J. Heat Transfer. 2004;126(5):669. doi:10.1115/1.1804203.
Topics: Heat transfer
Commentary by Dr. Valentin Fuster


J. Heat Transfer. 2004;126(5):670-675. doi:10.1115/1.1798913.

It is demonstrated by a concise standard derivation, motivated by principles of rational continuum mechanics and irreversible thermodynamics augmented by novel detailed examples, that for heat conduction in linearly anisotropic solids: (1) common restrictions placed on the form of the thermal conductivity tensor are insufficient to guarantee satisfaction of the second law of thermodynamics, and (2) satisfaction of the first and second laws of thermodynamics alone is still insufficient to insure agreement between heat flow predictions and observation. An additional constraint beyond that given in many standard studies, namely that all three principal invariants of the conductivity tensor be positive semi-definite, is imposed in order to guarantee satisfaction of the entropy inequality. Thus constrained, such a theory remains under-restricted and can admit purely cyclic heat fluxes, which are not observed in nature. Imposition of the conjectures of Duhamel and Stokes, which are in fact earlier specific incarnations of Onsager’s reciprocity theory, on the constitutive model relating heat flux to temperature gradient is a sufficient remedy.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2004;126(5):676-686. doi:10.1115/1.1777586.

The paper presents accurate numerical solutions of the full two-dimensional governing equations for steady and unsteady laminar/laminar internal condensing flows. The results relate to issues of better design and integration of condenser-sections in thermal management systems (looped heat pipes, etc.). The flow geometry, in normal or zero gravity, is chosen to be the inside of a channel with film condensation on one of the walls. In normal gravity, film condensation is on the bottom wall of a tilted (from vertical to horizontal) channel. It is found that it is important to know whether the exit conditions are constrained or unconstrained because nearly incompressible vapor flows occur only for exit conditions that are unconstrained. For the incompressible vapor flow situations, a method for computationally obtaining the requisite exit condition and associated stable steady/quasi-steady solutions is given here and the resulting solutions are shown to be in good agreement with some relevant experimental data for horizontal channels. These solutions are shown to be sensitive to the frequency and amplitude of the various Fourier components that represent the ever-present and minuscule transverse vibrations (standing waves) of the condensing surface. Compared to a vertical channel in normal gravity, shear driven zero gravity cases have much larger pressure drops, much slower wave speeds, much larger noise sensitive wave amplitudes that are controlled by surface tension, and narrower flow regime boundaries within which vapor flow can be considered incompressible. It is shown that significant enhancement in wave-energy and/or heat-transfer rates, if desired, are possible by designing the condensing surface noise to be in resonance with the intrinsic waves.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):687-696. doi:10.1115/1.1795240.

This paper presents a study of pressure drops during condensation inside a smooth, an 18-deg helical microfin, and a herringbone microfin tube. Measurements were conducted with refrigerant flowing through the tube of a concentric heat exchanger, with water flowing in a counterflow direction in the annulus. Each tube was part of a condenser consisting of eight subcondensers with instrumentation preceding each subcondenser. Three refrigerants were used, namely, R-22, R-407C, and R-134a, all operating at a saturation temperature of 40 °C with mass fluxes ranging from 400 to 800 kg/m2 s. Inlet qualities ranged from 0.85 to 0.95 and outlet qualities ranged from 0.05 to 0.15. The test results showed that on average for the three refrigerants the pressure gradients of the herringbone microfin tube were about 79% higher than that of the smooth tube and about 27% higher than that of the helical microfin tube. Further, a correlation from the literature for predicting pressure drops inside a helical microfin tube was modified for the herringbone microfin tube. The modified correlation predicted the data to within an error of 1% and had an absolute mean deviation of 6.8%. This modified correlation compared well with a correlation from the literature that predicted the data to within an error of 7%.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Forced Convection

