicit format) is proposed and shown to be very effective in eliminating inconsistencies found in previous studies. The predictions of the proposed numerical model are compared to previous theoretical, modeling and experimental results, and reasonable agreement is achieved. It is shown that the consistent update technique (CUT) algorithm is much more efficient (CPU time reduce by an order of magnitude) than the SIMPLE algorithm for solving melting problems. Furthermore, it is demonstrated that the central difference scheme is much more accurate than the power law scheme, and that the Richardson extrapolation method provides a powerful tool for grid and time step independence tests as well as discretization error estimates. Finally, it is found that melting phenomena of octadecane and sodium nitrate, both melting in a square cavity with a Rayleigh number of 10

^{8}and a Stefan number of 0.1, are essentially identical; such a similarity can be used as a foundation for conducting room temperature experiments to investigate the melting/solidification characteristics of high temperature phase change materials (PCMs). A benchmark solution for the entire melting process of sodium nitrate is provided as well.**Keywords:**Solid–liquid phase change; Melting; Solidification; Natural convection; Numerical model;

A three-dimensional theoretical model for predicting transient thermal behavior of thermoelectric coolers by Chin-Hsiang Cheng; Shu-Yu Huang; Tsung-Chieh Cheng

*(2001-2011)*. A simulation model is developed and used to predict transient thermal behavior of the thermoelectric coolers. The present model amends the previous models, in which the P–N pair is simply treated as a single bulk material so that the temperature difference between the semiconductor elements was not possible to evaluate. Based on the present simulation model, the thermoelectric cooler is divided into four major regions, namely, cold end (region 1), hot end (region 2), and the P-type and N-type thermoelectric elements (regions 3 and 4). Solutions for the three-dimensional temperature fields in the P-type and the N-type semiconductor elements and transient temperature variations in the cold and the hot ends have been carried out. The magnitude of the coefficient of performance (COP) of the thermoelectric cooler are calculated in wide ranges of physical and geometrical parameters. To verify the numerical predictions, experiments have been conducted to measure the temperature variations of both the cold and the hot ends. Close agreement between the numerical and the experimental data of the temperature variations has been observed.

**Keywords:**Thermoelectric cooler; Theoretical model; Transient behavior; Experiment;

Finite element modeling of coating formation and transient heat transfer in the electric arc spray process by Yongxiong Chen; Xiubing Liang; Yan Liu; Jinyuan Bai; Binshi Xu

*(2012-2021)*. The electric arc sprayed coating can be described as a superposition of Gaussian profile particles whose overlapping depends on the movement of spray gun. The heat transfer behavior during the deposition has a significant influence on the performance of the process. In this paper, simulation of the coating formation and analysis of the transient heat transfer were performed based on a newly developed finite element model, in which the dynamic stochastic multiple particles deposition characteristic of the process was taken into account. In order to investigate the effects of the kinematics and dimensional aspects on the coating/substrate temperature distribution, a traditional layer-by-layer finite element model without consideration of gun movement and particles Gaussian profile was also performed as a comparison. The stochastic deposition model provided a more objective result of the transient heat transfer of the coating/substrate than that of the layer-by-layer model, especially the severely inhomogeneous temperature distribution characteristics in different locations and spraying conditions. Finally, the molding results were experimentally compared with the temperature measurements on the coating surface and substrate back face using an infrared thermal imaging video camera, which shows that most of the modeling findings are consistent with that of the experiment.

**Keywords:**Thermal spraying; Finite element analysis; Arc sprayed coating; Transient heat transfer;

Convective heat transfer enhancement in low Reynolds number flows with wavy walls by Fernando V. Castellões; João N.N. Quaresma; Renato M. Cotta

*(2022-2034)*. The present work reports the analysis of combining low Reynolds number flows and channels with wall corrugation and the corresponding thermal exchange intensification achieved. The proposed model involves axial heat diffusion along the fluid and adiabatic regions both upstream and downstream to the corrugated heat transfer section, in light of the lower values of Reynolds numbers (and consequently Peclet numbers) that can be encountered in the present class of problems. Aimed at developing a fast and reliable methodology for optimization purposes, the related laminar velocity field is obtained by an approximate analytical solution valid for smooth corrugations and low Reynolds numbers, typical for instance of micro-channel configurations, locally satisfying the continuity equation. A hybrid numerical-analytical solution methodology for the energy equation is proposed, based on the Generalized Integral Transform Technique (GITT) in partial transformation mode for a transient formulation. The hybrid approach is first demonstrated for the case of a smooth parallel-plates channel situation, and the importance of axial heat conduction along the fluid is then illustrated. Heat transfer enhancement is analyzed in terms of the local Nusselt number and dimensionless bulk temperature along the heat transfer section. An illustrative sinusoidal corrugation shape is adopted and the influence of Reynolds number and corrugation geometric parameters is then discussed.

