# International Journal of Heat and Mass Transfer (v.52, #3-4)

On the scale effect and scale-up in the column apparatuses 1. Influence of the velocity distribution by K. Panayotova; M. Doichinova; Chr. Boyadjiev

*(543-547)*. A diffusion type of model is proposed for modeling of the scale effect in column apparatuses. The mass transfer with chemical reaction model is investigated. The influence of the radial non-uniformity of the velocity distribution on the mass transfer efficiency, column height and scale-up is obtained. The effect of Fourier and Damkohler numbers on the process efficiency is analyzed. The present data show that mass transfer efficiency in column apparatuses decreases with the column diameter increase.

**Keywords:**Column apparatuses; Mass transfer; Velocity distribution; Scale-up;

About use of a method of direct numerical solution for simulation of bulk condensation of supersaturated vapor by N.M. Kortsensteyn; E.V. Samuilov; A.K. Yastrebov

*(548-556)*. The results of direct numerical solution of the kinetic equation for the droplet size distribution function are presented. This method which is not restricted by the Knudsen number was developed using the analogy with a similar method of solution of the Boltzmann kinetic equation. The simulation of vapor behavior at fast creation of supersaturation state in vapor–gas mixture by means of adiabatic expansion was carried out for the verification of the method. The results obtained by this method were compared with those which were obtained by using the method of moments over a broad range of Knudsen number. The relevance of taking into account the dependence between saturation pressure and droplet size on the dynamics of condensational relaxation was studied.

**Keywords:**Nucleation; Bulk condensation; Distribution function; Kinetic equation; Numerical solution;

Heat transfer in all pipe flow regimes: laminar, transitional/intermittent, and turbulent by J.P. Abraham; E.M. Sparrow; J.C.K. Tong

*(557-563)*. A predictive theory is presented which is capable of providing quantitative results for the heat transfer coefficients in round pipes for the three possible flow regimes: laminar, transitional, and turbulent. The theory is based on a model of laminar-to-turbulent transition which is also viable for purely laminar and purely turbulent flow. Fully developed heat transfer coefficients were predicted for the three regimes. The present predictions were brought together with the most accurate experimental data known to the authors as well as with several algebraic formulas which are purported to be able to provide fully developed heat transfer coefficients in the so-called transition regime between

*Re*= 2300 and 10,000. It was found that over the range*Re*> 4800, both the present predictions and those of the Gnielinski formula [V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359–367] are very well supported by the experimental data. However, the Gnielinski model is less successful in the range from 2300 to 3100. In that range, the present predictions and those of Churchill [S. Churchill, Comprehensive correlating equations for heat, mass, and momentum transfer in fully developed flow in smooth tubes, Ind. Eng. Chem. Fundam. 16 (1977) 109–116] are mutually reinforcing. Heat transfer results in the development region have also been obtained. Typically, regardless of the Reynolds number, the region immediately downstream of the inlet is characterized by laminar heat transfer. After the breakdown of laminar flow, a region characterized by intermittent heat transfer occurs. Subsequently, the flow may become turbulent and fully developed or the intermittent state may persist as a fully developed regime. The investigation covered both of the basic thermal boundary conditions of uniform heat flux (UHF) and uniform wall temperature (UWT). In the development region, the difference between the respective heat transfer coefficients for the two cases was approximately 25% (UHF > UWT). For the fully developed case, the respective heat transfer coefficients are essentially equal in the turbulent regime but differ by about 25% in the intermittent regime. The reported results are for a turbulence intensity of 5% and flat velocity and temperature profiles at the inlet. Gold nanoshell density variation with laser power for induced hyperthermia by Jerry Vera; Yildiz Bayazitoglu

*(564-573)*. The thermal profile effects of nanoshell density, laser power, and laser arrangement are presented for ideal cases of nanoshell-assisted photothermal therapy. A one-dimensional thermal model utilizing the P

_{1}approximation is used to simulate the penetration of laser radiation and subsequent heating of 1-cm slabs of nanoshell-embedded tissue exposed to a 633-nm collimated light source. It is shown that adding too many nanoshells or increasing power can cause overheating in the entry region while leaving the rear region heated only by conduction, producing an undesirable temperature differential. An opposing dual-laser approach is presented that mitigates this issue.**Keywords:**Photothermal therapy; Hyperthermia; Lasers; Nanoshell; Cancer therapy; Tissue optics;

Biofilm affected characteristics of porous structures by Maryam Shafahi; Kambiz Vafai

*(574-581)*. Formation of biofilm within a porous matrix reduces the pore size and the total open space of the system, altering the porosity and permeability of the medium. This change in the pore size distribution can be quantified by expressing the porous structure with a proper geometrical model. A set of pertinent multispecies biofilm models is used to arrive at the dynamic biofilm thickness distribution. The obtained results are utilized within a modified Kozeny–Carman framework to establish permeability and porosity distribution during the biofilm formation. The biofilm thickness and the obtained permeability profile for a special microorganism,

*Pseudomonas aeruginosa*, are compared with available experimental data. The potential reasons attributing to the differences between the numerical and experimental data are discussed.**Keywords:**Biofilm; Porous media; Permeability; Porosity;

Approximate model for break-up of solidifying melt particles due to thermal stresses in surface crust layer by Leonid A. Dombrovsky

*(582-587)*. Fast cooling and solidification of high-temperature droplets of opaque melt is considered. The problem parameters correspond to interaction of core melt with ambient water in hypothetical severe accident in some industrial nuclear reactors. A recently suggested approximation for transient temperature profile in the particle during solidification is employed. This approach is combined with an analytical solution for quasi-steady stress–strain state of growing solid crust layer. A computational analysis showed that the resulting tensile stress on the particle surface is maximal at a certain position of solidification front. The latter is considered to be a reason of mechanical breakage of corium particles at time preceding this stress maximum. The results obtained are in qualitative agreement with recently reported observations of some fragments of thick-wall hollow spherical particles in laboratory experiments.

**Keywords:**Melt droplet; Solidification; Corium; Thermal stresses; Breakage; Fuel–coolant interaction;

Laminar and turbulent free convection in a composite enclosure by Edimilson J. Braga; Marcelo J.S. de Lemos

*(588-596)*. Turbulent natural convection in a two-dimensional horizontal composite square cavity, isothermally heated at the left side and cooled from the opposing surface, is numerically analyzed using the finite volume method. The composite square cavity is formed by three distinct regions, namely, clear, porous and solid region. The development of a numerical tool able to treat all these regions as one computational domain is of advantage for engineering design and analysis of passive thermal control systems. Governing equations are written in terms of primitive variables and are recast into a general form. It was found that the fluid begins to permeate the porous medium for values of

*Ra*greater than 10^{6}. Nusselt number values show that for the range of*Ra*analyzed there is no significant variation between the laminar and turbulent model solution. When comparing the effects of*Ra*,*k*_{s}/*k*_{f}and*Da*on*Nu*, results indicate that the solid phase properties have a greater influence in enhancing the overall heat transferred trough the cavity.**Keywords:**Porous media; Heat transfer; Natural convection; Turbulence modeling;

Numerical simulation of parabolic trough solar collector: Improvement using counter flow concentric circular heat exchangers by O. García-Valladares; N. Velázquez

*(597-609)*. Detailed numerical simulations of thermal and fluid-dynamic behavior of a single-pass and double-pass solar parabolic trough collector are carried out. The governing equations inside the receiver tube, together with the energy equation in the tube walls and cover wall and the thermal analysis in the solar concentrator were solved iteratively in a segregated manner. The single-pass solar device numerical model has been carefully validated with experimental data obtained by Sandia National Laboratories. The effects of recycle at the ends on the heat transfer are studied numerically shown that the double-pass can enhance the thermal efficiency compared with the single-pass.

