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Research Papers: Conduction

J. Heat Transfer. 2014;136(9):091301-091301-7. doi:10.1115/1.4027771.

Despite numerous studies of conjugate gradient methods (CGMs), the “sensitivity problem” and the “adjoint problem” are inevitable for nonlinear inverse heat conduction problems (IHCPs), which are accompanied by some assumptions and complicated differentiating processes. In this paper, a modified CGM (MCGM) is presented for the solution of a specified transient nonlinear IHCP, to recover temperature-dependent thermal conductivities for a case study. By introducing the complex-variable-differentiation method (CVDM) for sensitivity analysis, the sensitivity problem and the adjoint problem are circumvented. Five test examples are given to validate and assess the performance of the MCGM.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):091302-091302-9. doi:10.1115/1.4027770.

The paper presents a new approximate method of solving non-Fourier heat conduction problems. The approach described here is suitable for solving both direct and inverse problems. The way of generating Trefftz functions for non-Fourier heat conduction equation has been shown. Obtained functions have been used for solving direct and boundary inverse problems (identification of boundary condition). As a rule, inverse problems are ill-posed. Therefore, each method of solving these problems has to be checked according to disturbance of the input data. Presented examples confirm high usability of the presented approach for solving direct and inverse non-Fourier heat conduction problems.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):091303-091303-11. doi:10.1115/1.4027838.

The computation of the analytical solution of the steady temperature distribution in multilayered media can become numerically unstable if there are different longitudinal (i.e., the directions parallel to the layers) boundary conditions for each layer. In this study, we develop a method to resolve these computational difficulties by approximating the temperatures at the junctions step-by-step and solving for the thermal field separately in only the single layers. First, we solve a two-layer medium problem and then show that multilayered media can be represented as a hierarchy of two-layered media; thus, the developed method is generalized to an arbitrary number of layers. To improve the computational efficiency and speed, we use varying weighting coefficients during the iterations, and we present a method to decompose the multilayered media into two-layered media. The developed method involves the steady-state solution of the diffusion equation, which is illustrated for 2D slabs using separation of variables (SOV). A numerical example of four layers is also included, and the results are compared to a numerical solution.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2014;136(9):091501-091501-9. doi:10.1115/1.4027552.

A critical heat flux (CHF) correlation is developed for jet impingement boiling of a single round jet on a flat circular surface. The correlation is valid for submerged jets as well as for free surface jets with Reynolds numbers (Re) between 4000 and 60,000. Data for the correlation are obtained from an extensive experimental study of submerged jet impingement boiling performed by the authors with water at subatmospheric pressures and with FC-72 at atmospheric pressure. Additional experimental data from a free surface jet study are also incorporated to include the effect of variation in surface diameter relative to a fixed nozzle diameter, additional working fluids (water and R-113 both at atmospheric pressure), and jet configuration. The range of parameters considered include Re from 0 (pool boiling) to 60,000, jet diameter to capillary length scale ratios (dj/Lc) ranging from 0.44 to 5.50, surface diameter to capillary length scale ratios (ds/Lc) ranging from 4.47 to 38.42, and liquid-to-vapor density ratios from 119 to 8502. The proposed correlation is built on the framework of a forced convective CHF model. Using this correlation, 95% of the experimental CHF jet impingement data can be predicted within ±22% error. The corresponding average absolute error and the maximum absolute error are 8% and 36%, respectively, over the range of parameters considered.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2014;136(9):091701-091701-6. doi:10.1115/1.4027786.

This work is aimed at contributing to the thermal analysis of slip flow through circular microducts, providing an analytical solution to the energy conservation equation for partially heated walls. A uniform wall heat flux (H2 boundary conditions) is considered on the heated perimeter of the cross section while the remaining arc length is assumed to be adiabatic. The gaseous flow is considered laminar, fully developed, in steady state condition, and forced convection. The temperature profile, wall temperature distribution, and Nusselt number are presented as functions of both the heated perimeter of the cross section and the Knudsen number, resorting to simple converging series of trigonometric functions. The proposed solution can be useful for the design of the microfluidic devices such as micro heat sinks and micro heat exchangers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):091702-091702-7. doi:10.1115/1.4027863.

This paper presents results from theoretical and numerical studies of a single-phase, temperature sensitive magnetic fluid operating under steady-state laminar flow conditions in a partially heated thermomagnetic circulation loop under the influence of an external magnetic field (created by a solenoid). A one-dimensional theoretical model has been developed using scaling arguments to characterize thermomagnetic circulation in this loop in terms of the geometric length scales, magnetic fluid properties, and the strength of the imposed magnetic field. In parallel to this theoretical analysis, supporting numerical simulations using Comsol Multiphysics simulation software have been undertaken to obtain data for use in this 1D model. Comparison between experimental data and numerical simulation results and also a grid sensitivity analysis was carried out to validate the numerical simulation. A correlation for the nondimensional heat transfer (Nusselt number) as a function of the appropriate magnetic Rayleigh number and a correlation for the mass flow rate based on the system's properties are developed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):091703-091703-9. doi:10.1115/1.4027840.