**Keywords:**Low Reynolds number flows; Micro-channels; Wavy walls; Heat transfer enhancement; Forced convection; Integral transforms;

Investigation of steel emissivity behaviors: Examination of Multispectral Radiation Thermometry (MRT) emissivity models by Chang-Da Wen

*(2035-2043)*. Steel emissivity behaviors were investigated in this study. Experiments were conducted to measure emissivity. Six emissivity models were then applied to examine Multispectral Radiation Thermometry (MRT) on inferring surface temperature. The data show that emissivity decreases with increasing wavelength. For steel containing high chromium, emissivity is usually lower than others because of the chromium oxide protection layer. Two emissivity models provide the best overall compensation for different alloys, number of wavelengths, and temperatures. The results reveal that if the emissivity model can well represent the real emissivity behaviors, the more accurate inferred temperature can be achieved.

**Keywords:**Steel; Emissivity; Temperature measurement; Multispectral Radiation Thermometry;

Thermocapillarity and magnetic field effects in a thin liquid film on an unsteady stretching surface by N.F.M. Noor; I. Hashim

*(2044-2051)*. In this paper, the effects of thermocapillarity and a magnetic field on the flow and heat transfer in a liquid film over an unsteady elastic stretching surface is analyzed. Similarity transformations are used to transform the governing equations to a set of coupled ordinary differential equations. The differential equations are solved analytically by the homotopy analysis method (HAM). The effects of various parameters in this study are discussed and presented graphically.

**Keywords:**Thermocapillarity; Thin film; Unsteady stretching; Magnetic field; Homotopy analysis method;

Comparison of frictional pressure drop models during annular flow condensation of R600a in a horizontal tube at low mass flux and of R134a in a vertical tube at high mass flux by A.S. Dalkilic; O. Agra; I. Teke; S. Wongwises

*(2052-2064)*. This study compares well-known two-phase pressure drop models with the experimental results of a condensation pressure drop of (i) R600a in a 1 m long horizontal smooth copper tube with an inner diameter of 4 mm, outer diameter of 6 mm and (ii) R134a in a 0.5 m vertical smooth copper tube with an inner diameter of 8.1 mm and outer diameter of 9.52 mm. Different vapour qualities (0.45–0.9 for R600a and 0.7–0.95 for R134a), various mass fluxes (75–115 kg m

^{−2}s^{−1}for R600a and 300–400 for R134a kg m^{−2}s^{−1}) and different condensing temperatures (30–43 °C for R600a and 40–50 °C for R134a) were tested under annular flow conditions. The quality of the refrigerant in the test section was calculated considering the temperature and pressure obtained from the experiment. The pressure drop across the test section was directly measured with a differential pressure transducer. The most agreeable correlations of various available options were then identified according to the results of analysis during annular flow regime.**Keywords:**Condensation; Pressure drop; Horizontal flow; Downward flow; R600a; R134a;

Line fountain behavior at low-Reynolds number by N. Srinarayana; N. Williamson; S.W. Armfield; Wenxian Lin

*(2065-2073)*. In this paper, we present line fountain behavior at low-Reynolds numbers obtained by experiments. The experiments are conducted over the range of Reynolds number 2.1 ≲ Re ≲ 127 and Froude number 0.4 ≲ Fr ≲ 42 . It is observed that the fountain behavior can be categorized broadly into four regimes: the steady; flapping; laminar mixing; and jet-type mixing behavior, at full development. The critical Froude number for transition from a steady to unsteady flow varies with the Reynolds number. For Re ≳ 60 , the transition is independent of

*Re*and is well described by the Fr ∼ 1.0 line. Over the range 10 < Re ≲ 50 , the transition can be approximated by a constant FrRe 2 / 3 line. For Re ≲ 10 , there is a higher dependency on the Reynolds number with a very sharp increase in the critical Froude number and it is hypothesized that the demarcation line follows Fr ∼ Re - n , where n ≈ 2 – 4 . The fountain exhibits flapping behavior in the range 13 Re - 2 / 3 ≲ Fr ≲ 37 Re - 2 / 3 . These observed fountain behaviors are mapped on to a Re – Fr plot. In addition, the observed, non-dimensionalised fountain height z m is found to be in reasonable agreement with previous results on laminar line fountains. In particular, the experimental results confirm the scaling z m ∼ FrRe - 1 / 2 in the steady regime which was obtained previously by scaling analysis.**Keywords:**Line fountain; Flapping; Buoyancy; Laminar; Transition; Unsteadiness;

Effect of turbulence and devolatilization models on coal gasification simulation in an entrained-flow gasifier by Armin Silaen; Ting Wang

