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HEAT TRANSFER GALLERY

J. Heat Transfer. 2000;122(3):421. doi:10.1115/1.1289628.
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Aziz,  S. D., and Chandra,  S., 2000, “ Impact, Recoil and Splashing of Molten Metal Droplets,” Int. J. Heat Mass Transf., IJHMAK43, pp. 2841–2857.Bussmann,  M., Mostaghimi,  J., and Chandra,  S., 1999, “ On a Three-Dimensional Volume Tracking Model of Droplet Impact,” Phys. Fluids, PHFLE611, pp. 1406–1417.Cerza, M., Boughey, B., and Lindler, K. W., 2000, “A Flat Heat Pipe for Use as a Cold Side Heat Sink,” Session on Heat Pipes, Proceedings of the 35th Intersociety Energy Conversion Engineering Conference, AIAA, July 24–28, AIAA, Washington, DC, pp. 1418–1427.Kim,  Kyung Chun, and Kim,  Sang Ki, 1998, “ Flow Visualization Study on Plume Behavior in Thermally Stratified Wind,” Int. J. Environ. Conscious Design Manuf., ZZZZZZ7, No. 4, pp. 25–35.Kihm, K. D., Kim, H. J., and Pratt, D. M., 1999, “Image Corrections for Heated Micro-Scale Capillary Pore Flows,” 2nd Pacific Symposium on Flow Visualization and Image Processing (PSFVIP-2), Paper No. OF203, May, Honolulu, HI.Kihm, K. D., and Pratt, D. M., 1999, “Contour Mapping of Thin Liquid Film Thickness Using Fizeau Interferometer,” Paper No. NHTC99-224, Aug., Albuquerque, NM.Mao,  S. S., Mao,  X. L., Grief,  R., and Russo,  R. E., 2000, “ Dynamics of an Air Breakdown Plasma on a Solid Surface During Picosecond Laser Ablation,” Appl. Phys. Lett., APPLAB76, p. 31.Mukherjee,  D. K., Prasad,  V., Dutta,  P., and Yuan,  T., 1996, “ Liquid Crystal Visualization of the Effects of Crucible and Crystal Rotation on the CZ Melt Flows,” J. Cryst. Growth, JCRGAE169, pp. 136–146.Narumi, A., Ohishi, S., Nakane, I., and Kashiwagi, T., 1995, “Flow Visualization of Convective Interference of Water Around Two Cooling Tubes by Holographic Interferometry,” Proceedings, 7th International Symposium on Flow Visualization, J. P. Crowder, ed., Begell House, New York, pp. 314–319.Russo,  R. E., Mao,  X. L., Liu,  H. C., Yoo,  J. H., and Mao,  S. S., 1999, “ Time-Resolved Plasma Diagnostics and Mass Removal During Single-Pulse Laser Ablation,” Appl. Phys. A: Mater. Sci. Process., APAMFC69A, p. S887.

Topics: Heat transfer
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):426. doi:10.1115/1.1289644.
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Topics: Cooling , Convection , Water
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):428. doi:10.1115/1.1289646.
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Topics: Flat heat pipes
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):429. doi:10.1115/1.1289647.
FREE TO VIEW
Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: 1999 Max Jakob Memorial Award Lecture

J. Heat Transfer. 2000;122(3):430-449. doi:10.1115/1.1288406.

This lecture reviews a relatively recent body of heat transfer work that bases on a deterministic (constructal) principle the occurrence of geometric form in systems with internal flows. The same principle of global optimization subject to constraints allow us to anticipate the natural (animate and inanimate) flow architectures that surround us. The lecture starts with the example of the optimal spatial distribution of material (e.g., heat exchanger equipment) in power plants. Similarly, void space can be allocated optimally to construct flow channels in the volume occupied by a heat generating system. The lecture continues with the optimization of the path for heat flow between a volume and one point. It shows that when the heat flow can choose between at least two paths, low conductivity versus high conductivity, the optimal flow structure for minimal global resistance in steady flow is a tree. Nearly the same tree is deduced by minimizing the time of discharge in the flow from a volume to one point. Analogous tree-shaped flows are constructed in pure fluid flows, and in flow through a heterogeneous porous medium. The optimization of trees that combine heat transfer and fluid flow is illustrated by means of two-dimensional trees of plate fins. The method is extended to the superposition of two fluid trees in counterflow, as in vascularized tissues under the skin. The two trees in counterflow are one tree of convective heat currents that effect the loss of body heat. It is shown that the optimized geometry of the tree is responsible for the proportionalities between body heat loss and body size raised to the power 3/4, and between breathing time and body size raised to the power 1/4. The optimized structures are robust with respect to changes in some of the externally specified parameters. When more degrees-of-freedom are allowed, the optimized structure looks more natural. The lecture outlines a unique opportunity for engineers to venture beyond their discipline, and to construct an engineering theory on the origin and workings of naturally organized systems. [S0022-1481(00)02403-8]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Conduction Heat Transfer