**Keywords:**Concentration; PTC; Numerical model; Solar energy; Heat exchanger; Double pipe;

CHF determination for high-heat flux phase change cooling system incorporating both micro-channel flow and jet impingement by Myung Ki Sung; Issam Mudawar

*(610-619)*. This paper explores the subcooled nucleate boiling and critical heat flux (CHF) characteristics of a hybrid cooling module that combines the cooling attributes of micro-channel flow and jet impingement. A test module was constructed and tested using HFE-7100 as working fluid. Increasing the coolant’s flow rate and/or subcooling shifted both the onset of boiling (ONB) and CHF to higher heat fluxes and higher wall temperatures. The hybrid module yielded heat fluxes as high as 1127 W/cm

^{2}, which is the highest value ever achieved for a dielectric coolant at near atmospheric pressure. It is shown the hybrid cooling configuration involves complex interactions between circular jets and micro-channel flow, and unusual spatial variations of void fraction and liquid velocity. These variations are ascertained using the Developing Homogeneous Layer Model (DHLM) in which the micro-channel flow is described as consisting of a homogeneous two-phase layer along the heated wall and a bulk liquid layer. CHF is determined by a superpositioning technique that consists of dividing the heated wall into two portions, one dominated by jet impingement and the other micro-channel flow. This technique is shown to be highly effective at predicting the CHF data for the hybrid cooling configuration. Transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity by Feng Xu; John C. Patterson; Chengwang Lei

*(620-628)*. The transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity is numerically investigated. The numerical results are compared with a previously reported experiment. It is demonstrated that the transient flow obtained numerically shows features consistent with the experimental flow. Based on the present numerical results, the temporal development and spatial structures of the thermal flow around the fin are described, and the separation of the thermal flow above the fin is discussed. It is found that the presence of the fin changes the flow regime and results in the transition of the thermal flow to a periodic flow. The present numerical results also indicate that the unstable temperature configuration above the fin results in intermittent plumes at the leeward side of the fin, which in turn induce strong oscillations of the downstream boundary layer flow. It is demonstrated that the oscillations of the boundary layer flow significantly enhance the heat transfer through the finned sidewall (by up to 23%).

**Keywords:**Fin; Differentially heated cavity; Oscillations; Heat transfer;

Multi-artery, heat-pipe spreader by D.H. Min; G.S. Hwang; M. Kaviany

*(629-635)*. Multiple, columnar liquid vapor chamber allows for effective heat removal from finite, concentrated heat source by heat spreading via lateral vapor flow, while minimizing conduction resistance through thinner evaporator wick. The individual liquid arteries are designed by wick coated solid pillar. We optimize the artery geometry, numbers, and distribution, for both liquid and air-cooled, finned condensers, and show that the overall thermal resistance is substantially lower than the uniform wick vapor chamber.

**Keywords:**Multiple liquid artery; Vapor chamber; Heat pipe; Optimal design; Dry out; Wick superheat;

Study on flow and heat transfer characteristics of heat pipe with axial “

*Ω*”-shaped microgrooves by Yongping Chen; Chengbin Zhang; Mingheng Shi; Jiafeng Wu; G.P. Peterson*(636-643)*. A theoretical model of fluid flow and heat transfer in a heat pipe with axial “

*Ω*”-shaped grooves has been conducted to study the maximum heat transport capability of these types of heat pipes. The influence of variations in the capillary radius, liquid–vapor interfacial shear stress and the contact angle are all considered and analyzed. The effect of vapor core and wick structure on the fluid flow characteristics and the effect of the heat load on the capillary radius at the evaporator end cap, as well as the effect of the wick structure on the heat transfer performance are all analyzed numerically and discussed. The axial distribution of the capillary radius, fluid pressure and mean velocity are obtained. In addition, the calculated maximum heat transport capability of the heat pipe at different working temperatures is compared with that obtained from a traditional capillary pressure balance model, in which the interfacial shear stress is neglected. The accuracy of the present model is verified by experimental data obtained in this paper.**Keywords:**Heat pipe; Microgrooves; Capillary radius; Maximum heat transport capability;

Incorporating boundary conditions in the heat conduction model by V. Bertola; E. Cafaro

*(644-646)*. This note introduces a mathematical derivation of the heat conduction model that incorporates boundary conditions. In particular, in the present approach boundary conditions are derived in parallel to the heat equation, while in the standard approach to heat conduction modelling they are appended at a later stage. Because of its peculiar mathematical formulation, this method allows modelling heat sources or sinks placed on the boundary. Furthermore, it is shown that when such heat sources depend linearly on the surface temperature and the heat flux, each of their points can be described as a point source emitting a heat wave directed into an infinitesimal volume in the neighbourhood of the surface.

Pulsating flow and convective heat transfer in a cavity with inlet and outlet sections by A. Velazquez; J.R. Arias; J.L. Montanes

*(647-654)*. This paper deals with the study of 2-D, laminar, pulsating flow inside a heated rectangular cavity with different aspect ratios. The cooling liquid (water with temperature dependent viscosity and thermal conductivity) comes and leaves the cavity via inlet and outlet ports. The flow topology is characterised by the large recirculation regions that exist at inner corners of the cavity. These low velocity regions cause the heat transfer to be small when compared, for instance, to that of a straight channel. We study the effect that a prescribed pulsation at the inlet port has on the cavity heat transfer. This pulsating boundary condition, of the unsteady Poiseuille type, is described by its frequency and the amplitude of the pressure gradient. The time averaged Reynolds number of the flow, based on the hydraulic diameter of the inlet channel, is 100 and we consider that the dimensionless pulsation frequency (Strouhal number) varies in the range from 0.0 to 0.4. We show that the prescribed pulsation enhances heat transfer in the cavity and that the mechanism that causes this enhancement appears to be the periodic change in the recirculation flow pattern generated by the pulsation. Regarding the quantitative extent of heat transfer recovery, we find that appropriate selection of the pulsation parameters allows for the cavity to behave like a straight channel that is the configuration with the highest Nusselt number.

**Keywords:**Cavity; Unsteady flow; Convective heat transfer;

Low Reynolds number scalar transport enhancement in viscous and non-Newtonian fluids by D.R. Lester; M. Rudman; G. Metcalfe

*(655-664)*.**Keywords:**Heat and mass transfer; Chaotic advection; Parametric variation; Numerical methods;

Thermal conductivity of a clay-based aerogel by S.R. Hostler; A.R. Abramson; M.D. Gawryla; S.A. Bandi; D.A. Schiraldi

*(665-669)*. Aerogel materials exhibit superior thermal insulation characteristics due largely to their highly porous internal structure. A recently developed class of montmorillonite clay-based aerogels provides the attractive thermal properties of traditional aerogel materials using constituents that are chemically benign and abundantly available. Results are compared for aerogels made from clay alone and those with polyvinyl alcohol introduced during processing. Results demonstrate that as well as strength advantages, the addition of the polymer also leads to a reduction in thermal conductivity. Experimental thermal conductivity data as well as a model to describe the mechanisms involved in impeding thermal transport are presented.