*(2074-2091)*. Numerical simulations of the oxygen-blown coal gasification process inside a generic entrained-flow gasifier are carried out. The Eulerian–Lagrangian approach is applied to solve the Navier–Stokes equations and the particle dynamics. Seven species transport equations are solved with three heterogeneous global reactions and two homogeneous reactions. Finite rates are used for the heterogeneous solid-to-gas reactions. Both finite rate and eddy-dissipation combustion models are calculated for each homogeneous gas-to-gas reaction, and the smaller of the two rates is used. Four different devolatilization models are employed and compared. The Kobayashi model produces slower devolatilization rate than the other models. The constant rate model produces the fastest devolatilization rate. The single rate model and the chemical percolation model produce moderate and consistent devolatilization rate. Slower devolatilization rate produces higher exit gas temperature and higher CO and CO

_{2}mass fractions, but lower H_{2}and heating value, and hence, achieves lower gasification efficiency. Combustion of volatiles is modeled with two-stage global reactions with an intermediate stage via benzene.Turbulence models significantly affect the simulated results. Among five turbulence models employed, the standard*k*–*ε*and the RSM models give consistent results. The time scale for employing stochastic time tracking of particles also affects simulated result. Caution has to be exerted to select the appropriate time constant value. Smaller particles have a higher surface/volume ratio and react faster than larger particles. However, large particles possessing higher inertia could impinge on the opposing jet and change the thermal-flow filed and the reaction rates.**Keywords:**Gasification modeling; Entrained-flow gasifier; Clean coal technology; Syngas production; Multiphase flow;

Flow dynamical behaviors and characteristics of aligned and staggered viscous pumps by Jianfeng Lu; Jing Ding

*(2092-2099)*. The flow dynamical behaviors and characteristics of the aligned and staggered viscous pumps are numerically investigated by two-dimensional laminar model. The flow fluxes and driving powers of the pumps are calculated and compared in dimensionless quantities by considering the effects of pump type, Reynolds number, rotor eccentricity, and rotor spacing. The increase of Reynolds number can reduce the dimensionless flow flux and increase the dimensionless driving power, while the rotor eccentricity can enlarge the dimensionless flow flux and driving power. The rotor spacing can also play an important role in the dynamical performance of the aligned and staggered pumps. As rotor spacing rises, the flow stream lines between the two cylinders can bend more smoothly, so the flow flux grows with the driving power dropping, and these phenomena mostly exist in the pump with small rotor spacing. On the other hand, the vortex between the two cylinders probably develops as rotor spacing rising, then the flow flux is reduced with the driving power increasing, and these phenomena mainly exist in the pump with large rotor spacing. According to the simulation results and mechanism analyses, the staggered pump with optimal rotor spacing has the best dynamical performance with the highest flow rate and low driving power.

**Keywords:**Viscous pump; Staggered pump; Flow pattern; Driving power;

Visualization of heat transport due to natural convection for hot materials confined within two entrapped porous triangular cavities via heatline concept by Tanmay Basak; S. Roy; D. Ramakrishna; I. Pop

*(2100-2112)*. This paper analyzes the detailed heat transfer within two entrapped porous triangular cavities involving cold inclined walls and hot horizontal walls. A penalty finite element analysis with bi-quadratic elements is performed to investigate the results in terms of isotherms, streamlines and heatlines and local and average Nusselt numbers. The parameters for this study are Darcy number, Da ( 10 - 5 – 10 - 3 ) , Prandtl number, Pr ( 0.015 – 1000 ) and Rayleigh number ( 10 3 – 5 × 10 5 ) . It has been found that at small Darcy number ( Da = 10 - 5 ) , heat transfer is primarily conduction dominant and heatlines are found to be orthogonal to the isotherms. The presence of multiple circulations in streamlines and heatlines are observed within the lower triangle at small Prandtl number Pr = 0.015 with high Darcy number ( Da = 10 - 3 ) whereas only single pair of circulations are observed for higher Prandtl numbers. The convective cells in heatlines gradually become enhanced as

*Pr*increases from 0.015 to 1000. In contrast, variation of Prandtl number gives negligible change in heating pattern within the upper triangle and intensity of streamlines and heatlines are less irrespective of Prandtl number. Heat transfer rates are estimated in terms of local ( Nu l , Nu h ) and average Nusselt numbers ( Nu l ¯ , Nu h ¯ ) . Heat transfer rates are also explained based on heatlines. Local Nusselt numbers with spatial distribution exhibit monotonic trend irrespective of*Da*and*Pr*for the upper triangle whereas wavy distribution of local Nusselt number occur for the lower triangle. For Da = 10 - 3 , average Nusselt numbers ( Nu h ¯ and Nu l ¯ ) increase exponentially with*Ra*at higher Rayleigh numbers. But, overall lower heat transfer rates are observed for the upper triangle. Finally, it is concluded that lower triangle has always has higher heat recovery capacity compared to upper triangle. To achieve efficient heat transfer, fluids with high Prandtl numbers are recommended for the lower triangle whereas any fluid with any Prandtl number may be acceptable for the upper triangle.**Keywords:**Penalty finite element method; Natural convection; Porous medium; Inverted triangular cavity; Streamlines; Isotherms; Heatlines; Heat recovery;