J. Heat Transfer. 2004;126(5):697-707. doi:10.1115/1.1798971.

In this paper, a numerical investigation of air side performance of strip fin surface is presented. Three-dimensional numerical computation was made for a model of a two-row finned tube heat exchanger. The tube configuration is simulated with step-wise approximation, and the fin efficiency is also calculated with conjugated computation. Four types of fin surfaces were studied: A-the whole plain plate fin; B-the strip fin with strips located in the upstream part of the fin; C-the strip fin with strips located in the downstream part of the fin; and D-the strip fin with strips covering the whole fin surface. It is found that the strip fin with strips located in the downstream part of the fin surface (fin C) has higher heat transfer rate than that with strips in the upstream part (fin B) at the same conditions, while the pressure drop of fin C is a bit lower than that of fin B. A comprehensive performance comparison was conducted by using the goodness factor and the pumping power consumption per unit surface area. It is revealed that between the two strip fins the performance of fin C is better than fin B with same strip number. Detailed discussion is provided from the view point of synergy between velocity and temperature gradient. It is shown that the synergy between velocity and temperature field becomes worse in the downstream part of the fin surface, and it is this place that enhancement technique is highly needed. The strip location of fin C just fits this situation. The present numerical work provides useful information on where the enhancement element should be positioned.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Heat and Mass Transfer

J. Heat Transfer. 2004;126(5):708-712. doi:10.1115/1.1795791.

The objective of this paper is to provide optimization of falling film LiBr solution on a horizontal single tube based on minimization of entropy generation. Flow regime is considered to be laminar. The effect of boiling has been ignored and wall temperature is constant. Velocity, temperature and concentration distributions are numerically determined and dimensionless correlations are obtained to predict the average heat transfer coefficient and average evaporation factor on the horizontal tube. Thermodynamic imperfection due to passing lithium bromide solution is attributed to nonisothermal heat transfer; fluid flow friction and mass transfer irreversibility. Scale analysis shows that the momentum and mass transfer irreversibilities can be ignored at the expense of heat transfer irreversibility. In the process of optimization, for a specified evaporation heat flux, the entropy generation accompanying the developed dimensionless heat and mass transfer correlations has been minimized and the optimal geometry and the optimum thermal hydraulic parameters are revealed. The investigation cited here indicates the promise of entropy generation minimization as an efficient design and optimization tool.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Heat Transfer in Manufacturing

J. Heat Transfer. 2004;126(5):713-722. doi:10.1115/1.1795237.

This paper presents a complete two-dimensional (2D) thermofluid model for predicting the neck-down shape in the fiber drawing process. This model uses the controlled draw tension to calculate the Neumann boundary condition at the furnace exit; thus, it does not require specifying the speed (or diameter) of the fiber as most previous studies did. The model presented here can be applied to optimization of the high-speed draw process with large-diameter preforms. In this study, the radiative transfer equation is directly solved for the radiation fluxes using the discrete ordinate method coupled with the solution of the free surface flow, which does not assume that the glass is optically thick and does not neglect the glass absorption at the short-wavelength band. The artificial compressibility method is used to solve the Navier-Stokes equations. A staggered-grid computation scheme that is shown to be efficient and robust was used to reduce the computation load in solving the complete 2D model. The neck-down profile of a large preform (9 cm dia) drawn at a relatively high speed of 25 m/s was experimentally measured. The measured profile well matches that derived numerically. Results also show that the free surface calculated using the Dirichlet boundary condition deviates considerably from the measured profile, particularly near the furnace exit where the actual diameter (and, hence, the speed of the glass) is essentially unknown. Although the difference between the numerical results obtained from the full and semi-2D models was small, this difference could be significant if the location at which the glass converges to 125 μm dia is of interest, especially when the preform has a large diameter drawn at a high speed.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2004;126(5):723-726. doi:10.1115/1.1795224.