J. Heat Transfer. 2000;122(3):450-459. doi:10.1115/1.1287726.

An inverse computational method has been developed for the nonintrusive and nondestructive evaluation of the temperature-dependence of thermal conductivity. The methodology is based on an inverse computational procedure that can be used in conjunction with an experiment. Given steady-state heat flux measurements or convection heat transfer coefficients on the surface of the specimen, in addition to a finite number of steady-state surface temperature measurements, the algorithm can predict the variation of thermal conductivity over the entire range of measured temperatures. Thus, this method requires only one temperature probe and one heat flux probe. The thermal conductivity dependence on temperature (k-T curve) can be completely arbitrary, although a priori knowledge of the general form of the k-T curve substantially improves the accuracy of the algorithm. The influence of errors of measured surface temperatures and heat fluxes on the predicted thermal conductivity has been evaluated. It was found that measurement errors of temperature up to five percent standard deviation were not magnified by this inverse procedure, while the effect of errors in measured heat fluxes were even lower. The method is applicable to two-dimensional and three-dimensional solids of arbitrary shape and size. [S0022-1481(00)01703-5]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Forced Convection

J. Heat Transfer. 2000;122(3):460-464. doi:10.1115/1.1287169.

An inverse problem for unsteady forced convection in an annular duct is presented. The simulated temperature data taken at the outer wall are used to estimate the time-dependent axially varying surface heat flux distribution at the inner wall of the annular passage. No prior information on the functional form of the unknown wall heat flux is needed in the inverse method. The effects of the functional form of the wall heat flux, the number of the measurement points, and the measurement errors on the accuracy of the estimation are investigated. It is shown that the reconstruction of the timewise and spatial variations of the wall heat flux is satisfactory even if the estimated function is not smooth. [S0022-1481(00)01003-3]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1999;122(3):465-475. doi:10.1115/1.1287502.

Heat transfer and pressure drop characteristics of water flow in horizontal tubes with/without longitudinal inserts used as a heat exchanger tubing was experimentally studied. Testing was performed on bare tubes and tubes with square and rectangular as well as crossed-strip inserts with aspect ratios AR=1 and 4 and varied ratios of inlet mixed mean temperature to wall temperature of 0.88 to 0.97. The Reynolds number ranged from approximately 250 to 1750 for flow visualization and from 1700 to 4000 for the pressure drop and heat transfer measurements. Flow visualization, using a dye injection method, revealed a highly complex flow pattern including a secondary flow formed in the cross section for crossed-strip inserts. The thermal entrance length was found and correlated in terms of Re for this type of inserted tubes. The enhancement of heat transfer as compared to a conventional bare tube at the same Reynolds number based on the hydraulic diameter was found to be about a factor of 16 at Re≤4000, while the friction factor rise was only about a factor of 4.5 at Re≤4000. [S0022-1481(00)01303-7]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Natural and Mixed Convection

J. Heat Transfer. 2000;122(3):476-484. doi:10.1115/1.1286995.

Similarity solution for the problem of hydrodynamic dispersion in mixed convection heat and mass transfer from vertical surface embedded in porous media has been presented. The flow induced by the density variations is comparable with the freestream flow. The heat and mass transfer in the boundary layer region for aiding and opposing buoyancies in both aiding and opposing flows has been analyzed. The structure of the flow, temperature, and concentration fields in the Darcy and non-Darcy porous media are governed by complex interactions among the diffusion rate (Le) and buoyancy ratio (N) in addition to the flow driving parameter (Ra/Pe). The flow, temperature, and concentration fields are analyzed and the variation of heat and mass transfer coefficients with the governing parameters are presented. [S0022-1481(00)00703-9]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):485-491. doi:10.1115/1.1288707.