This paper presents a computational fluid dynamics (CFD) methodology to accurately predict the heat transfer characteristics of an unconfined steady impinging air jet in the transitional flow regime, impinging on a planar constant-temperature surface. The CFD methodology is validated using detailed experimental measurements of the local surface heat transfer coefficient. The numerical model employs a transitional turbulence model which captures the laminar–turbulent transition in the wall jet which precisely predicts the intensity and extent of the secondary peak in the radial Nusselt number distribution. The paper proposes a computationally low-cost turbulence model which yields the most accurate results for a wide range of operating and geometrical conditions. A detailed analysis of the effect of mesh grid size and properties, inflow conditions, turbulence model, and turbulent Prandtl number Prt is presented. The numerical uncertainty is quantified by the grid convergence index (GCI) method. In the range of Reynolds number 6000 ≤ Re ≤ 14,000 and nozzle-to-surface distance 1 ≤ H/D ≤ 6, the model is in excellent agreement with the experimental data. For the case of H/D = 1 and Re = 14,000, the maximum deviations are 5%, 3%, and 2% in terms of local, area-averaged and stagnation point Nusselt numbers, respectively. Experimental and numerical correlations are presented for the stagnation point Nusselt number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):091704-091704-8. doi:10.1115/1.4027773.

This work numerically examined effects of nanofluids flow on heat transfer in a C-shaped geometry with the aim to evaluate potential advantages of using nanofluids in a chaotic flow. Numerical computations revealed that the combination of nanofluids and chaotic advection can be an effective way to improve thermal performance of laminar flows. The results indicated that addition of only 1–3% CuO or Al2O3 nanoparticles (volumetric concentration) to the chaotic flow improved heat transfer by 4–14% and 4–18%, respectively, with a marginal increase in the pressure drop.

Commentary by Dr. Valentin Fuster

Research Papers: Heat Transfer Enhancement

J. Heat Transfer. 2014;136(9):091901-091901-6. doi:10.1115/1.4027772.

Fins are essentially used in diverse engineering applications to increase the heat transfer between the hot and cold media. In this paper, a technique for computing the analytic approximate solution of the nonlinear differential equations resulting from heat transfer problems, in particular through fins, is developed. The simplicity of the approach presented here is due to its base functions, which makes this method straightforward to apply and formulate without any need for discretization. Analysis of the error and comparisons with the other methods are presented. A few physically interesting fin problems of heat transfer are treated to illustrate that the proposed algorithm generates highly accurate solutions.

Commentary by Dr. Valentin Fuster

Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2014;136(9):092401-092401-6. doi:10.1115/1.4027785.

It has recently been demonstrated that under certain conditions of electron nonequilibrium, electron to substrate energy coupling could represent a unique mechanism to enhance heat flow across interfaces. In this work, we present a coupled thermodynamic and quantum mechanical derivation of electron–phonon scattering at free electron metal/nonmetal substrate interfaces. A simplified approach to the Fermi's Golden Rule with electron energy transitions between only three energy levels is adopted to derive an electron–phonon diffuse mismatch model, that account for the electron–phonon thermal boundary conductance at metal/insulator interfaces increases with electron temperature. Our approach demonstrates that the metal-electron/nonmetal phonon conductance at interfaces can be an order of magnitude larger than purely phonon driven processes when the electrons are driven out of equilibrium with the phonons, consistent with recent experimental observations.

Commentary by Dr. Valentin Fuster

Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2014;136(9):092501-092501-9. doi:10.1115/1.4027781.

This paper reports the average Nusselt number for steady, laminar natural convection between a vertical surface and otherwise quiescent pseudoplastic and dilatant fluids under a constant and uniform surface heat flux boundary condition. Models for the fluids' apparent viscosity were utilized that are valid in all five regions of the flow curve. The results are thus applicable for whatever shear rates may exist within the flow field and a dimensionless shear rate parameter was identified that quantifies the shear rate region where the given system is operating. The data indicate that the average Nusselt numbers approach the corresponding Newtonian values when the shear rates are predominantly in either the zero or the infinite shear rate Newtonian regions. However, power law values are approached only when both of the following two conditions are met: (1) the shear rates are principally in the power law region and (2) the fluid's limiting zero and infinite shear rate Newtonian viscosities differ sufficiently, by approximately 4 orders of magnitude or more. For all other cases, the average Nusselt number was found to reside between the Newtonian and the power law asymptotes. Results are provided in both graphical and tabular form over a broad range of system parameters.