The ablation of crystalline silicon by ultrashort laser pulses is studied experimentally. A pump-and-probe experiment is implemented in a collinear arrangement, utilizing a time-delayed frequency-doubled probe beam for in situ reflectance measurement and ultrafast microscopy observation. Enhanced surface reflectivity in sub-picosecond time scale at the center of the irradiated spot indicates nonthermal liquid layer formation. A short-lived nonthermal liquid phase was detected at fluence of 1.5 J/cm2. In addition to this observation, the reflected images for pump beam fluences ranging from 1.5 to 4.6 J/cm2 provide evidence of plasma expansion above the irradiated target.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):727-734. doi:10.1115/1.1797011.

In this work, Molecular Dynamics (MD) simulation is employed to investigate femtosecond laser ablation of copper, with an emphasis on the understanding of the mechanism of phase change during laser ablation. Laser induced heat transfer, melting, surface evaporation, and material ablation are studied. Theoretically, it has been suggested that under intense femtosecond laser irradiation, the material undergoes a volumetric phase change process; its maximum temperature can be close to or even above the thermodynamic critical point. The MD simulations allow us to determine the transient temperature history of the irradiated material and to reveal the exact phase change process, which explains the mechanisms of femtosecond laser ablation. A finite difference calculation is also performed, which is used to compare results of heating and melting prior to a significant amount of material being ablated.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):735-743. doi:10.1115/1.1795233.

This paper presents a new numerical scheme for simulating multidimensional transient and steady-state microscale energy transport. The new method is based on the method of characteristics that follows heat carriers along their pathline. Unlike traditional methods, it uses a fixed computational grid and follows the heat carriers backward in time. The method 1) is accurate, 2) is unconditionally stable, 3) can deal with complex geometries without a large increase in computational cost, and 4) can be used for solving coupled equations using other numerical schemes. First, the numerical scheme is described. Then, simulations for transient and steady-state phonon transport in dielectric thin films are discussed. Numerical results are compared with analytical and reported numerical solutions and good agreement is obtained.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):744-752. doi:10.1115/1.1795236.

Heat transfer through a fractal-like branching flow network is investigated using a three-dimensional computational fluid dynamics approach. Results are used for the purpose of assessing the validity of, and providing insight for improving, assumptions imposed in a previously developed one-dimensional model for predicting wall temperature distributions through fractal-like flow networks. As currently modeled, the one-dimensional code fairly well predicts the general wall temperature trend simulated by the three-dimensional model; hence, demonstrating its suitability as a tool for design of fractal-like flow networks. Due to the asymmetry in the branching flow network, wall temperature distributions for the proposed branching flow network are found to vary with flow path and between the various walls forming the channel network. Three-dimensional temperature distributions along the various walls in the branching channel network are compared to those along a straight channel. Surface temperature distributions on a heat sink with a branching flow network and a heat sink with a series of straight, parallel channels are also analyzed and compared. For the same observed maximum surface temperature on these two heat sinks, a lower temperature variation is noted for the fractal-like heat sink.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):753-763. doi:10.1115/1.1797036.

This paper presents an experimental investigation of laminar gas flow through microchannels. The independent variables: relative surface roughness, Knudsen number and Mach number were systematically varied to determine their influence on the friction factor. The microchannels were etched into silicon wafers, capped with glass, and have hydraulic diameters between 5 and 96 μm. The pressure was measured at seven locations along the channel length to determine local values of Knudsen number, Mach number and friction factor. All measurements were made in the laminar flow regime with Reynolds numbers ranging from 0.1 to 1000. The results show close agreement for the friction factor in the limiting case of low Ma and low Kn with the incompressible continuum flow theory. The effect of compressibility is observed to have a mild (8 percent) increase in the friction factor as the Mach number approaches 0.35. A 50 percent decrease in the friction factor was seen as the Knudsen number was increased to 0.15. Finally, the influence of surface roughness on the friction factor was shown to be insignificant for both continuum and slip flow regimes.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Natural and Mixed Convection