**Keywords:**Aerogel; Clay; Thermal conductivity; Effective medium;

Dynamics and temperature of droplets impacting onto a heated wall by G. Castanet; T. Liénart; F. Lemoine

*(670-679)*. This paper presents results of an experimental investigation of water droplet impacts onto a smooth heated plate made of nickel. A high-speed camera is used to observe the impact regimes (rebound, splashing, and deposition of a liquid film) for a large set of impact conditions (wall temperature, droplet incidence angle, velocity and size). The observations help specifying the conditions of existence of the regimes. In a second part of the paper, the emphasis is placed on the droplet heating during an interaction with the heated wall. The droplet temperature is measured with the help of the two-colour laser-induced fluorescence thermometry in the case of the different impact regimes. The droplet change in temperature during an impact is found to be dependent on the normal velocity but not on the wall temperature when it exceeds the Leidenfrost temperature.

**Keywords:**Drop impact; Laser-induced fluorescence; Temperature measurement; Spray cooling;

Simulation of turbulent impinging jet into a cylindrical chamber with and without a porous layer at the bottom by Daniel R. Graminho; Marcelo J.S. de Lemos

*(680-693)*. Turbulent impinging jets on heated surfaces are widely used in industry to modify local heat transfer coefficients. The addition of a porous substrate covering the surface contributes to a better flow distribution, which favors many engineering applications. Motivated by this, this work shows numerical results for a turbulent impinging jet into a cylindrical enclosure with and without a porous layer at the bottom. The macroscopic time-averaged equations for mass and momentum are obtained based on a concept called double decomposition, which considers spatial deviations and temporal fluctuations of flow properties. Turbulence is handled with a macroscopic

*k*–*ε*model, which uses the same set of equations for both the fluid layer and the porous matrix. The numerical technique employed is the control volume method in conjunction with a boundary-fitted coordinate system. One unique computational grid is used to compute the entire heterogeneous medium. The SIMPLE algorithm is applied to relax the system of algebraic equations. Results indicate that the permeability of the porous layer and the height of the fluid layer significantly affect the flow pattern. The effect of the porous layer thickness was less pronounced in affecting the flow behavior in the fluid layer.**Keywords:**Turbulent flow; Porous media; Numerical methods; Impinging jet; Modeling;

Numerical solution for the linear transient heat conduction equation using an Explicit Green’s Approach by W.J. Mansur; C.A.B. Vasconcellos; N.J.M. Zambrozuski; O.C. Rotunno Filho

*(694-701)*. This paper presents a novel numerical solution algorithm for the linear transient heat conduction equation using the ‘Explicit Green’s Approach’ (ExGA). The method uses the Green’s matrix that represents the domain of the problem to be solved in terms of the physical properties and geometrical characteristic. The Green’s matrix is the problem discrete Green’s function determined numerically by the Finite Element Method (FEM). The ExGA allows explicit time marching with time step larger than the one required by FEM, without losing precision. The ExGA numerical results are quite accurate when compared to analytical solutions and to numerical solutions obtained by the FEM.

**Keywords:**Linear transient heat conduction; Numerical Green’s matrix; ExGA; Time integration;

Approximate solutions of lean premixed combustion in porous media with reciprocating flow by Jun-Rui Shi; Mao-Zhao Xie; Gang Li; Hong Liu; Ji-Tang Liu; Hong-Tao Li

*(702-708)*. Based on the analogy with the steady countercurrent reactor, a simplified theoretical solution is presented, which is applicable to adiabatic inert porous media combustors with reciprocating flow. The model consists of two ordinary differential equations that link all major controlling parameters, which allow for a good physical understanding of the process. The maximum temperatures in the burner predicted by the simplified model show the same trends as those in experimental results, but are generally higher, and the discrepancy between the experimental data and predications is less than 20%. By analyzing experimental and simulation results, a simplified theoretical solution for the temperature profile in the burner is further developed, which is expressed in terms of a piecewise linear function and the lean flammability limit is presented by a implicit expression. Results show that the lean flammability limit can be extended by using porous media of smaller pore size. The predicted lean flammability limit provides guidelines for the design of the combustor and some indications for further improving the combustor performances.

**Keywords:**Premixed combustion; Reciprocating flow; Flammability limit; Approximate solution;

Stability of conducting viscous film flowing down an inclined plane with linear temperature variation in the presence of a uniform normal electric field by Asim Mukhopadhyay; Anandamoy Mukhopadhyay

*(709-715)*. Weakly nonlinear stability analysis of a thin liquid film falling down a heated inclined plane with linear temperature variation in the presence of a uniform normal electric field has been investigated within the finite amplitude regime. A generalized kinematic equation for the development of free surface is derived by using long wave expansion method. A normal mode approach and the method of multiple scales are used to investigate the linear and weakly nonlinear stability analysis of film flow, respectively. It is found that both Marangoni and electric Weber numbers have destabilizing effect on the film flow. The study reveals that both supercritical stability and subcritical instability are possible for this type of film flow. It is interesting to note that both the Marangoni and electric Weber numbers have qualitatively same influence on the stability characteristics but the effect of Marangoni number is much stronger compare to the electric Weber number. Scrutinizing the effect of Marangoni and electric Weber numbers on the amplitude and speed of waves it is found that, in the supercritical region amplitude and speed of the nonlinear waves increases with the increase in Marangoni and electric Weber numbers, while in the subcritical region the threshold amplitude decreases with the increase in Marangoni and electric Weber numbers. Finally, we obtain that spatially uniform solution is side-band stable in the supercritical region for our considered parameter range.

**Keywords:**Thin film; Finite amplitude stability analysis; Electrodynamic instability; Marangoni instability;

Theoretical model for fast bubble growth in small channels with reference to startup of capillary pumped loops used in spacecraft thermal management systems by Tim J. LaClair; Issam Mudawar

*(716-723)*. A capillary pumped loop (CPL) is a closed two-phase loop in which capillary forces developed in a wicked evaporator passively pump the working fluid over long distances to dissipate heat from electronic and power sources. Because it has no moving parts and requires minimal power to sustain operation, the CPL is considered an enabling technology for thermal management of spacecraft. While the steady-state operation of a CPL is fairly well understood, its thermal response during startup remains very illusive. During the startup, initial vapor bubble growth in the evaporator is responsible for liquid acceleration that results in a differential pressure spike. A large pressure spike can deprime the evaporator by forcing vapor into the evaporator’s liquid-saturated wick, which is the only failure mode of a CPL other than fluid loss or physical damage to the loop. In this study, a numerical transient 3D model is constructed to predict the initial bubble growth. This model is used to examine the influence of initial system superheat, evaporator groove shape and size, and wick material. A simplified model is also presented which facilitates the assessment of parametric influences by analytic means. It is shown how these design parameters may be optimized to greatly reduce the bubble growth rate and therefore help prevent a deprime.