Direct numerical simulation for a time-developing combined-convection boundary layer along a vertical flat plate by Mohammad Zoynal Abedin; Toshihiro Tsuji; Yasuo Hattori

*(2113-2122)*. Time-developing combined-convection boundary layers induced by imposing aiding and opposing flows to the natural-convection boundary layer in air along a hot vertical flat plate have been examined with a direct numerical simulation. As the freestream velocity increases, the transition from laminar to turbulence delays for aiding flow and quickens for opposing flow, corresponding well to actual observations in space-developing flows. The calculated profiles of mean streamwise velocity, mean temperature, intensities of streamwise velocity fluctuation and temperature fluctuation in the laminarization process of the boundary layer for aiding flow agree relatively well with the existing data. Also, the distributions of turbulent statistics and instantaneous fluid motions in the combined-convection boundary layers with adding and opposing flows are displayed, and the regimes of the boundary layer flows obtained from the calculations are compared with those observed in the experiment.

**Keywords:**Combined convection; Turbulent boundary layer; Direct numerical simulation; Convective heat transfer; Transition;

A fitting algorithm for solving inverse problems of heat conduction by Andrzej Fra¸ckowiak; Nikolai D. Botkin; Michał Ciałkowski; Karl-Heinz Hoffmann

*(2123-2127)*. The paper presents an algorithm for solving inverse problems of heat transfer. The method is based on iterative solving of direct and adjoint model equations with the aim to minimize a fitting functional. An optimal choice of the step length along the descent direction is proposed. The algorithm has been used for the treatment of a steady-state problem of heat transfer in a region with holes. The temperature and the heat flux density were known on the outer boundary of the region, whereas these values on the boundaries of the holes are to be determined. The idea of the algorithm consist in solving of Neumann problems where the heat flux on the outer boundary is prescribed, whereas the heat flux on the inner boundary is guessed. The guess is being improved iteratively to minimize the mean quadratic deviation of the solution on the outer boundary from the given distribution.The results obtained show that the algorithm provides smooth, non-oscillating, and stable solutions to inverse problems of heat transfer, that is, it avoids disadvantages inherent in other computational methods for such problems. The ill-conditioning of inverse problems in the Hadamard sense is exhibited in that a very quick convergence of the fitting functional to its minimum does not imply a comparable rate of convergence of the recovered temperature on the inner boundary to the true distribution.The considered method can easily be extended to nonlinear problems.Numerical calculation has been carried out with the FE program Felics developed at the Chair of Mathematical Modelling of the Technical University of Munich.

**Keywords:**Inverse problems; Fitting functional; Adjoint equations; Finite Element Method;

On the scale effect and scale-up in the column apparatuses. 3. Circulation zones by K. Panayotova; M. Doichinova; Chr. Boyadjiev

*(2128-2132)*. A diffusion type of model is proposed for modeling of the mass transfer with chemical reaction in the column apparatuses in the cases of circulation zones. The presence of rising and descending flows (the change of the velocity direction) leads to using three coordinate systems. An iterative algorithm for the concentration distribution calculation is proposed. The influence of the zones breadths on the mass transfer efficiency in the column is investigated.

**Keywords:**Column apparatuses; Mass transfer; Velocity distribution; Circulation zones;

An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates by Prashant K. Jain; Suneet Singh; Rizwan-uddin

*(2133-2142)*. Analytical series solution is proposed for the transient boundary-value problem of

*multilayer heat conduction*in*r*–*θ*spherical coordinates. Spatially non-uniform, but time-independent, volumetric heat sources may exist in the concentric layers. Proposed solution is valid for any combination of homogenous boundary conditions of the*first*or*second*kind in the*θ*-direction. However, inhomogeneous boundary conditions of the*first*,*second*or*third*kind may be applied at the inner and outer radial boundaries of the concentric layers. It is noted that the proposed solution is “free” from imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of radial eigenvalues on those in the*θ*-direction. Solution is shown to be relatively simple for the most common spherical geometries−(multilayer) hemisphere and full sphere. An illustrative problem of heat conduction in a three-layer hemisphere is solved. Results along with the isotherms are shown graphically and discussed.**Keywords:**Transient; Multilayer; Spherical; Analytical; Conduction; Hemisphere; Cones and wedges;

Optimization of capillary structures for inverted meniscus evaporators of loop heat pipes and heat switches by Valery M. Kiseev; Valeri V. Vlassov; Issamu Muraoka

*(2143-2148)*. Loop heat pipes (LHPs) and other two-phase heat transfer devices are used in the thermal management of electronic devices with high density of heat dissipation. In these two-phase thermal devices, the key component is the capillary structure (CS) that pumps the working fluid using the capillary forces generated by the meniscus, which are formed due to evaporation. The evaporator’s performance depends greatly on the internal structure and external configurations of the CS. However, there is not enough experimental and theoretical data on the optimization of the capillary structures of evaporators. This paper covers some important aspects of the CS design for evaporators working in an “inverted meniscus” scheme and proposes a methodology for analysis and selection of the CS pores size for LHP, flat heat pipes and heat switches, aiming for maximum heat transport capacity. Based on this methodology, two examples of capillary evaporators have been designed and evaluated.