A numerical study of natural convection in an isosceles triangular enclosure with a heated horizontal base and cooled upper walls is presented. Nearly every previous study conducted on this subject to date has assumed that the geometric plane of symmetry is also a plane of symmetry for the flow. This problem is re-examined over aspect ratios ranging from 0.2 to 1.0 and Grashof numbers from 103 to 105. It is found that a pitchfork bifurcation occurs at a critical Grashof number for each of the aspect ratios considered, above which the symmetric solutions are unstable to finite perturbations and asymmetric solutions are instead obtained. Results are presented detailing the occurrence of the pitchfork bifurcation in each of the aspect ratios considered, and the resulting flow patterns are described. A flow visualization study is used to validate the numerical observations. Computed local and mean heat transfer coefficients are also presented and compared with results obtained when flow symmetry is assumed. Differences in local values of the Nusselt number between asymmetric and symmetric solutions are found to be more than 500 percent due to the shifting of the buoyancy-driven cells. [S0022-1481(00)02503-2]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Radiative Transfer

J. Heat Transfer. 2000;122(3):492-502. doi:10.1115/1.1288774.

Inverse solution techniques are applied to the design of heat transfer systems where radiation is important. Various solutions using inverse methods are demonstrated, and it is argued that inverse design techniques provide an alternative to conventional iterative design methods that is more accurate and faster, and can provide a greatly improved first estimate of a thermal design. This estimate can then be used as a trial design in more complete thermal analysis programs for predicting system behavior, eliminating many faulty first design trials. [S0022-1481(00)02703-1]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):503-508. doi:10.1115/1.1287727.

A Monte Carlo technique follows radiation intensity rays through a dispersion of particles. Rays reflect from and are absorbed by the surfaces of the particles that they encounter. Transmitted radiative fluxes are compared with Monte Carlo simulations of a radiative continuum, using properties from both independent and correlated scattering theories. Whereas both discontinuous (surface) and continuous representations of the medium yield similar results for high porosities (low volume fractions), the continuous representation yields transmission overpredictions for porosities less than 0.9, using independent scattering properties, and for porosities less than 0.7, using correlated scattering properties. The overprediction is less severe for less reflective particle surfaces. [S0022-1481(00)01603-0]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Boiling and Condensation

J. Heat Transfer. 2000;122(3):509-516. doi:10.1115/1.1288708.

The present research is an experimental study of “double enhancement” behavior in pool boiling from heater surfaces simulating microelectronic devices immersed in saturated FC-72 at atmospheric pressure. The term “double enhancement” refers to the combination of two different enhancement techniques: a large-scale area enhancement (square pin fin array) and a small-scale surface enhancement (microporous coating). Fin lengths were varied from 0 (flat surface) to 8 mm. Effects of this double enhancement technique on critical heat flux (CHF) and nucleate boiling heat transfer in the horizontal orientation (fins are vertical) are investigated. Results showed significant increases in nucleate boiling heat transfer coefficients with the application of the microporous coating to the heater surfaces. CHF was found to be relatively insensitive to surface microstructure for the finned surfaces except in the case of the surface with 8-mm-long fins. The nucleate boiling and CHF behavior has been found to be the result of multiple, counteracting mechanisms: surface area enhancement, fin efficiency, surface microstructure (active nucleation site density), vapor bubble departure resistance, and re-wetting liquid flow resistance. [S0022-1481(00)02603-7]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Combustion