Numerical prediction of natural convection in vented cavities using restricted domain approach by S. Anil Lal; C. Reji

*(724-734)*. The present study reports the numerical simulation of natural convection heat transfer from an open square cavity with two side vents provided symmetrically on the side walls. The top wall which is maintained at a constant temperature (

*T*_{w}), is the heat source for the cavity and the side walls are adiabatic. A restricted domain approach that predicts the regions of inflow, outflow and velocity distributions is employed. The applicability of two types of pressure boundary conditions at entry and exit regions are studied and compared. Non-linear coupled partial differential equations governing natural convection are solved on a structured non-uniform staggered grid using a second-order accurate upwind least square scheme for discretising the convection terms, central difference scheme for diffusion terms and SIMPLER algorithm for pressure–velocity decoupling. An in-house code is developed and is validated with the results of three classical natural convection problems. Simulations have been carried out for a wide range of thermal parameter, Rayleigh numbers (10^{4}⩽*Ra*⩽ 10^{8}), orientation of the cavity about horizontal (0 ⩽*δ*⩽ 180) and geometrical parameter, vent ratio ( 0.05 ⩽ D L ⩽ 0.25 ) . The numerical simulation predicts the dimensionless mass flow rate through the cavity and variation of local Nusselt number over the hot wall. A correlation for average Nusselt number is developed in terms of Rayleigh number and angle of tilt of the cavity for D L ⩾ 0.1 .**Keywords:**Natural convection; Vented cavities; Restricted domain approach; SIMPLER algorithm; Upwind least square scheme;

Transport properties of liquid argon in krypton nanochannels: Anisotropy and non-homogeneity introduced by the solid walls by F. Sofos; T. Karakasidis; A. Liakopoulos

*(735-743)*. In this work we calculate the transport properties of liquid argon flowing through a nanochannel formed by krypton walls. Non-equilibrium molecular dynamics (NEMD) simulations are performed assuming flow conditions corresponding to the macroscopic equivalent of planar Poiseuille flow. We examine the effect of channel width and system temperature on diffusion coefficient, shear viscosity and thermal conductivity. The results show clearly the existence of a critical width, in the range 7–18

*σ*, below which the behavior of transport properties is affected in comparison to bulk properties. In fact for small width values, diffusion coefficient is highly anisotropic, the component normal to the wall being the smaller one. For the same width range, diffusivities along all directions are higher in the central layers than those close to the walls. Similarly, shear viscosity increases for small channel width values while thermal conductivity decreases. All properties approach bulk values as the channel width increases. The layers close to the walls always present distinctly different behavior due to the interaction with the wall atoms. The observed behavior is of particular importance in the design of nanofluidic devices.**Keywords:**NEMD simulation; Nanofluid dynamics; Nanoscale phenomena; Transport properties; Non-continuum effects;

Boiling behaviors and critical heat flux on a horizontal plate in saturated pool boiling of water at high pressures by Hiroto Sakashita; Ayako Ono

*(744-750)*. Observations of boiling behaviors and measurements of critical heat flux (CHF) were carried out for saturated water boiling on a horizontal, upward-facing plate at pressures from atmospheric to 7 MPa. The primary bubbles diminish in size almost in inverse proportion to pressure and commence to coalesce in the very low heat flux region. The diameter of detached coalesced bubbles increases with increases in the heat flux and reaches about 10 mm even at a pressure of 5 MPa. Detachment frequency of the coalesced bubbles was unaffected by the heat flux and pressure. The CHF predicted based on the macrolayer dryout model agrees well with the measured data.

**Keywords:**Pool boiling; Critical heat flux; High pressure; Macrolayer; Observation; Primary bubble; Coalesced bubble;

Coupled heat and mass transfer through asymmetric porous membranes with finger-like macrovoids structure by Li-Zhi Zhang

*(751-759)*. Asymmetric porous membranes with finger-like macrovoids have been extensively used in various processes, either directly as the transfer media or indirectly as the substrate for active layer. Heat and mass transfer through such membranes are the key parameters influencing system performance. However, previous studies on heat and mass transport only treated these membranes as a black box of homogeneous porous media by neglecting their asymmetric nature in structure, which fails to disclose the relations between the membrane structure and system performance. To solve this problem, this study gives a more detailed investigation of the thermal and mass diffusion through these membranes, with the help of scanning electron microscope (SEM) observations of membrane surface and cross-sectional structures. In the model setup, the whole membrane is classified into three layers: a sponge-like porous support layer, a layer of porous media with finger-like macrovoids, and a thin denser skin layer with smaller pores. The model is then incorporated into the analysis of coupled heat and mass transfer in a membrane exchanger for moisture permeations. Results show that the effective diffusivity of the membrane has been dramatically improved due to the existence of more than 70,000 per meter large finger-like voids inside.

**Keywords:**Heat transfer; Mass transfer; Asymmetric membranes; Finger-like macrovoids;

Modeling of the heat transfer and flow features of the thermal plasma reactor with counter-flow gas injection by Gui-Qing Wu; He-Ping Li; Cheng-Yu Bao; Xi Chen

*(760-766)*. Modeling study is conducted to reveal the heat transfer and flow features of the thermal plasma reactor with a counter-flow gas injection and used for nano-particle synthesis. The modeling results show that a variety of parameters, such as the temperature and flow rate of the carrier gas, the operation conditions of the plasma torch, the distance between the plasma torch exit and the carrier-gas injector exit, the swirling of the plasma jet or the carrier gas, etc., can all affect appreciably the temperature and flow fields and the locations of the stagnation layers formed in the plasma reactor. An appropriate combination of the operation parameters of the reactor is thus required in order to obtain a suitable stagnation layer for the synthesis of nano-scale particles.

**Keywords:**Thermal plasma; Reactor; Modeling; Counter-flow injection; Swirling effect;

Bubble growth with chemical reactions in microchannels by B.R. Fu; Chin Pan

*(767-776)*. This work investigates the nucleation and growth of CO

_{2}bubbles due to chemical reactions of sulfuric acid and sodium bicarbonate in three types of microchannels: one with uniform cross-section, one converging, and another one diverging. The Y-shaped test section, composed of main and two front microchannels, was made of P-type 〈1 0 0〉 orientation SOI (silicon on insulator) wafer. Bubble nucleation and growth in microchannels under various conditions were observed using a high-speed digital camera. The theoretical model for bubble dynamics with a chemical reaction is reviewed or developed. In the present study, no bubble was nucleated at the given inlet concentration and in the range of flow rate in the converging microchannel while the nucleation and growth of bubbles were observed in the diverging and uniform cross-section microchannels. Bubbles are nucleated at the channel wall and the equivalent bubble radius increases linearly during the initial period of the bubble growth. The bubble growth behavior for a particular case, without relative motion between the bubble and liquid, shows that the mass diffusion controls the bubble growth; consequently, the bubble radius grows as a square root of the time and agrees very well with the model in the literature. On the other hand, for other cases the bubbles stay almost at the nucleation site while growing with a constant gas product generation rate resulting in the instant bubble radius following the one-third power of the time.**Keywords:**Bubble growth; Microchannel; Two-phase flow; Chemical reaction;

Heat transfer in particulate flows with Direct Numerical Simulation (DNS) by Zhi-Gang Feng; Efstathios E. Michaelides

*(777-786)*. A Direct Numerical Simulation (DNS) method has been developed to solve the heat transfer equations for the computation of thermal convection in particulate flows. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. The numerical methods developed in this paper have been validated extensively by comparing the present simulation results with those obtained by others.

**Keywords:**Particulate flow; Solid and fluid interaction; Heat transfer; Immersed boundary method;

Experimental and numerical studies of AISI1020 steel in grind-hardening by Jianhua Zhang; Peiqi Ge; Tien-Chien Jen; Lei Zhang

*(787-795)*. Currently, most of the researches studying grind-hardening have used Design of Experiments approach to obtain empirical correlations without any in-depth theoretical analyzes. In this paper, a comprehensive numerical model is developed to simulate the temporal and spatial temperature distributions of the workpiece under the dry grind-hardening condition using finite element method. The simulated hardness penetration depth is deduced from the local temperature distribution and time history of workpiece and its martensitic phase transformation conditions. The results from simulations are validated with experiments. The effect of two major grinding parameters, workpiece speed and depth of cut, on the hardness penetration depth are discussed.