**Keywords:**Loop heat pipe; Inverted meniscus; Capillary structure; Heat switch;

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel by M. Dogan; M. Sivrioglu

*(2149-2158)*. Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ⩽

*w*_{in}⩽ 0.16 m/s) using a flow rate control valve so that Reynolds number was always about*Re*= 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10^{7}<*Ra*^{∗}< 8 × 10^{8}and Richardson number 0.4 <*Ri*< 5. Dimensionless fin spacing was varied from*S*/*H*= 0.04 to*S*/*H*= 0.018 and fin height was varied from*H*_{f}/*H*= 0.25 to*H*_{f}/*H*= 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is*S*= 8–9 mm and optimum fin spacing depends on the value of*Ra*^{∗}.**Keywords:**Mixed convection; Fins; Fin spacing; Fin height; Channel; Heat transfer;

Experimental study on microchannel heat sinks considering mass flow distribution with non-uniform heat flux conditions by Eun Seok Cho; Jong Won Choi; Jae Sung Yoon; Min Soo Kim

*(2159-2168)*. This study investigates cooling performance of microchannel heat sinks under various heat flux conditions for different geometry of the channels and headers. Thermal load is applied to the microchannel heat sinks by nine separate heaters in order to provide uniform or non-uniform heat flux. Straight or diverging channels have been made with rectangular or trapezoidal headers, so four kinds of microchannel heat sinks have been fabricated by the microfabrication processes, such as deep reactive ion etch (DRIE), anodic bonding techniques, and so on. The temperatures of the heaters have been measured under the uniform and non-uniform heat flux conditions, including local heating at hotspots. Moreover, the maximum temperatures for different microchannel heat sink under various heating conditions have been obtained as well as the pressure drops.

**Keywords:**Microchannel heat sinks; Two-phase flow; Evaporation; Non-uniform heat flux; Header;

Hybrid modeling of interfacial region thermophysics and intrinsic stability of thin free liquid films by Yu Gan; Van P. Carey

*(2169-2182)*. The film rupture process that dictates merging of adjacent bubbles is particularly important in nucleate boiling heat transfer, bubbly two-phase flow in small tubes, and the mechanisms that dictate the Leidenfrost transition. To understand the mechanisms of bubble merging in nanostructured boiling surfaces and in nanotubes, it is useful to explore film stability and onset of rupture at the molecular level. This paper reports the results of such an investigation using a hybrid analysis scheme that combines a new formulation of capillarity theory for free liquid films with molecular dynamics (MD) simulations that use similar interaction potentials. Two forms of our molecular film capillarity theory are developed here: one for non-polar fluids based on a Lennard-Jones interaction potential, and a second specifically for water using a modified treatment of the SPC/E interaction potential that accounts for water dipole interactions. The hybrid model has the advantage that the capillarity theory provides theoretical relationships among parameters that govern film structure and thermophysical behavior, while the companion MD simulations allow more detailed molecular level exploration of the film thermophysics. Results obtained with the hybrid model indicate that wave instability predominates as an onset of rupture mechanism for liquid films of macroscopic extent, but for free liquid films with nanoscale lateral extent (in, for example, nanostructured boiling surfaces), lack of core stability is more likely to be the mechanism. The implications of these predictions for film rupture and bubble merging in nanostructured surfaces and nanotubes are examined in detail.

**Keywords:**Free liquid film; Bubble merging; Molecular capillarity theory; Liquid film stability; Nanoscale boiling;

Effect of nanofluids on the thermal performance of a flat micro heat pipe with a rectangular grooved wick by Kyu Hyung Do; Seok Pil Jang

*(2183-2192)*. In this paper, the effect of water-based Al

_{2}O_{3}nanofluids as working fluid on the thermal performance of a flat micro-heat pipe with a rectangular grooved wick is investigated. For the purpose, the axial variations of the wall temperature, the evaporation and condensation rates are considered by solving the one-dimensional conduction equation for the wall and the augmented Young–Laplace equation for the phase change process. In particular, the thermophysical properties of nanofluids as well as the surface characteristics formed by nanoparticles such as a thin porous coating are considered. From the comparison of the thermal performance using both DI water and nanofluids, it is found that the thin porous coating layer formed by nanoparticles suspended in nanofluids is a key effect of the heat transfer enhancement for the heat pipe using nanofluids. Also, the effects of the volume fraction and the size of nanoparticles on the thermal performance are studied. The results shows the feasibility of enhancing the thermal performance up to 100% although water-based Al_{2}O_{3}nanofluids with the concentration less than 1.0% is used as working fluid. Finally, it is shown that the thermal resistance of the nanofluid heat pipe tends to decrease with increasing the nanoparticle size, which corresponds to the previous experimental results.**Keywords:**Water-based Al