J. Heat Transfer. 2000;122(3):517-524. doi:10.1115/1.1288025.

Nonintrusive measurements of the optical properties of soot at visible wavelengths (351.2–800.0 nm) were completed for soot in the overfire region of large (2–7 kW) buoyant turbulent diffusion flames burning in still air at standard temperature and pressure, where soot properties are independent of position and characteristic flame residence time for a particular fuel. Soot from flames fueled with gaseous (acetylene, ethylene, propylene, and butadiene) and liquid (benzene, cyclohexane, toluene, and n-heptane) hydrocarbon fuels were studied. Scattering and extinction measurements were interpreted to find soot optical properties using the Rayleigh-Debye-Gans/polydisperse-fractal-aggregate theory after establishing that this theory provided good predictions of scattering patterns over the present test range. Effects of fuel type on soot optical properties were comparable to experimental uncertainties. Dimensionless extinction coefficients were relatively independent of wavelength for wavelengths of 400–800 nm and yielded a mean value of 8.4 in good agreement with earlier measurements. Present measurements of the refractive index function for absorption, E(m), were in good agreement with earlier independent measurements of Dalzell and Sarofim and Stagg and Charalampopoulos. Present values of the refractive index function for scattering, F(m), however, only agreed with these earlier measurements for wavelengths of 400–550 nm but otherwise increased with increasing wavelength more rapidly than the rest. The comparison between present and earlier measurements of the real and imaginary parts of the complex refractive index was similar to E(m) and F(m).[S0022-1481(00)02203-9]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Heat Pipes

J. Heat Transfer. 2000;122(3):525-535. doi:10.1115/1.1287725.

This work presents an experimental investigation of the thermal performance of a flat-plate heat pipe during startup and shutdown operations. Using the analytical model developed in a previously study, analytical and experimental results on the effect of input power and cooling heat transfer coefficient on the thermal performance of the heat pipe are presented and discussed. The results indicate that the wick in the evaporator section provides the largest resistance to the heat transfer process followed by the wick in the condenser section. It is found that the heat transfer coefficient has an insignificant effect on the maximum temperature difference across the heat pipe where this difference refers to the maximum difference on the outside surfaces of the flat-plate heat pipe. However, as expected, the input heat flux has a substantial effect on the temperature rise where the temperature rise refers to the temperature increase on the outside surface of the heat pipe. It is found that the temperature difference across the heat pipe depends mainly on the input power. The heat transfer coefficient strongly affects the time it takes to reach steady state while input power has a substantially smaller effect. Empirical correlations for the maximum temperature rise, the maximum temperature difference and the time constants are obtained. The experimental results are compared with the analytical results and are found to be in very good agreement. [S0022-1481(00)01803-X]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Microscale Heat Transfer

J. Heat Transfer. 2000;122(3):536-543. doi:10.1115/1.1288405.

This study uses the molecular dynamics computational technique to investigate the thermal conductivity of solid thin films in the direction perpendicular to the film plane. In order to establish a benchmark reference, the computations are based on the widely used Lennard-Jones argon model due to its agreement with experimental liquid-phase data, its physically meaningful parameters, and its simple two-body form. Thermal conductivity increases with film thickness, as expected from thin-film experimental data and theoretical predictions. The calculated values are roughly 30 percent higher than anticipated. Varying the boundary conditions, heat flux, and lateral dimensions of the films causes no observable change in the thermal conductivity values. The present study also delineates the conditions necessary for meaningful thermal conductivity calculations and offers recommendations for efficient simulations. This work shows that molecular dynamics, applied under the correct conditions, is a viable tool for calculating the thermal conductivity of solid thin films. More generally, it demonstrates the potential of molecular dynamics for ascertaining microscale thermophysical properties in complex structures. [S0022-1481(00)02303-3]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):544-556. doi:10.1115/1.1287587.

The basic problem of the impact and solidification of molten droplets on a substrate is of central importance to a host of processes. An important and novel such process in the area of micromanufacturing is solder jetting where microscopic solder droplets are dispensed for the attachment of microelectronic components. Despite the recent appearance of a few numerical studies focusing on the complex transient aspects of this process, no analogous experimental results have been reported to date to the best of our knowledge. Such a study is reported in this paper. Eutectic solder (63Sn37Pb) was melted to a preset superheat and used in a specially designed droplet generator to produce droplets with diameters in the range 50–100 μm. In a first series of experiments, the size, temperature, and impacting speed of the molten droplets were maintained constant. The primary variable was the temperature of the substrate that was controlled in the range from 48°C to 135°C. The dynamics of molten solder microdroplet impact and solidification on the substrate was investigated using a flash microscopy technique. The time for the completion of solidification from the moment of a solder droplet impact on the substrate varies between 150 μs and 350 μs. The dynamic interaction between the oscillation in the liquid region and the rapid advance of the solidification front was visualized, quantified, and presented in this paper. In a second series of experiments, the evolution of the wetting angle between the spreading drop and the substrate was recorded and analyzed. No quantitative agreement with Hoffman’s correlation for wetting was found. It was established that the wetting angle dynamics is strongly coupled with the evolution of the droplet free surface. Two successive regimes were distinguished during the spreading. The influence of the initial impact velocity and substrate temperature on the dynamics of the measured wetting angle was described in both regimes. To the best of our knowledge, this study presents the first published experimental results on the transient fluid dynamics and solidification of molten microdroplets impacting on a substrate at the above-mentioned time and length scales that are directly relevant to the novel solder jetting technology. [S0022-1481(00)01403-1]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Porous Media, Particles, and Droplets