J. Heat Transfer. 2004;126(5):764-775. doi:10.1115/1.1795232.

A systematic numerical study has been conducted of the mixed convection flow in a novel impinging jet chemical vapor deposition (CVD) reactor for deposition of thin films at atmospheric pressure. The geometry resembles that of a pancake reactor but the inflow gases enter through a small nozzle to provide high inlet momentum. A finite-volume-based computational procedure is used to integrate the governing flow, energy, and scalar transport equations with high accuracy. The effects of the temperature dependent properties are fully accounted for. The effects of operating pressure, wafer rotation rate, and inlet flow rate of the carrier gas are investigated. The main benefit of the new geometry is the suppression of the buoyancy-driven flow even at atmospheric pressures due to the lower mixed convection parameter. We show that the new geometry can produce thin films of high radial uniformity and also with high growth rate. Comparisons are also made with a conventional stagnation flow reactor for which it is shown that beyond a moderate pressure (∼0.1 atm), the flow is dominated by natural convection, and the reactor is unsuitable for practical use.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):776-785. doi:10.1115/1.1795234.

Determining the temperature rise of contact interfaces subject to surface heating is essential to controlling thermally induced failures in manufacturing processes and tribology. This paper provides a summary of solutions to problems of a stationary/moving half-space or half-plane without/with surface convection. In the first two sections, basic formulations for bodies with negligible surface convection are grouped as explicitly and completely as possible in terms of the Green’s function, the influence coefficients, and the frequency response function. In the final section, the influence coefficients are applied to solve surface-heating problems with surface convection. The time required to reach approximately steady state is found for bodies subject to a unit heat flux. The effect of convection is found to be dependent on the Péclet number and location.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Radiative Heat Transfer

J. Heat Transfer. 2004;126(5):786-792. doi:10.1115/1.1795241.

Radiative properties have been studied for one-dimensional dielectric multilayer structures subjected to blackbody radiation sources. The total hemispherical transmittances are calculated for periodic structures and structures with random variation in layer thickness, using wave-optics and ray-tracing methods. Simulation results show that for periodic structures, the transmittance calculated using wave optics approaches a nonzero constant value with an increasing number of layers, while the transmittance obtained using the ray-tracing method asymptotically approaches zero. For random structures, the transmittance given by wave optics drops to zero at different rates depending on the order of random variations in layer thickness. It is found that the wave interference effect always plays a role when dealing with multilayer structures. The results are explained based on extended and localized waves.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):793-804. doi:10.1115/1.1795243.

Scattering theory for the scattering of phonons by particulate scatterers is developed in this paper. Recently the author introduced the generalized equation of phonon radiative transport (GEPRT) in particulate media, which included a phase function to account for the anisotropic scattering of phonons by particulate scatterer. Solution of the GEPRT showed that scattering cross section is different from the thermal transport cross-section. In this paper formulations for the scattering and transport cross section for horizontally shear (SH) wave phonon or transverse wave phonon without mode conversion is developed. The development of the theory of scattering and the transport cross section is exactly analogous to the Mie scattering theory for photon transport in particulate media. Results show that transport cross section is very different from the scattering cross section. The theory of phonon scattering developed in this paper will be useful for the predictive modeling of thermal conductivity of practical systems, such as nanocomposites, nano-micro-particle-laden systems, etc.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):805-808. doi:10.1115/1.1797034.

An integral relation is obtained between local temperature and local temperature gradient for the dual-lag model of heat transport, which substitutes classical Fourier law at short time scales. Both the heat flux lag and the temperature gradient lag are considered, however, it is shown that only difference between the two affects temperature profile. Being applied at exposed surface of material, the integral equation predicts surface temperature variation for any form of imposed heat flux. The solution is tested considering solid heating by a picosecond laser impulse. Results are compared with the classical solution of the parabolic heat transfer equation and available experimental data.

Commentary by Dr. Valentin Fuster


J. Heat Transfer. 2004;126(5):809-817. doi:10.1115/1.1795811.

Parameter estimation is based upon a comparison of predicted deterministic model responses to data. The models are often numerical, e.g., finite volume, with intrinsic inaccuracies. In addition, the models typically assume a full knowledge of the physical processes. By using the concept of state variables and employing the extended Kalman filter approach it is possible to include additional effects in the model to achieve better agreement between the model and the data. This paper describes such an approach to the estimation of thermal conductivity in a transiently heated and cooled one-dimensional system and shows that it leads to a resolution of questions about the time behavior of the residuals previously observed in an estimation based upon the least squares analysis.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):818-825. doi:10.1115/1.1795812.