_{2}O

_{3}nanofluids; Heat transfer enhancement; Flat micro-heat pipe; Grooved wick structure; Thin porous coating layer;

Multi-parameter model reduction in multi-scale convective systems by Emad Samadiani; Yogendra Joshi

*(2193-2205)*. A new Proper Orthogonal Decomposition (POD) based reduced order modeling approach for temperature field calculation in multi-scale convective systems is presented. Using POD modes for the entire domain, the energy equation is solved only at the most important scales via Galerkin projection to have an efficient and accurate enough model for design. Comparing with Computational Fluid Dynamics/Heat Transfer simulation shows that the method can predict the temperature field at the rack scale of a sample air-cooled data center with the average error norm of ∼6% for different sets of design parameters, while it can be up to ∼250 times faster.

**Keywords:**Multi-scale thermal-fluid systems; Reduced order modeling; Proper orthogonal decomposition; Galerkin projection; Data center;

Macroscopic modeling of thermal dispersion for turbulent flows in channels by M. Drouin; O. Grégoire; O. Simonin; A. Chanoine

*(2206-2217)*. In this paper, laminar and turbulent flows in channels are considered. The primary interest for industrial purpose is a macroscale description of mean flow quantities derived from the microscopic details of the flow in each subchannel. A double averaging procedure has been used to derive balance equations for mean flow variables within laminar and turbulent regimes. This up-scaling procedure results in additional contributions, amongst which dispersion predominates. Thermal dispersion might be seen as the sum of a first contribution, hereafter denoted “passive”, due to velocity heterogeneities, and a second one, called “active”, due to wall heat transfer. The aim of the present work is to propose practical models for thermal dispersion that account for laminar and turbulent regimes. Embedded in CFD code, they are validated against RANS simulations. Our results illustrate the importance of thermal dispersion for heated flows in the presence of nonuniform wall heat flux or temperature jumps.

**Keywords:**Porous media; Turbulence; Thermal dispersion; Heat exchangers; Double averaging;

Experimental study of R-134a evaporation heat transfer in a narrow annular duct by C.A. Chen; C.Y. Lee; T.F. Lin

*(2218-2228)*. An experiment is carried out here to investigate the evaporation heat transfer and associated evaporating flow pattern for refrigerant R-134a flowing in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm. In the experiment, the effects of the duct gap, refrigerant vapor quality, mass flux and saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient

*h*_{r}are examined in detail. For the duct gap of 2.0 mm, the refrigerant mass flux*G*is varied from 300 to 500 kg/m^{2}s, imposed heat flux*q*from 5 to 15 kW/m^{2}, vapor quality*x*_{m}from 0.05 to 0.95, and refrigerant saturation temperature*T*_{sat}from 5 to 15 °C. While for the gap of 1.0 mm,*G*is varied from 500 to 700 kg/m^{2}s with the other parameters varied in the same ranges as that for*δ*= 2.0 mm. The experimental data clearly show that the evaporation heat transfer coefficient increases almost linearly with the vapor quality of the refrigerant and the increase is more significant at a higher*G*. Besides, the evaporation heat transfer coefficient also rises substantially at increasing*q*. Moreover, a significant increase in the evaporation heat transfer coefficient results for a rise in*T*_{sat}, but the effects are less pronounced in the narrower duct at a low imposed heat flux and a high refrigerant mass flux. Furthermore, the evaporation heat transfer coefficient increases substantially with the refrigerant mass flux except at low vapor quality. We also note that reducing the duct gap causes a significant increase in*h*_{r}. In addition to the heat transfer data, photos of R-134a evaporating flow taken from the duct side show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. Finally, an empirical correlation for the present measured heat transfer coefficient for the R-134a evaporation in the narrow annular ducts is proposed.**Keywords:**R-134a; Evaporation heat transfer; Mini-channel; Evaporating flow pattern;

Study of heat transfer and kinetics parameters influencing the design of heat exchangers for hydrogen storage in high-pressure metal hydrides by Milan Visaria; Issam Mudawar; Timothée Pourpoint; Sudarshan Kumar

*(2229-2239)*. This paper discusses the challenges of using hydrogen fuel cells to power light-duty vehicles. Storing sufficient amounts of hydrogen to cover adequate travel distances before refueling is one of the more pressing challenges, and different materials have been recommended to enhance storage capacity. This study concerns one class of storage materials called high-pressure metal hydrides (HPMHs). The most important component of a hydrogen storage system utilizing HPMHs is the heat exchanger, which, aside from storing the HPMH, must providing sufficient cooling during the hydrogen refueling to achieve the required short fill time of less than 5 min. Discussed in this paper are practical heat exchanger design guidelines for storage systems employing materials with high rates of heat generation during refueling. Most important among those is the maximum distance between the HPMH powder and the cooling surface, which, for Ti