J. Heat Transfer. 2000;122(3):557-565. doi:10.1115/1.1287793.

This paper reports an experimental and numerical study of forced convection in high porosity (ε∼0.89–0.97) metal foams. Experiments have been conducted with aluminum metal foams in a variety of porosities and pore densities using air as the fluid medium. Nusselt number data has been obtained as a function of the pore Reynolds number. In the numerical study, a semi-empirical volume-averaged form of the governing equations is used. The velocity profile is obtained by adapting an exact solution to the momentum equation. The energy transport is modeled without invoking the assumption of local thermal equilibrium. Models for the thermal dispersion conductivity, kd, and the interstitial heat transfer coefficient, hsf, are postulated based on physical arguments. The empirical constants in these models are determined by matching the numerical results with the experimental data obtained in this study as well as those in the open literature. Excellent agreement is achieved in the entire range of the parameters studied, indicating that the proposed treatment is sufficient to model forced convection in metal foams for most practical applications. [S0022-1481(00)01903-4]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Heat Exchangers

J. Heat Transfer. 2000;122(3):566-571. doi:10.1115/1.1287159.

Multipass heat exchangers are often designed by using the rule of thumb FT≥0.75, which is rather arbitrary. FT falls sharply with the increase in temperature cross. Hence, only a limited temperature cross can be allowed. The ability to accommodate temperature cross increases rapidly as the number of shell passes is increased. Though many investigators have emphasized the importance of temperature cross in exchanger design, it has as yet not been explicitly accounted for in the design. This paper introduces a new approach for estimating the number shells in a shell and tube exchanger which directly accounts for temperature cross, rather than routing this effect through FT or XP (Ahmad et al.’s parameter, which is again a correction factor not directly related to temperature cross). The approach is compatible with the established design procedures and bypasses the FT. It generates better designs by defining maximum permissible temperature cross, than the traditional designs based on specifying minimum permissible FT. Expressions have also been provided which correlate the present formulation with that of Ahmad et al. [S0022-1481(00)00803-3]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):572-578. doi:10.1115/1.1287170.

The present experimental study investigates the impact of porous fins on the pressure drop and heat transfer characteristics in plate-fin heat exchangers. Systematic experiments have been carried out in a simplified model of a plate-porous fin heat exchanger at a controlled test environment. The porous fins are made of 6101 aluminum-alloy foam materials with different permeabilities and porosities. Comparison of performance between the porous fins and the conventional louvered fins has been made. The experimental results indicate that friction and heat transfer rate are significantly affected by permeability as well as porosity of the porous fin. The porous fins used in the present study show similar thermal performance to the conventional louvered fin. However, the louvered fin shows a little better performance in terms of pressure drop. For compactness of the heat exchanger, the porous fins with high pore density and low porosity are preferable. Useful correlations for the friction factor and the modified j-factor are also given for the design of a plate-porous fin heat exchanger. [S0022-1481(00)01103-8]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):579-586. doi:10.1115/1.1287588.