Thermal analysis of laser densification of a dental porcelain powder bed has been investigated using a three-dimensional thermal finite element model, which encompasses (i) the incoming laser beam power with a Gaussian distribution, (ii) optical pyrometer simulation in addition to the closed-loop temperature control, (iii) powder-to-solid transition, (iv) temperature-dependent thermal convection, and (v) temperature and porosity-dependent thermal conduction and radiation. The simulation results are compared with the experiments. It is found that the predicted temperature distribution in the porcelain body matches the experiments very well. Further, the maximum discrepancy between experimental and simulated pyrometer temperatures is less than 8 percent. The simulation predicts that in order to achieve the desired microstructure of a dense dental porcelain body, the maximum local temperature during laser densification should be below 1573 K or the nominal surface temperature should be below 1273 K. Otherwise, the undesired microstructure (i.e., a leucite-free glass phase) forms.

Commentary by Dr. Valentin Fuster


J. Heat Transfer. 2004;126(5):826-835. doi:10.1115/1.1795239.

This paper presents the results of an experimental study of forced convection heat transfer in a narrow rectangular duct fitted with an elliptical tube and one or two delta-winglet pairs. The duct was designed to simulate a single passage in a fin-tube heat exchanger. Heat transfer measurements were obtained using a transient technique in which a heated airflow is suddenly introduced to the test section. High-resolution local fin-surface temperature distributions were obtained at several times after initiation of the transient using an imaging infrared camera. Corresponding local fin-surface heat transfer coefficients were then calculated from a locally applied one-dimensional semi-infinite inverse heat conduction model. Heat transfer results were obtained over a Reynolds number range based on duct height of 670–6300. Pressure-drop measurements have also been obtained for similar elliptical-tube and winglet geometries, using a separate single-channel, multiple-tube-row pressure-drop apparatus. The pressure-drop apparatus includes four tube rows in a staggered array. Comparisons of heat transfer and pressure-drop results for the elliptical tube versus a circular tube with and without winglets are provided. Mean heat transfer results indicated that the addition of the single winglet pair to the oval-tube geometry yielded significant heat transfer enhancement, averaging 38% higher than the oval-tube, no-winglet case. The corresponding increase in friction factor associated with the addition of the single winglet pair to the oval-tube geometry was very modest, less than 10% at ReDh=500 and less than 5% at ReDh=5000.

Commentary by Dr. Valentin Fuster


J. Heat Transfer. 2004;126(5):836-839. doi:10.1115/1.1795242.

Simulations of three-dimensional laminar forced convection in a plane symmetric sudden expansion are presented for Reynolds numbers where the flow is steady and symmetric. A swirling “jetlike” flow develops near the sidewalls in the separating shear layer, and its impingement on the stepped wall is responsible for the maximum that develops in the Nusselt number adjacent to the sidewalls and for the reverse flow that develops in that region. The maximum Nusselt number on the stepped wall is located inside the primary recirculation flow region and its location does not coincide with the jetlike flow impingement region. The results reveal that the location where the streamwise component of wall shear stress is zero on the stepped walls does not coincide with the outer edge of the primary recirculation flow region near the sidewalls.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):840-842. doi:10.1115/1.1800511.

This paper deals with heat transfer in fully developed laminar flow in cylindrical ducts. For this type of flow, the product of friction factor with Reynolds number f Re and the Nusselt number are both constants. It is known that the Nusselt number increases with the shift of boundary condition from constant wall temperature to constant heat flux. Also, the ratio of the Nusselt number to f Re increases when the convexity of the duct is reduced, e.g., a cylinder visavis parallel plates. This paper gives a simple physical explanation for these two phenomenona.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):843-848. doi:10.1115/1.1797032.