_{1.1}CrMn, must be kept below 10 mm to achieve a fill time of 5 min. A new parameter called non-dimensional conductance (NDC) is developed, which serves as a characteristic parameter to estimate the effects of various parameters on the reaction rate. Overall, it is shown that the hydrogen fill time is sensitive mostly to the effective thermal conductivity of the HPMH and the coolant’s temperature, followed by the contact resistance between the powder and cooling surface.**Keywords:**Hydrogen storage; Heat exchanger; High-pressure metal hydride;

The meshless analog equation method for solving heat transfer to molten polymer flow in tubes by S.P. Hu; C.M. Fan; D.L. Young

*(2240-2247)*. In this paper, we proposed a meshless analog equation method (MAEM) to solve a heat transfer problem of molten polymer flow, which is considered to be a generalized Newtonian viscous flow. The MAEM, free from mesh generation and numerical integration, is a powerful meshless method. The numerical solutions are expressed by a linear combination of the derived radial basis functions (RBFs). This paper considers two different viscosity models for the molten polymer; one is temperature-independent power-law model and the other is temperature-dependent power-law model. The viscous dissipation term is included in the energy equation to capture the relevant physical phenomena. From the comparisons of numerical simulation, the meshless solutions are in good agreement with some analytical solutions and other finite element solutions. Moreover, the MAEM uses much less CPU-time and computer memory to simulate molten polymer flows. Therefore, it is believed that the RBF-based meshless method of the MAEM is a promising and flexible numerical scheme for molten polymer flow simulation.

**Keywords:**Heat transfer; Viscous dissipation; Polymer flows; Power-law flow; Meshless method; Radial basis functions; Analog equation method;

Constructal architecture for heating a stream by convection by Deok-Hong Kang; Sylvie Lorente; Adrian Bejan

*(2248-2255)*. In this paper we consider the fundamental problem of how to heat a stream to a specified exit temperature such that the overall fuel consumption is minimal. As illustration, we consider metal slabs that move at constant speed through a very slender enclosure with fixed total volume and arbitrary (nonuniform) distribution of cross-sectional area (heat transfer contact area). The heating is provided by a large number of heaters, which are distributed arbitrarily along the enclosure. The combustion gases flow in the

*x*direction, which is oriented against the direction of the metal stream. The heat transfer is by convection. We show that minimal heat consumption is achieved when the heaters and the heat transfer contact area are distributed nonuniformly. The density of heaters per unit length must decrease as*x*^{−0.8}toward the entrance of the metal stream, and the heat transfer contact area must increase in proportion with*x*. These features suggest that the metal must move not as a single stream but as a tree-shaped flow. The metal enters in several parallel streams, which serve as tributaries to larger streams, leading to a single stream that exits at the specified temperature.**Keywords:**Constructal; Dendritic furnace; Distributed energy systems; Steel heating; Reheating furnace; Sustainable industries; Green energy;

Numerical simulation of reactive flow in liquid composite molding using flux-corrected transport (FCT) based finite element/control volume (FE/CV) method by Hua Tan; Krishna M. Pillai

*(2256-2271)*. The mold-filling simulation of liquid composite molding (LCM) is of great importance in optimizing this cost-effective polymer-composites manufacturing process. The flow in LCM is a convection-dominated reactive, non-isothermal flow involving a moving boundary, so the Galerkin finite element method (FEM) has to be adapted with stabilization techniques to solve such problems. The streamline-upwind Petrov–Galerkin (SUPG) method is one of the most popular stabilized methods. However, the use of SUPG still leads to localized numerical wiggles in the vicinity of sharp solution gradients, which is often encountered in the 3D mold-filling simulation of LCM for thick parts. In this study, we propose to use the flux-corrected transport (FCT) based FEM to solve a set of highly convective transport equations. The numerical examples presented in this paper demonstrate the excellent performance of FCT based FEM in suppressing spurious oscillations in the regions of steep solution-gradients as opposed to the numerical instability of SUPG in such regions. For the first time, the FCT based FEM combined with the control-volume method is employed to simulate the non-isothermal mold-filling process in LCM. We have developed a simulation code PORE-FLOW© based on the scheme proposed in the study. Numerical studies have proven the stability of the FCT based FEM while modeling the mold-filling process of LCM.

**Keywords:**Streamline-upwind Petrov–Galerkin (SUPG); Flux-Corrected Transport (FCT); Liquid Composite Molding; Mold Filling; PORE-FLOW;

Three-dimensional adaptive phase field modeling of directional solidification of a binary alloy: 2D–3D transitions by Y.L. Tsai; C.C. Chen; C.W. Lan

*(2272-2283)*. Morphological instability is an important subject in alloy directional solidification, and the development of cell allay is important to alloy properties. In nature, as a result of cell arrangement, this problem is often three-dimensional (3D), even for thin-film, and its simulation is rather difficult. We have developed a 3D adaptive phase field model to simulate efficiently the directional solidification of a binary alloy. The morphological transition from 2D to 3D approximations are illustrated, and compared with available analytical and simulated results. The effect of anisotropy on the cell arrangement is discussed as well.