Matrix heat exchangers are used in a number of applications such as helium liquefiers, sorption refrigerators, and in Kleemenko cryocoolers. In this paper the methods for the optimum sizing of balanced flow and unbalanced flow matrix heat exchangers of rectangular and circular shapes are presented. Using the methods developed, the relative size of matrix heat exchangers of rectangular and circular shapes are compared. [S0022-1481(00)01503-6]

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Heat Transfer Enhancement

J. Heat Transfer. 2000;122(3):587-597. doi:10.1115/1.1289020.

Detailed heat transfer distributions are presented inside a two-pass coolant channel with crossflow-induced swirl and impingement. The impingement and passage crossflow are generated from one coolant passage to the adjoining coolant passage through a series of straight or angled holes along the dividing wall. The holes provide for the flow turning from one passage to another typically achieved in a conventional design by a 180-deg U-bend. The holes direct the flow laterally from one passage to another and generate different secondary flow patterns in the second pass. These secondary flows produce impingement and swirl and lead to higher heat transfer enhancement. Three different lateral hole configurations are tested for three Reynolds numbers (Re=10,000, 25,000, 50,000). The configurations were varied by angle of delivery and location on the divider wall. A transient liquid crystal technique is used to measure the detailed heat transfer coefficient distributions inside the passages. Results with the new crossflow feed system are compared with the results from the traditional 180-deg turn passage. Results show that the crossflow feed configurations produce significantly higher Nusselt numbers on the second pass walls without affecting the first pass heat transfer levels. The heat transfer enhancement is as high as seven to eight times greater than obtained in the second pass for a channel with a 180-deg turn. The increased measured pressure drop (rise in friction factor) caused by flow through the crossflow holes are compensated by the significant heat transfer enhancement obtained by the new configuration. [S0022-1481(00)03103-0]

Commentary by Dr. Valentin Fuster

TECHNICAL NOTES

J. Heat Transfer. 2000;122(3):598-601. doi:10.1115/1.1286673.

This study deals with the numerical analysis of transient heat and species transfer by natural convection in a binary fluid vertical layer. The cavity is differentially heated and a solutal buoyancy force is created by imposing a concentration step at one vertical wall: This refers to the experimental situation where the composition gradient inducing the solutal buoyancy force is created by melting of pure ice in a salty solution. The constitution of the flow structure and the time evolution of the heat and mass transfer characteristics are studied for opposing body forces over a range of thermal and solutal Rayleigh numbers. The numerical results allow to provide a better insight into the mechanisms driving the heat and species transfer at high Lewis number thermohaline convection. [S0022-1481(00)00303-0]

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2000;122(3):602-605. doi:10.1115/1.1286816.