**Keywords:**Grind-hardening; Numerical study; Surface hardening; Grinding temperature field;

Assessment of structure effects on the thermal conductivity of two-phase porous geomaterials by Jean Côté; Jean-Marie Konrad

*(796-804)*. The effect of structure on the thermal conductivity of geomaterials is studied for solid–fluid combinations representing a wide variety of two-phase porous geomaterials. Nearly 200 thermal conductivity data sets from the literature were analyzed for geomaterials made of natural soil particles, crushed rock particles and sedimentary rock. Two analog models are studied to quantify the effect of structure. It appears that the effect of structure increases with decreasing fluid/solid thermal conductivity ratio and structure effects are negligible from a ratio of approximately 1/15 and higher. A new simplified model is proposed to compute the effective thermal conductivity as a function of the fluid/solid thermal conductivity ratio and the structure of geomaterials. The model applies well to independent data of homogeneous and heterogeneous materials including industrial cement concrete.

**Keywords:**Thermal conductivity; Solid; Fluid; Porosity; Particles shape; Cement;

Study on condensation heat transfer characteristics of wet paper in steam heating process by Tsutomu Kawamizu; Takeshi Kaneko; Setsuo Suzuki; Takaharu Tsuruta

*(805-813)*. Effects of suction pressure and permeability on the steam heating characteristics of the wet paper are studied. Experimental results show that suction pressure enhances the energy absorption in the wet paper and effects of suction pressure strongly appear in the high-permeability paper, and also absorbed energy rate is decreased with increasing in heating time. From the numerical simulation results it is found that increase in moisture content and decrease of pressure gradient reduce the absorbed energy rate. Dimensionless numbers are derived from the basic equations to summarize the experimental and numerical simulation results.

**Keywords:**Porous media; Permeability; Suction pressure; Condensation; Heat transfer; Mass transfer;

Measurement of surface dryout near heating surface at high heat fluxes in subcooled pool boiling by Ayako Ono; Hiroto Sakashita

*(814-821)*. The authors have conducted measurements of liquid–vapor behavior in the vicinity of a heating surface for saturated and subcooled pool boiling on an upward-facing copper surface by using a conductance probe method. A previous paper [A. Ono, H. Sakashita, Liquid–vapor structure near heating surface at high heat flux in subcooled pool boiling, Int. J. Heat Mass Transfer 50 (2007) 3481–3489] reported that thicknesses of a liquid rich layer (a so-called macrolayer) forming in subcooled boiling are comparable to or thicker than those formed near the critical heat flux (CHF) in saturated boiling. This paper examines the dryout behavior of the heating surface by utilizing the feature that a thin conductance probe placed very close to the heating surface can detect the formation and dryout of the macrolayer. It was found that the dryout of the macrolayer formed beneath a vapor mass occurs in the latter half of the hovering period of the vapor mass. Two-dimensional measurements conducted at 121 grid points in a 1-mm × 1-mm area at the center of the heating surface showed that the dryout commences at specific areas and spreads over the heating surface as the heat flux approaches the CHF. Furthermore, transient measurements of wall void fractions from nucleate boiling to transition boiling were conducted under the transient heating mode, showing that the wall void fraction has small values (<10%) in the nucleate boiling region, and then steeply increases in the transition boiling region. These findings strongly suggest that the macrolayer dryout model is the most appropriate model of the CHF for saturated and subcooled pool boiling of water on upward facing copper surfaces.

**Keywords:**Pool boiling; Critical heat flux; Macrolayer; Dryout; Subcooled boiling; Conductance probe;

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio by Vinoj Kurian; Mahesh N. Varma; A. Kannan

*(822-838)*. The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10

^{3}to 3.1 × 10^{4}by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.**Keywords:**Natural convection; Cylinder inclination; Flow patterns; Maximum convective velocity; Nusselt number; Critical Rayleigh number;

Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime by Akhilesh K. Sahu; R.P. Chhabra; V. Eswaran

*(839-850)*. The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 ⩽

*Re*⩽ 160 and 0.7 ⩽*Pr*⩽ 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.**Keywords:**Square cylinder; Unsteady flow; Prandtl number; Nusselt number; Strouhal number;

Numerical heat transfer analysis of encapsulated ice thermal energy storage system with variable heat transfer coefficient in downstream by Aytunc Erek; Ibrahim Dincer

*(851-859)*. During charging and discharging processes, the heat transfer behavior of the encapsulated ice thermal energy storage (TES) system changes during downstream case and this should be taken into account since the temperature of heat transfer fluid (HTF) and especially the heat transfer coefficient varies considerably around each capsule. This requires a careful study of the problem with variable heat transfer coefficient to contribute to the state-of-the-art. This has been the primary motivation behind the present study. Here, we first develop a new heat transfer coefficient correlation by simulating a series of 120 numerical experiments for different capsule diameters, mass flow rates and temperatures of HTF and second undertake a comprehensive numerical analysis using the temperature based fixed grid solution with control volume approach for studying the heat transfer behavior of an encapsulated ice TES system. Thirdly, we validate the present numerical model and the new correlation with some experimental data obtained from the literature, and hence a good agreement is obtained between the model results and experimental data. The results indicate that the heat transfer coefficient varies greatly during downstream and highly affects the heat transfer taking place during the process. So, the solutions with constant heat transfer coefficient appear to be unreliable for analysis and system optimization. The results also show that the solidification process is chiefly governed by the magnitude of Stefan number, capsule diameter and capsule row number.

**Keywords:**Heat transfer; Phase change; Solidification; Phase change; Encapsulated ice; Energy storage;

Modeling heat transfer in Bi

_{2}Te_{3}–Sb_{2}Te_{3}nanostructures by Arvind Pattamatta; Cyrus K. Madnia*(860-869)*. Bi

_{2}Te_{3}–Sb_{2}Te_{3}nanostructures are gaining importance for use in thermoelectric applications following the finding that the Bi_{2}Te_{3}–Sb_{2}Te_{3}superlattice exhibits a figure of merit, ZT = 2.4, which is higher than conventional thermoelectric materials. In this paper, thermal transport in the cross-plane direction for Bi_{2}Te_{3}–Sb_{2}Te_{3}nanostructures is simulated using the Boltzmann transport equation (BTE) for phonon intensity. The phonon group velocity, specific heat, and relaxation time are calculated based on phonon dispersion model. The interfaces are modeled using a combination of diffuse mismatch model (DMM), and the elastic acoustic mismatch model (AMM). The thermal conductivity for the Bi_{2}Te_{3}–Sb_{2}Te_{3}superlattice is compared with the experimental data, and the best match is obtained for specularity parameter,*p*, of 0.9. The present model is extended to solve for thermal transport in 2-D nanowire composite in which Sb_{2}Te_{3}wires are embedded in a host material of Bi_{2}Te_{3}. Unlike in bulk composites, the results show a strong dependence of thermal conductivity, temperature, and heat flux on the wire size, wire atomic percentage, and interface specularity parameter. The thermal conductivity of the nanowire is found to be in the range of 0.034–0.74 depending on the atomic percentage and the value of*p*.**Keywords:**Bi

_{2}Te

_{3}; Sb

_{2}Te

_{3}; Boltzmann equation; Nanostructures; Superlattice; Nanowire;

Critical review of flow boiling heat transfer of CO

_{2}–lubricant mixtures by Xiumin Zhao; Pradeep Bansal*(870-879)*. This paper presents a comprehensive review on the flow boiling heat transfer of CO

_{2}–lubricant mixtures. Some of the immiscible lubricants in CO_{2}include alkyl naphthalene/alkylbenzne (AN/AB) and polyalphaolefin (PAO), while polyalkylene glycol (PAG) is partially miscible, and polyol ester (POE) is completely miscible. The effect of oil concentration, vapour quality, heat and mass fluxes and saturation temperature is addressed. One database has been created by collecting the experimental data from the open literature on the flow boiling heat transfer of CO_{2}–lubricant mixtures, along with empirical correlations. A simple simulation model has been developed in EES software package to compare the empirical correlations with the CO_{2}–lubricant mixtures experimental database. Most empirical correlations fail to predict the flow boiling heat transfer coefficient in good agreement with the experimental data. Hence, further research is needed to develop appropriate correlations for the flow boiling heat transfer of CO_{2}–lubricant mixtures.**Keywords:**Flow boiling heat transfer; CO