**Keywords:**Three-dimensional; Adaptive; Phase field modeling; Directional solidification; Morphological instability;

Momentum interaction in buoyancy-driven gas–liquid vertical channel flows by L.F. Echeverri; S. Acharya; P.W. Rein

*(2284-2293)*. Drag coefficient correlations for bubbles in buoyancy-driven two-phase flows have generally been derived from data on low-viscosity media and within the bubbly flow regime. In a number of applications, e.g. evaporative crystallizers, there is a need to extend this correlation to higher viscosity flows and slug regimes. In this paper, the momentum interaction in gas–liquid vertical channel flow has been studied experimentally over a wide range of void fractions using a circulation loop facility where the buoyancy is the only driving force for liquid circulation. A model for the drag in gas–liquid buoyant flows has been developed, and is applicable for a wide range of viscosity and void fractions.

**Keywords:**Drag coefficient correlations; Buoyancy-driven two-phase flows; Gas–liquid vertical channel flow; Circulation loop facility; Momentum interaction;

Modeling of unsteady and steady fluid flow, heat transfer and dispersion in porous media using unit cell scale by A.A. Alshare; P.J. Strykowski; T.W. Simon

*(2294-2310)*. A unit cell scale computation of laminar steady and unsteady fluid flow and heat transfer is presented for a spatially periodic array of square rods representing two-dimensional isotropic or anisotropic porous media. In the model, a unit cell is taken as a representative elementary control volume and uniform heat flux boundary conditions are imposed on the solid–fluid interface. The governing equations are discretized by means of the finite volume approach; boundaries between adjacent cells are taken to be spatially periodic. Computations obtained using the SIMPLER algorithm, are made by varying the macroscopic flow direction from 0° to 90° relative to the unit cell, and varying the Reynolds number over the range 1–10

^{3}spanning the Darcian and the inertial flow regimes to construct a database of local flow and heat transfer resistances in terms of permeabilities, inertial coefficients, Nusselt numbers, and thermal dispersion coefficients. The resulting database is utilized in a system scale analysis of a serpentine heat exchanger, where these directional terms from the microscale analysis provide closure to the porous-continuum model.**Keywords:**Porous media; Heat transfer; Unit cell; Heat exchanger; Steady and transient;

Pool boiling of R-123/oil mixtures on enhanced tubes having different pore sizes by Nae-Hyun Kim; Do-Young Kim

*(2311-2317)*. The effect of enhanced geometry (pore diameter, gap width) is investigated on the pool boiling of R-123/oil mixture for the enhanced tubes having pores with connecting gaps. Tubes having different pore diameters (and corresponding gap widths) are specially made. Significant heat transfer degradation by oil is observed for the present enhanced tubes. At 5% oil concentration, the degradation is 26–49% for

*T*_{sat}= 4.4 °C. The degradation increases 50–67% for*T*_{sat}= 26.7 °C. The heat transfer degradation is significant even with small amount of oil (20–38% degradation at 1% oil concentration for*T*_{sat}= 4.4 °C), probably due to the accumulation of oil in sub-tunnels. The pore size (or gap width) has a significant effect on the heat transfer degradation. The maximum degradation is observed for*d*_{p}= 0.20 mm tube at*T*_{sat}= 4.4 °C, and*d*_{p}= 0.23 mm tube at*T*_{sat}= 26.7 °C. The minimum degradation is observed for*d*_{p}= 0.27 mm tube for both saturation temperatures. It appears that the oil removal is facilitated for the larger pore diameter (along with larger gap) tube. The highest heat transfer coefficient with oil is obtained for*d*_{p}= 0.23 mm tube, which yielded the highest heat transfer coefficient for pure R-123. The optimum tube significantly (more than 3 times) outperforms the smooth tube even with oil. The heat transfer degradation increases as the heat flux decreases.**Keywords:**R-123/oil mixture; Enhanced tube; Pore; Gap; Pool boiling;

Analytical and experimental investigations on fluid flow and thermal characteristics of a plate-fin heat sink subject to a uniformly impinging jet by Kyu Hyung Do; Tae Hoon Kim; Sung Jin Kim

*(2318-2323)*. In this paper, modified similarity solutions for velocity and temperature distributions in the heat sink subject to a uniformly impinging jet are presented. A heat sink is modeled as a fluid-saturated porous medium and a similarity transformation is employed. The Brinkman-extended Darcy equations for fluid flow and two-equation model for heat transfer are used as the governing equations. Specifically, a method for analytically determining the permeability and the interstitial heat transfer coefficient is presented. Experimental investigations are conducted to validate the proposed similarity solutions. From comparison of experimental and analytical results, the analytical results are shown to accurately predict the pressure drop and thermal resistance of the heat sink subject to the uniformly impinging jet.

**Keywords:**Heat sink; Uniformly impinging jet; Volume averaging technique; Similarity transformation;