A numerical investigation of the temperature field in a turbulent flume is presented. We consider the effect of the Prandtl number on the convection velocity of temperature fluctuations in a turbulent boundary layer, and focus also on the effect of the Prandtl number on the connection between the velocity and the temperature fluctuations. Close to the wall, y+<2, convection velocities of the temperature fluctuations decrease with an increase in the Prandtl number, i.e., the scale dependence becomes significantly important. In the region y+<2 the relation of the convection velocity of the temperature fluctuation to that of the velocity fluctuation may be expressed as UcT+=Ucu+Pr−1/3 and Ucq+=Ucu+Pr−1/2 for isothermal and isoflux wall boundary condition, respectively.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):849-851. doi:10.1115/1.1795245.

Results of an experimental study of natural convection and surface radiation between three parallel vertical plates, symmetrically spaced, with air as the intervening medium are presented. The analysis consists of heating the central plate at different levels and recording the temperatures of both the central and the side plates at steady state conditions. Based on the measurements, a correlation for the maximum temperature excess of the “hot” plate in terms of the emissivity of the central and the side plates, the aspect ratio, and the dimensionless total heat flux is given, valid for a range of emissivity 0.05≤εc,εs≤0.85, aspect ratio 2.38≤A≤17, and total heat flux 32≤q≤1590 W/m2. Through this, the heat transfer enhancement due to radiation has been succinctly brought out.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):852-857. doi:10.1115/1.1795246.

The domain of operating conditions, in which the optical fiber-drawing process is successful, is an important consideration. Such a domain is mainly determined by the stresses acting on the fiber and by the stability of the process. This paper considers an electrical resistance furnace for fiber drawing and examines conditions for process feasibility. In actual practice, it is known that only certain ranges of furnace temperature and draw speed lead to successful fiber drawing. The results obtained here show that the length of the heated zone and the furnace temperature distribution are other important parameters that can be varied to obtain a feasible process. Physical behavior close to the boundary of the feasible domain is also studied. It is found that the iterative scheme for neck-down profile determination diverges rapidly when the draw temperature is lower than that at the acceptable domain boundary due to the lack of material flow. However, the divergence rate becomes much smaller as the temperature is brought close to the domain boundary. Additional information on the profile determination as one approaches the acceptable region is obtained. It is found that it is computationally expensive and time-consuming to locate the exact boundary of the feasible drawing domain. From the results obtained, along with practical considerations of material rupture, defect concentration, and flow instability, an optimum design of a fiber-drawing system can be obtained for the best fiber quality.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):858-861. doi:10.1115/1.1798951.

The importance of combined Lorentz-Doppler (or Voigt) broadening of spectral lines in high-temperature radiative heat transfer applications is investigated. Employing narrow-band transmissivities as the criterion, the critical total pressure below which, and the critical temperature above which Doppler broadening has a significant effect on the absorption coefficient is established for gaseous H2O and CO2.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):862-868. doi:10.1115/1.1798911.

An analytical method based on Frobenius power series expansion has been developed for the performance prediction of fully wet fins. Fins of different geometries, namely, longitudinal, annular and spine having both trapezoidal and triangular profiles have been considered. Unlike dry fins, the efficiency and effectiveness of wet fins depend on the fin base temperature and psychrometric condition of the ambient air. A generalized criterion has been derived for the optimization of wet fins having the above geometries. A method for constructing design curves for the optimum fins has also been discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(5):869-875. doi:10.1115/1.1800492.

In the present work, a computational model is developed to investigate and predict the thermal performance of high melting point phase change material during its melting and solidification processes within a cylindrical enclosure. In this model the phases are assumed to be homogeneous and a source term, S, arises from melting or solidification process is considered as a function of the latent heat of fusion and the liquid phase fraction. The numerical model is verified with a test problem and an experiment is performed to assess the validity of the assumptions of it and an agreement between experimental and computational results is achieved. The findings show that utilizing of PCMs of high melting points is a promising technique especially in space applications.

Commentary by Dr. Valentin Fuster

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