_{2}–lubricant mixture; In-tube flow;

Heat transfer in tilted reciprocating anti-gravity open thermosyphon by Tsun Lirng Yang; Shyy Woei Chang

*(880-893)*. This experimental study generates a new set of Nusselt number (

*Nu*) data from two opposite upper and lower edges of a tilted reciprocating anti-gravity open tubular thermosyphon that emulates closely the realistic ‘*shaker-bored*’ cooling conditions inside a piston of marine propulsive diesel engine. The impacts of thermosyphon inclination on heat transfer are described by way of comparisons between two sets of*Nu*data generated from the vertical and tilted reciprocating thermosyphons. Nusselt number differences between two opposite upper (*Nu*_{Upper}) and lower (*Nu*_{Lower}) edges along the tilted thermosyphon are amplified as the reciprocating force increases; while no appreciable differences between*Nu*_{Upper}and*Nu*_{Lower}are observed in the*tilted static*thermosyphon or in the*vertical*static and reciprocating thermosyphon. For such tilted reciprocating open thermosyphon, the individual and interactive influences of inertial, reciprocating and buoyancy forces on heat transfer are described for both sub-cooled (single phase) and superheated (two phase) conditions. Due to the synergistic effects of inertial force, reciprocating force and buoyancy interactions for all the experimental conditions tested, the worst heat transfer scenarios in terms of the axially averaged*Nu*values in the*tilted reciprocating open thermosyphon*fall to the level of 0.82 times of the static levels. A set of empirical heat transfer correlations which permits the evaluation of axially averaged Nusselt numbers is developed to assist the design activity of such piston cooling system.**Keywords:**Open thermosyphon; Reciprocating flow; Piston cooling;

Non-uniform double slot suction (injection) into water boundary layer flows over a cylinder by P. Saikrishnan; S. Roy; I. Mohammed Rizwan Sadiq; Bishun D. Pandey

*(894-898)*. An analysis is performed to study the effect of non-uniform double slot suction (injection) into a steady two-dimensional laminar boundary layer flow when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Non-similar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. By applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the streamwise direction, the difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome. The results indicate that the separation can be delayed by non-uniform double slot suction and also by moving the slot downstream. However, the effect of non-uniform double slot injection is just the opposite.

Three dimensional mixed convection in plane symmetric-sudden expansion: Symmetric flow regime by M. Thiruvengadam; B.F. Armaly; J.A. Drallmeier

*(899-907)*. Three-dimensional simulations of laminar buoyancy assisting mixed convection in a vertical duct with a plane symmetric sudden expansion are presented to illustrate the effects of the buoyancy assisting force and the duct’s aspect ratio on the flow and heat transfer. This geometry and flow conditions appear in many engineering applications, but 3-D heat transfer results have not appeared in the literature. This study focuses on the regime where the flow and thermal fields are symmetric in this geometry. The buoyancy force is varied by changing the heat flux on the stepped walls that are downstream from the sudden expansion, and the duct’s aspect ratio is varied by changing the width of the duct while keeping the expansion ratio constant. Results are presented for duct’s aspect ratio of 4, 8, 12, 16, and ∞ (2-D flow), and for wall heat fluxes between 5–35 W/m

^{2}. The Reynolds number and the range of wall heat flux are selected to insure that the flow remains laminar and symmetric in this geometry and reverse flow does not develop at the exit section of the duct. Results for the velocity, temperature, and the Nusselt number distributions are presented, and the effects of the buoyancy force and the duct’s aspect ratio on these results are discussed.**Keywords:**Laminar mixed convection; Internal flow; Separated flow; Heat transfer; 3-D Numerical simulation;

Investigation of coated tubes in cross-flow boiling by Vikas J. Lakhera; Akhilesh Gupta; Ravi Kumar

*(908-920)*. The boiling in cross-flow is investigated for coated tubes (low-porosity, flame-sprayed) in this paper. The effect of surface roughness on flow boiling heat transfer for a horizontal tube surface in cross-flow is studied for saturated boiling of water at atmospheric pressure. The parameters varied were for flow velocity up to 3.24 kg/s (

*G*= 258.49 kg/m^{2}s), heat flux from 12 to 45 kW/m^{2}, surface roughness (*Ra*) from 0.3296 to 4.731 μm. Nominal enhancement in heat transfer coefficient at higher mass flux may be attributed to the continued nucleation at the uppermost surfaces (in the wake region of the flow) of the rougher tubes thereby increasing the overall heat transfer rate. The flow boiling data was found to best fit the Kutateladze asymptotic equation*h*=*h*_{l}[1 + (*h*_{npb}/*h*_{l})^{ n }]^{1/n }with the value of*n*= 2.258 (which is close to the value of*n*= 2 suggested by Kutateladze).**Keywords:**Boiling heat transfer; Cross-flow; Surface roughness; Enhancement;

Large-eddy simulation of an impinging jet in a cross-flow on a heated wall-mounted cube by D. Rundström; B. Moshfegh

*(921-931)*. A large-eddy simulation (LES) is performed in order to predict the mean velocity field, the turbulence characteristics and the heat transfer rate of an impinging jet in cross-flow configuration on a heated wall-mounted cube. The WALE model was used to model the subgrid-scale tensor. The results from the LES are compared with a Reynolds stress model (RSM) and against earlier measurements with identical set-up. A comparison between the results from the predictions and the measurements shows that in general the LES has better agreement with the measurements compared to the RSM and particularly in the stagnation region of the impinging jet.

**Keywords:**Large-eddy simulation; Impinging jet in a cross-flow; Reynolds stress model; Electronic cooling;

Pulsating convective cooling across two porous-covering heated blocks by Po-Chuan Huang; Yen-Jen Chen; Meir-Chyun Tzou

*(932-951)*. A numerical study has been undertaken to analyze the flow and thermal characteristics of forced pulsating flow through a channel with two porous-covering heated blocks in tandem. Solution of the coupled governing equations for the fluid/porous/solid composite system is obtained by utilizing a control-volume method through the use of a stream function-vorticity approach. This study details the effects of variations in the Darcy number, pulsation frequency and amplitude, three pertinent geometric parameters and effective conductivity ratio, to illustrate important fundamental and practical results. The results show that the periodic alteration in the structure of recirculation flow inside the inter-block region and behind the downstream block significantly enhances the heat transfer rate on the block right faces.

Capillary-assisted flow and evaporation inside circumferential rectangular micro groove by Z.Z. Xia; G.Z. Yang; R.Z. Wang

*(952-961)*. To introduce capillary-assisted evaporation from micro-size fields to normal-size fields, an inclined circumferential micro groove with rectangular cross sections is investigated analytically and a systematic mathematical model is developed. The model is composed of five sub-models: a natural convection model, a liquid axial flow model, a heat transfer model in and below the intrinsic meniscus, an evaporation thin film region model and an adsorbed region model. In this model, for the extended meniscuses formed at groove cross sections, both the intrinsic meniscus and evaporation thin film region are considered when calculating heat absorbing. Through solving the model, the influences of dynamic contact angle on the heat absorbing in the intrinsic meniscus and evaporation thin film region are investigated. Moreover, the factors affecting the whole-groove equivalent heat transfer coefficient have been investigated.