Commentary by Dr. Valentin Fuster

Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2014;136(9):092701-092701-7. doi:10.1115/1.4027768.

A combination of experimental measurements with a numerical model is used to find the volume-averaged radiation properties—extinction coefficient, scattering albedo and approximated scattering phase function—of SiC particle suspensions with varying particle loadings. The experimentally determined angular radiation distribution of irradiated SiC samples is applied to fit a collision-based Monte Carlo (MC) model with a continuous participating media defining the particle suspension. A validation case with glass microspheres and Mie theory is implemented to verify the modeling procedure. Two types of SiC particles with dissimilar optical characteristics are examined and the respective radiation properties are determined for particle loadings between 0.05 and 0.30. The extinction coefficients of both types of SiC particle are in good agreement with the dependent scattering correlation of Kaviany and Singh.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):092702-092702-11. doi:10.1115/1.4025133.

Distributions of ratios of energy scattered or reflected (DRESOR) method is a very efficient tool used to calculate radiative intensity with high directional resolution, which is very useful for inverse analysis. The method is based on the Monte Carlo (MC) method and it can solve radiative problems of great complexity. Unfortunately, it suffers from the drawbacks of the Monte Carlo method, which are large computation time and unavoidable statistical errors. In this work, an equation solving method is applied to calculate DRESOR values instead of using the Monte Carlo sampling in the DRESOR method. The equation solving method obtains very accurate results in much shorter computation time than when using the Monte Carlo method. Radiative intensity with high directional resolution calculated by these two kinds of DRESOR method is compared with that of the reverse Monte Carlo (RMC) method. The equation solving DRESOR (ES-DRESOR) method has better accuracy and much better time efficiency than the Monte Carlo based DRESOR (original DRESOR) method. The ES-DRESOR method shows a distinct advantage for calculating radiative intensity with high directional resolution compared with the reverse Monte Carlo method and the discrete ordinates method (DOM). Heat flux comparisons are also given and the ES-DRESOR method shows very good accuracy.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):092703-092703-8. doi:10.1115/1.4027802.

This work addresses the validity of the local effective medium theory (EMT) in predicting the near-field radiative heat transfer between multilayered metamaterials, separated by a vacuum gap. Doped silicon and germanium are used to form the metallodielectric superlattice. Different configurations are considered by setting the layers adjacent to the vacuum spacer as metal–metal (MM), metal–dielectric (MD), or dielectric–dielectric (DD) (where M refers to metallic doped silicon and D refers to dielectric germanium). The calculation is based on fluctuational electrodynamics using the Green's function formulation. The cutoff wave vectors for surface plasmon polaritons (SPPs) and hyperbolic modes are evaluated. Combining the Bloch theory with the cutoff wave vector, the application condition of EMT in predicting near-field radiative heat transfer is presented quantitatively and is verified by exact calculations based on the multilayer formulation.

Commentary by Dr. Valentin Fuster

Research Papers: Two-Phase Flow and Heat Transfer

J. Heat Transfer. 2014;136(9):092901-092901-11. doi:10.1115/1.4027553.

Various ways developed so far in modeling oscillating/pulsating heat pipes (OHPs/PHPs) are briefly reviewed to find which way would be serviceable for design purposes and also be helpful to mathematically plainly describe oscillatory/circulatory motions of the charged working fluid. A selected way basically follows Ma's approach but a theoretically new attempt is made to derive the oscillation angular frequency ratio from two differently represented expressions of the oscillation velocity. A two-phase flow and evaporative/condensing heat transfer analysis is then carried out to get the wave equation of pressure oscillation. Finally obtained are closed-form algebraic expressions, providing us with convenient means of predicting the oscillation frequency- and-amplitude and the wave velocity. To demonstrate the applicability of those expressions, numerical comparisons are extensively done between our predictions and many other ones.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):092902-092902-7. doi:10.1115/1.4027856.

We use pump–probe thermal transport measurements and high speed imaging to study the residence time and heat transfer of small (360 μm diameter) water droplets that bounce from hydrophobic surfaces whose temperature exceeds the boiling point. The structure of the hydrophobic surface is a 10 nm thick fluorocarbon coating on a Si substrate; the Si substrate is also patterned with micron-scale ridges using photolithography to further increase the contact angle. The residence time determined by high-speed imaging is constant at ≈1 ms over the temperature range of our study, 110 < T < 210 °C. Measurements of the thermal conductance of the interface show that the time of intimate contact between liquid water and the hydrophobic surface is reduced by the rapid formation of a vapor layer and reaches a minimum value of ≈0.025 ms at T>190 °C. We tentatively associate this time-scale with a ∼1 m s 1 velocity of the liquid/vapor/solid contact line. The amount of heat transferred during the impact, normalized by the droplet volume, ranges from 0.028 J mm 3 to 0.048 J mm 3 in the temperature range 110 < T < 210 °C. This amount of heat transfer is ≈1–2% of the latent heat of evaporation.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Heat Transfer. 2014;136(9):094501-094501-3. doi:10.1115/1.4027689.