Etherington, H., 1958, Nuclear Engineering Handbook, McGraw-Hill, New York.Lighthill,  M. J., 1953, “ Theoretical Considerations on Free Convection in Tubes,” Q. J. Mech. Appl. Math., QJMMAV6, Part 5, pp. 398–439.Wilkes,  J. O., and Churchill,  S. W., 1966, “ The Finite Difference Computation of Natural Convection in a Rectangular Enclosure,” AIChE J., AICEAC12, No. 1, pp. 161–166.Eckert,  E. R. G., and Carlson,  W. O., 1961, “ Natural Convection in an Air Layer Enclosed Between Two Vertical Plates With Different Temperatures,” Int. J. Heat Mass Transf., IJHMAK2, pp. 106–120.Elder,  W. J., 1965, “ Laminar Free Convection in a Vertical Slot,” J. Fluid Mech., JFLSA723, pp. 77–98.Polezhaev  V. I., 1967, “ Numerical Solution of a System of Two Dimensional Unsteady Navier-Stokes Equations for a Compressible Gas in a Closed Region,” Fluid Dyn., FLDYAH2, pp. 70–74.Catton,  I., Ayyaswamy,  P. S., and Clever,  R. M., 1974, “ Natural Convection Flow in a Finite, Rectangular Slot Arbitrarily Oriented With Respect to the Gravity Vector,” Int. J. Heat Mass Transf., IJHMAK17, pp. 173–184.Mallinson,  G. D., and de Vahl Davis,  G., 1977, “ Three Dimensional Natural Convection in a Box: A Numerical Study,” J. Fluid Mech., JFLSA783, 1–31.Jones, I. P., 1982, “Low Prandtl Number Free Convection in a Vertical Slot,” AERE Harewell Report R-10416.Hadid, H. B., and Roux, B., 1987, “Oscillatory Buoyancy Driven Flow in a Horizontal Liquid Metal Layer,” ESA-SP-256, pp. 477–485.Hall,  J. D., Bejan,  A., and Chaddock,  J. B., 1988, “ Transient Natural Convection in a Rectangular Enclosure With One Heated Side Wall,” Int. J. Heat Mass Transf., IJHMAK9, pp. 396–404.Nicolette,  V. F., Yang,  K. T., and Lloyd,  J. R., 1985, “ Transient Cooling by Natural Convection in Two-dimensional Square Enclosure,” Int. J. Heat Mass Transf., IJHMAK28, pp. 1721–1732.Jones,  D. N., and Briggs,  D. G., 1989, “ Periodic Two-Dimensional Cavity Flow: Effect of Linear Horizontal Thermal Boundary Condition,” ASME J. Heat Transfer, JHTRAO111, pp 86–91.Kazmierczak,  M., and Chinoda,  Z., 1992, “ Buoyancy Driven Flow in an Enclosure With Time Periodic Boundary Conditions,” Int. J. Heat Mass Transf., IJHMAK35, No. 6, pp. 1507–1518.Kwak,  H. S., and Hyun,  J. M., 1996, “ Natural Convection in an Enclosure Having a Vertical Side Wall With Time Varying Temperature,” J. Fluid Mech., JFLSA7329, pp. 65–88.Bergman,  T. L., and Hyun,  M. T., 1996, “ Simulation of Two-Dimensional Thermosolutal Convection in Liquid Metals Induced by Horizontal Temperature and Species Gradients,” Int. J. Heat Mass Transf., IJHMAK39, No. 12, pp. 2883–2894.Aydin,  O., Unal,  A., and Ayhan,  T., 1999, “ Natural Convection in Rectangular Enclosures Heated From One Side and Cooled From the Ceiling,” Int. J. Heat Mass Transf., IJHMAK42, pp. 2345–2355.Fumizawa,  M., 1980, “ Natural Convection Experiment With Liquid NaK Under Transverse Magnetic Field,” J. Nucl. Sci. Technol., JNSTAX17, No. 2, pp. 98–105.Okada,  K., and Ozoe,  H., 1992, “ Experimental Heat Transfer Rates of Natural Convection of Molten Gallium Suppressed Under an External Magnetic Field in Either x, y or z-direction,” ASME J. Heat Transfer, JHTRAO114, pp. 107–114.Tagawa,  T., and Ozoe,  H., 1997, “ Enhancement of Heat Transfer Rate by Application of a Static Magnetic Field During Natural Convection of Liquid Metal in Cube,” ASME J. Heat Transfer, JHTRAO119, pp. 265–271.Mobner,  R., and Muller,  U., 1999, “ A Numerical Investigation of Three-Dimensional Magnetoconvection in Rectangular Cavities,” Int. J. Heat Mass Transf., IJHMAK42, pp. 1111–1121.Bejan, A., 1984, Convection Heat Transfer, Wiley, New York.Gebhart, B., Jalurial, Y., Mahajan, R. L., and Sammakia, B., 1988, Buoyancy Induced Flows and Transports, Hemisphere, Washington, DC.Alchaar,  S., Vasseur,  P., and Bilgen,  E., 1995, “ Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field,” ASME J. Heat Transfer, JHTRAO117, pp. 668–673.Eckert,  E. R. G., Goldstein,  R. J., Ibele,  W. E., Patankar,  S. V., Simon,  T. W., Strykowski,  P. J., Tamma,  K. K., Kuehn,  T. H., Bar-Cohen,  A., Heberlein,  J. V. R., Davidson,  J. H., Bischof,  J., Kulacki,  F., and Kortshagen,  U., 1999, “ Heat Transfer—A Review of 1995 Literature,” Int. J. Heat Mass Transf., IJHMAK42, pp. 2717–2797.Lide, D. R., 1993, Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL.Hadid,  H. B., and Roux,  B., 1992, “ Buoyancy and Thermocapillary Driven Flows in Differentially Heated Cavities for Low Prandtl Number Fluids,” J. Fluid Mech., JFLSA7235, pp. 1–36.Rudraiah,  N., Venkatachalappa,  M., and Subbaraya,  C. K., 1995, “ Combined Surface Tension and Buoyancy Driven Convection in a Rectangular Open Cavity in the Presence of a Magnetic Field,” Int. J. Non-Linear Mech., IJNMAG35, pp. 759–770.Jones,  G. F., and Cai,  J., 1993, “ Analysis of a Transient Asymmetrically Heated/Cooled Open Thermosyphon,” ASME J. Heat Transfer, JHTRAO115, p. 621.Jaluria, M., and Torrance, K. E., 1986, Computational Heat Transfer, Hemisphere, pp. 178–183.Jakob, M., 1949, Heat Transfer, Vol. 1, John Wiley and Sons, New York.