**Keywords:**Capillary-assisted evaporation; Micro groove; Rectangular cross section; Extended meniscus;

Turbulent flow and heat transfer in discrete double inclined ribs tube by Xiao-wei Li; Ji-an Meng; Zeng-yuan Guo

*(962-970)*. The turbulent heat transfer and flow resistance in an enhanced heat transfer tube, the DDIR tube, were studied experimentally and numerically. Water was used as the working fluid with Reynolds numbers between 15,000 and 60,000. The numerical simulations solved the three dimensional Reynolds-averaged Navier–Stokes equations with the standard

*k*-*ε*model in the commercial CFD code, Fluent. The numerical results agree well with the experimental data, with the largest discrepancy of 10% for the Nusselt numbers and 15% for the friction factors. The heat transfer in the DDIR tube is enhanced 100 ∼ 120% compared with a plain tube and the pressure drop is increased 170 ∼ 250%. The heat transfer rate for the same pumping power is enhanced 30 ∼ 50%. Visualization of the flow field shows that in addition to the front and rear vortices around the ribs, main vortices and induced vortices are also generated by the ribs in the DDIR tube. The rear vortex and the main vortex contribute much to the heat transfer enhancement in the DDIR tubes. Optimum DDIR tube parameters are proposed for heat transfer enhancement at the same pumping power.**Keywords:**Field synergy principle; Heat transfer enhancement; DDIR tube; Longitudinal vortex;

Experimental study of multi-hole cooling for integrally-woven, ceramic matrix composite walls for gas turbine applications by Fengquan Zhong; Garry L. Brown

*(971-985)*. In this paper, multi-hole cooling is studied for an oxide/oxide ceramic specimen with normal injection holes and for a SiC/SiC ceramic specimen with oblique injection holes. A special purpose heat transfer tunnel was designed and built, which can provide a wide range of Reynolds numbers (10

^{5}∼10^{7}) and a large temperature ratio of the primary flow to the coolant (up to 2.5). Cooling effectiveness determined by the measured surface temperature for the two types of ceramic specimens is investigated. It is found that the multi-hole cooling system for both specimens has a high cooling efficiency and it is higher for the SiC/SiC specimen than for the oxide/oxide specimen. Effects on the cooling effectiveness of parameters including blowing ratio, Reynolds number and temperature ratio, are studied. In addition, profiles of the mean velocity and temperature above the cooling surface are measured to provide further understanding of the cooling process. Duplication of the key parameters for multi-hole cooling, for a representative combustor flow condition (without radiation effects), is achieved with parameter scaling and the results show the high efficiency of multi-hole cooling for the oblique hole, SiC/SiC specimen.**Keywords:**Integrally-woven ceramic matrix composite; Cooling effectiveness; Reynolds number; Blowing ratio; Temperature ratio;

Experimental and theoretical studies of a two-stage pulse tube cryocooler operating down to 3 K by S. Kasthurirengan; G. Srinivasa; G.S. Karthik; D.S. Nadig; U. Behera; K.A. Shafi

*(986-995)*. The development of a two-stage Pulse Tube Cryocooler (PTC) which produces a no-load temperature of ∼3 K and delivers a refrigeration power of ∼250 mW at 5 K is reported in this work. The system uses stainless steel meshes along with lead (Pb) granules and combinations of Pb, Er

_{3}Ni and HoCu_{2}in layered structures as the first and second stage regenerator materials respectively. With Helium as a working fluid, the pressure oscillations are generated using a 6 kW water-cooled Helium compressor along with an indigenous rotary valve. Different configurations of pulse tube systems have been experimentally studied, by both varying the dimensions of pulse tubes and regenerators as well as the second stage regenerator material composition. The pulse tube Cryocooler has been numerically analyzed by using both the isothermal model and the model based on solving the energy equations. The predicted refrigeration powers as well as the temperature profiles have been compared with the experimental results for specific pulse tube configurations.**Keywords:**Pulse tube; Cryocooler; Regenerator; Helium; Refrigeration; Numerical modeling;

Unsteady heat conduction involving phase changes for an irregular bubble/particle entrapped in a solid during freezing – An extension of the heat-balance integral method by K.R. Lin; P.S. Wei; S.Y. Hsiao

*(996-1004)*. Temperature distributions in the molten layer and solid with distinct properties around a bubble or particle entrapped in the solid during unidirectional solidification are determined by applying a heat-balance integral approximation method. The present model can be used to simulate growth, entrapment or departure of a bubble or particle inclusion in solids encountered in manufacturing and materials processing, MEMS, contact melting processes, drilling, etc. In this work, the proposed heat-balance equations are derived by integrating unsteady elliptic heat diffusion equations and introducing the Stefan boundary condition. Due to the time-dependent irregular shapes of phases, coefficients of assumed quadratic temperature profiles are considered to be functions of longitudinal coordinate and time. Temperature coefficients in distinct regions therefore are determined by solving equations governing temperature coefficients derived from heat-balance equations, imposing boundary conditions, and introducing a fictitious boundary condition. The computed temperature fields show agreement with predictions from the finite-difference method. Since the number of independent variables is reduced by one, this work provides an effective method to solve unsteady elliptic diffusion problems experiencing solid–liquid phase changes in irregular shapes.

**Keywords:**Integral method; Heat-balance integral method; Pore formation; Porosity; Bubble capture; Particle inclusion; Contact melting;

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace by Sang Heon Han; Seung Wook Baek; Man Young Kim

*(1005-1011)*. Transient radiative heating characteristics of slabs in a walking beam type reheating furnace is predicted by the finite-volume method (FVM) for radiation. The FVM can calculate the radiative intensity absorbed and emitted by hot gas as well as emitted by the wall with curvilinear geometry. The non-gray weighted sum of gray gas model (WSGGM) which is more realistic than the gray gas model is used for better accurate prediction of gas radiation. The block-off procedure is applied to the treatment of the slabs inside which intensity has no meaning. Entire domain is divided into eight sub-zones to specify temperature distribution, and each sub-zone has different temperatures and the same species composition. Temperature field of a slab is acquired by solving the transient 3D heat conduction equation. Incident radiation flux into a slab is used for the boundary condition of the heat conduction equation governing the slab temperature. The movement of the slabs is taken into account and calculation is performed during the residence time of a slab in the furnace. The slab heating characteristics is also investigated for the various slab residence times. Main interest of this study is the transient variation of the average temperature and temperature non-uniformity of the slabs.

**Keywords:**Reheating furnace; Radiative slab heating; Residence time;

Hybrid DNS/LES of high Schmidt number mass transfer across turbulent air–water interface by Yosuke Hasegawa; Nobuhide Kasagi

*(1012-1022)*. Numerical simulation of a coupled air–water turbulent flow and associated high Schmidt number mass transfer is carried out via a hybrid scheme of direct and large-eddy simulations (DNS/LES). Due to the large density ratio of water and air, the dynamical coupling between the air and water turbulent flows is found to be weak at the low wind velocity considered here. Instead, the self-sustaining mechanisms due to the mean shear, which are similar to those near a solid wall, are dominant even close to the air–water interface. The spatio-temporal correlations between the local mass transfer rate and velocity fluctuations around the interface reveal that impingement of fresh water on the interface governs the interfacial mass transfer. It is found that the local mass transfer rate can be predicted from the surface divergence by the Chan and Scriven’s stagnation flow model. This explains why the mass transfer rate is well correlated with the intensity of the surface divergence under a variety of flow conditions.