A new and simple expression for the calculation of the total gas emittance of H2O–CO2 mixtures for modeling radiation transfer in combustion furnaces is presented. Its accuracy is established by comparing the predictions with those based on the well established the model based on Hitemp database. The computational time was found to be reduced by a factor of 3 in comparison to other methods for computing the total emittance of combustion gas mixtures.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):094502-094502-6. doi:10.1115/1.4027780.

In this paper, we consider the heat transfer from a periodic array of isothermal pipes embedded in a rectangular slab. The upper surface of the slab is sustained at a constant temperature while the lower surface is insulated. The particular configuration is a classical heat conduction problem with a wide range of practical applications. We consider both the classical problem, i.e., estimating the shape factor of a given configuration, and the inverse problem, i.e., calculating the optimum shape that maximizes the heat transfer rate associated with a set of geometrical constraints. The way the present formulation differs from previous formulations is that: (i) the array of pipes does not have to be placed at the midsection of the slab and (ii) we have included an isoperimetric constraint (not changing in perimeter) through which we can control the deviation of the optimum shape from that of a circle. This is very important considering that most of the applications deal with buried pipes and a realistic shape is a practical necessity. The isoperimetric constraint is included through the isoperimetric quotient (IQ), which is the ratio between the area and the perimeter of a closed curve.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):094503-094503-6. doi:10.1115/1.4027769.

Heat transfer from a wedge to fluids at any Prandtl number can be predicted using the asymptotic model. In the asymptotic model, the dependent parameter Nux/Rex1/2 has two asymptotes. The first asymptote is Nux/Rex1/2Pr→0 that corresponds to very small value of the independent parameter Pr. The second asymptote is Nux/Rex1/2Pr→∞, that corresponds to very large value of the independent parameter Pr. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. The solution has two general cases. The first case is β ≠ −0.198838. The second case is the special case of separated wedge flow (β = −0.198838) where the surface shear stress is zero, but the heat transfer rate is not zero. The reason for this division is Nux/Rex1/2 ∼ Pr1/3 for Pr ⪢ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr ⪢ 1 in the second case. In the first case, there are only two common examples of the wedge flow in practice. The first common example is the flow over a flat plate at zero incidence with constant external velocity, known as Blasius flow and corresponds to β = 0. The second common example is the two-dimensional stagnation flow, known as Hiemenez flow and corresponds to β = 1 (wedge half-angle 90 deg). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniform-flux wedges can be determined.

Commentary by Dr. Valentin Fuster

Discussion

J. Heat Transfer. 2014;136(9):095501-095501-1. doi:10.1115/1.4027606.

In a recent paper by Makinde and Aziz [1], the effect of thermal buoyancy and internal heat generation along a stationary vertical plate in a uniform free stream was considered (Fig. 1Fig. 1

Flow configuration and coordinate system

Grahic Jump LocationFlow configuration and coordinate system

). The governing equations and the boundary conditions are as follows:

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2014;136(9):095502-095502-2. doi:10.1115/1.4027821.

The purpose of this discussion is to place in perspective the concept of entransy, in view of the critiques published by Grazzini et al. (2013, “Entropy Versus Entransy,” J. Non-Equilib. Thermodyn., 38, pp. 259–271), Herwig (2014, “Do We Really Need ‘Entransy’? A Critical Assessment of a New Quantity in Heat Transfer Analysis,” ASME J. Heat Trans., 136(4), 045501), and Bejan 2014, ““Entransy,” and Its Lack of Content in Physics,” ASME J. Heat Trans., 136(5), 055501), and especially the response just published by Guo et al. (2014, “A Response to Do We Really Need ‘Entransy’?” ASME J. Heat Trans., 136(4), 046001). The conclusion is that entransy is improper and not needed, and that Guo et al.'s own response actually confirms this conclusion.

Commentary by Dr. Valentin Fuster

Closure

J. Heat Transfer. 2014;136(9):096001-096001-3. doi:10.1115/1.4027822.

Entransy is a newly proposed concept for the analysis and optimization of heat transfer processes, and we do welcome any discussions, comments, and even objections on this topic from our counterparts including Awad's paper [1] entitled, “Entransy is Now Clear.” However, we do not accept the conclusions that “entransy is improper and not needed” because there are misreadings and incorrect interpretations in the paper.

Commentary by Dr. Valentin Fuster

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