J. Heat Transfer. 2000;122(3):606-612. doi:10.1115/1.1286672.

An approximate solution is presented for a class of radiative heat transfer problems within enclosures having black or diffuse-gray surfaces based on a modified Taylor series expansion method; such radiative transfer problems are generally represented by integral equations. The approach avoids use of any boundary/initial conditions associated with the original Taylor series expansion method and leads to an approximate solution in a simple closed form to the radiant integral equations, which can be computed straightforwardly on a modern personal computer using symbolic computing codes such as Maple. The method can be effectively and efficiently applied to deal with enclosures involving more than one or two surfaces, for which direct numerical integration may be subject to instability, or require an excessive amount of computation. The computed numerical results for representative thermal problems are in excellent agreement with those obtained by other numerical approaches. [S0022-1481(00)00203-6]

J. Heat Transfer. 2000;122(3):613-620. doi:10.1115/1.1286817.

An analytical model to predict condensation heat transfer coefficient in a horizontal rectangular channel was developed. The total local condensation heat transfer coefficient was represented as the weighted average of heat transfer coefficients for each wall. The analytical predictions compared well with the experimental data on the condensation of R-410A in a rectangular channel. The mean deviation was 6.75 percent. [S0022-1481(00)00503-X]

J. Heat Transfer. 2000;122(3):620-625. doi:10.1115/1.1286818.

Results are presented for new experimental data for subcooled flow boiling heat transfer in circumferentially nonuniform (single-side) and uniformly heated tubes. Although the Liu-Winterton correlation had better agreement at low power levels and axial locations, Shah’s correlation had better agreement at higher power levels and at axial locations near the center of the heated length. Both correlations overpredicted the data near the exit. Therefore, additional correlational developmental work is needed for local (axial) flow boiling heat transfer in circumferentially nonuniform heated channels. [S0022-1481(00)00603-4]

J. Heat Transfer. 2000;122(3):626-631. doi:10.1115/1.1286681.

Experiments on welding dissimilar metals, such as aluminum or copper to iron with an electron-beam welder, are conducted. It is found that the observed depth-to-width ratio of the fusion zone in aluminum can be greater than unity while that in iron is around unity. The former is attributed to the formation of a cavity resulting from a high vapor pressure. The difference in depths increases with beam power. The observed depth-to-width ratios of fusion zones in welding copper to iron can be greater than unity. A unique maximum depth is near the joint plane, as a result of strong convective mixing and high incident flux, even though the melting temperatures are different. Strong mixing is confirmed by measured concentration profiles across the fusion zones of dissimilar metals. To a first approximation fusion zone depths with depth-to-width ratios greater than or identical to unity are determined from scale analyses of heat conduction equations in welding the same metals with a high and low-power-density beam, respectively. The propositions are verified by experimental results. [S0022-1481(00)00103-1]

DISCUSSION

J. Heat Transfer. 2000;122(3):632-633. doi:10.1115/1.1289648.
FREE TO VIEW

Kuznetsov,  A. V., 1999, “ Fluid Mechanics and Heat Transfer in the Interface Region Between a Porous Medium and a Fluid Layer: A Boundary Layer Solution,” J. Porous Media, JPMEFB2, pp. 309–321.JPMEFB1091-028XCheng,  P., and Hsu,  C. T., 1986, “ Applications of Van Driest’s Mixing Length Theory to Transverse Thermal Dispersion in Forced Convective Flow Through a Packed Bed,” Int. Commun. Heat Mass Transfer, IHMTDL13, pp. 613–625.8voIHMTDL0735-1933Hunt,  M. L., and Tien,  C. L., 1988, “ Effects of Thermal Dispersion on Forced Convection in Fibrous Media,” Int. J. Heat Mass Transf., IJHMAK31, pp. 301–309.ijhIJHMAK0017-9310

Commentary by Dr. Valentin Fuster

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