**Keywords:**Turbulence; Air–water interface; Mass transfer; Schmidt number; Surface divergence;

Numerical study of mixed convection in a two-dimensional laminar incompressible offset jet flow by K. Kumar Raja; Manab Kumar Das; P. Rajesh Kanna

*(1023-1035)*. The mixed convection flow and heat transfer characteristics in a two-dimensional plane, laminar offset jet issuing parallel to an isothermal flat plate have been investigated numerically. The unsteady form of the vorticity transport equation has been solved to obtain the steady-state solution. The isothermal heated plate is 30 times the jet width and the offset ratio is 1. The behavior of the jet in the range of Reynolds number Re = 300 – 600 and Grashof number Gr = 10 3 – 10 7 is described in details. The medium considered is air (

*Pr*= 0.71). It is found that the reattachment length is strongly dependent on both*Re*and*Gr*for the range considered. Simulations are made to show the effect of entrainment on the recirculation eddy. The variation of the local Nusselt number is presented for various*Re*and*Gr*. An empirical correlation of average Nusselt number as a function of Richardson number ( Ri = Gr / Re 2 ) and*Re*has been given.**Keywords:**Offset jet; Mixed convection; Computation;

Laminar natural convection in a square cavity: Low Prandtl numbers and large density differences by T. Pesso; S. Piva

*(1036-1043)*. Steady natural convection at low Prandtl numbers caused by large density differences in a square cavity heated through the side walls is investigated numerically and theoretically. An appropriate dimensionless parameter characterizing the density differences of the working fluid is identified by the Gay-Lussac number. The Boussinesq assumption is achieved when the Gay-Lussac number tends to zero. The Nusselt number is derived for the ranges in Rayleigh number 10 ⩽

*Ra*⩽ 10^{8}, in Prandtl number 0.0071 ⩽*Pr*⩽ 7.1 and in Gay-Lussac number 0 ⩽*Ga*< 2. The effects of the Rayleigh, Prandtl and Gay-Lussac numbers on the Nusselt number are discussed on physical grounds by means of a scale analysis. Finally, based on physical arguments, a heat transfer correlation is proposed, valid for all Prandtl and Gay-Lussac number ranges addressed.**Keywords:**Natural convection; Heat transfer correlation; Square cavity; Variable properties;

Field synergy analysis of laminar forced convection between two parallel penetrable walls by Chenhua Gou; Ruixian Cai; Qibin Liu

*(1044-1052)*. In this paper, some exact solutions for 2-D convective heat transfer between two parallel penetrable walls were derived and analyzed based on field synergy theory. They are valuable to further develop the field synergy principle and understand how to improve or to weaken field synergy in practice. In addition, these solutions can be used as benchmarks to verify numerical solutions and to develop numerical schemes, grid generation methods and so forth. All solutions given in this paper can be proven easily by substituting them into the governing equations.

**Keywords:**Forced convection; Field synergy; Analytical solution;

Heat transfer enhancement by flow-induced vibration in heat exchangers by L. Cheng; T. Luan; W. Du; M. Xu

*(1053-1057)*. The flow-induced vibration in heat exchanger is usually considered as a detrimental factor for causing the heat exchanger damage and is strictly prevented from its occurrence. Its positive role for the possible heat transfer enhancement has been neglected. In this article a novel approach is proposed to enhance the heat transfer by using the flow-induced vibration of a new designed heat transfer device. Thus the flow-induced vibration is effectively utilized instead of strictly avoiding it in the heat exchanger design. A heat exchanger is constructed with the new designed heat transfer devices. The vibration and the heat transfer of these devices are studied numerically and experimentally, and the correlation of the shell-side convective heat transfer coefficient is obtained. It is found that the new designed heat exchanger can significantly increase the convective heat transfer coefficient and decrease the fouling resistance. Therefore, a lasting heat transfer enhancement by the flow-induced vibration can be achieved.

**Keywords:**Heat exchanger; Flow-induced vibration; Heat transfer enhancement;

Transitional flow patterns behind a backstep with porous-based fluid injection by Go-Long Tsai; Y.C. Lin; W.J. Ma; H.W. Wang; J.T. Yang

*(1058-1069)*. The flow structure downstream of a backstep with mass injection from a porous base was analyzed both qualitatively and quantitatively in the transitional flow regime of

*Re*_{h}= 2009–3061. By increasing the wall injection velocity ratio gradually, four distinct flow patterns, shifted from pattern A to B, C and D, were categorized. Pressure distributions of these patterns were dominated by the wall injection velocity ratio, and various downstream-flowing tendencies were produced correspondingly. The effect of flow stabilization by decreasing the Reynolds number became more prominent if the wall injection velocity ratio was increased. Due to the existence of a shear layer, a large value of the Reynolds stress was measured near the tip of the step in pattern A. Once the wall injection was initiated, the local strength of Reynolds stress at the same location was decreased. By increasing the wall injection velocity ratio, the region with decreased level of Reynolds stress extended gradually from the tip of backstep to the streamwise location*x*= 0.45*X*_{r}. The turbulent kinetic energy in pattern A was mostly contributed by the horizontal fluctuation of flow near the backstep in the recirculation zone, and the region with maximum horizontal fluctuation was found to evolve toward the base as the flow moves downstream. However, the weighting of vertical fluctuation became more significant as the wall injection velocity ratio increased.**Keywords:**Backstep; Flow pattern; Flow visualization; LDV;

An experimental and numerical study of forced convection in a microchannel with negligible axial heat conduction by Guodong Wang; Liang Hao; Ping Cheng

*(1070-1074)*. Experiments are conducted for laminar forced convection of water in a microchannel under partially-heated and fully-heated conditions on one wall with negligible axial heat conduction. The microchannel had a trapezoidal cross-sectional shape, with a hydraulic diameter of 155 μm and a heating length of 30 mm. Three-dimensional numerical simulations, based on the Navier–Stokes equations and energy equation, are obtained for forced convection of water in this microchannel under the same experimental conditions. It is found that the numerical predictions of wall temperatures and local Nusselt numbers are in good agreement with experimental data. This confirms that classical Navier–Stokes and energy equations are valid for the modeling of convection in a microchannel having a hydraulic diameter as small as 155 μm. For a microchannel with the same cross-sectional shape with one-wall heated and a heating length of 100 mm, numerical results show that the thermal entrance length is given by

*z*= 0.15RePrD_{h}, with the fully-developed Nusselt number approaching a constant value of 4.00.**Keywords:**Heat transfer; Laminar flow; Microchannel; Microheater; Numerical simulation;

Drag reduction and heat transfer enhancement over a heated wall of a vertical annular microchannel by Huei Chu Weng; Cha’o-Kuang Chen

*(1075-1079)*. An analysis for the effect of wall-surface curvature on gas microflow is performed to study the natural convection in an open-ended vertical annular microchannel with an isothermally heated inside wall. The fully developed solutions of the velocity, temperature, flow rate, shear stress, and heat flux are derived analytically and presented for air and various surfaces at the standard reference state. Results show that wall-surface curvature has a significant effect. This results in a nonlinear behavior in the temperature, which seems difficult to appear in a parallel-plate microchannel. Under certain rarefaction and fluid–wall interaction conditions, by decreasing the value of the curvature radius ratio, it is possible to obtain both reduced flow drag and enhanced heat transfer.

**Keywords:**Microfluidics; Natural convection; Rarefaction; Fluid–wall interaction; Annulus;

Erratum to “Flow boiling of liquid nitrogen in micro-tubes: Part II – Heat transfer characteristics and critical heat flux” [Int. J. Heat and Mass Transfer 50 (2007) 5017–5030] by S.L. Qi; P. Zhang; R.Z. Wang; L.X. Xu

*(1080)*.