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### Research Papers: Conduction

J. Heat Transfer. 2018;140(8):081301-081301-9. doi:10.1115/1.4039353.

This paper presents a systematic scaling analysis of the point heat source in steady-state on a semi-infinite solid. It is shown that all characteristic values related to an isotherm can be reduced to a dimensionless expression dependent only on the Rykalin number (Ry). The maximum width of an isotherm and its location are determined for the first time in explicit form for the whole range of Ry, with an error below 2% from the exact solution. The methodology employed involves normalization, dimensional analysis, asymptotic analysis, and blending techniques. The expressions developed can be calculated using a handheld calculator or a basic spreadsheet to estimate, for example, the width of a weld or the size of zone affected by the heat source in a number of processes. These expressions are also useful to verify numerical models.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2018;140(8):081701-081701-13. doi:10.1115/1.4038831.

We numerically compute Nusselt numbers for laminar, hydrodynamically, and thermally fully developed Poiseuille flow of liquid in the Cassie state through a parallel plate-geometry microchannel symmetrically textured by a periodic array of isoflux ridges oriented parallel to the flow. Our computations are performed using an efficient, multiple domain, Chebyshev collocation (spectral) method. The Nusselt numbers are a function of the solid fraction of the ridges, channel height to ridge pitch ratio, and protrusion angle of menisci. Significantly, our results span the entire range of these geometrical parameters. We quantify the accuracy of two asymptotic results for Nusselt numbers corresponding to small meniscus curvature, by direct comparison against the present results. The first comparison is with the exact solution of the dual series equations resulting from a small boundary perturbation (Kirk et al., 2017, “Nusselt Numbers for Poiseuille Flow Over Isoflux Parallel Ridges Accounting for Meniscus Curvature,” J. Fluid Mech., 811, pp. 315–349). The second comparison is with the asymptotic limit of this solution for large channel height to ridge pitch ratio.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2018;140(8):082001-082001-8. doi:10.1115/1.4039220.

In this study, the heat-blocking performance of intumescent coating under various combinations of external radiative and convective heat fluxes is investigated numerically. The results show that the temperature distribution and heat fluxes near the coating surface are significantly affected by the heat-source combination, and consequently, the thermal responses of coating are different. For the same magnitude of convective heat source, the higher flame temperature (lower heat convection coefficient) has larger thermal effect on coating response. For the same magnitude of heat source, the radiative heat source generates more thermal response of coating than the convective one. Moreover, if the external heat flux is not intense enough to cause large expansion ratio (2 < xL/L < 11) in 3600 s, the combination of heat source can significantly affect the substrate temperature and the total heat flux at the coating surface. However, if the expansion ratio is sufficiently large (xL/L > 11) at the quasi-steady-state (3600 s), the substrate temperature and the total heat flux are independent of the combination of heat source, which only affects the temperature and the radiative and convective heat fluxes near the coating surface (∼3 mm in this study).

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(8):082002-082002-17. doi:10.1115/1.4039420.

This paper describes a thermal homogenization approach to the application of a multiscale formulation for heat conduction with radiation problems in a porous material. The suggested formulation enables to evaluate the effective macroscopic thermal conductivity, based on the microscopic properties such as porosity, and can also provide the microscopic radiosity heat flux, based on the macroscopic temperature gradient field. This is done by scaling up and down between the microscopic and macroscopic models according to the suggested methodology. The proposed methodology involves a new iterative upscaling procedure, which uses heat conduction at macroscopic problem and heat transfer by conduction and radiation at microscopic problem. This reduces the required computational time, while maintaining the required level of accuracy. The suggested multiscale formulation has been verified by comparing its results with reference finite element (FE) solutions of porous (filled with air) materials examples; the results shows excellent agreement (up to 5% discrepancy) with reference solutions. The efficiency of the suggested formulation was demonstrated by solving a full-scale engineering transient problem.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(8):082003-082003-9. doi:10.1115/1.4038851.

This study introduces an analysis of high-order dual-phase-lag (DPL) heat transfer equation and its thermodynamic consistency. The frameworks of extended irreversible thermodynamics (EIT) and traditional second law are employed to investigate the compatibility of DPL model by evaluating the entropy production rates (EPR). Applying an analytical approach showed that both the first- and second-order approximations of the DPL model are compatible with the traditional second law of thermodynamics under certain circumstances. If the heat flux is the cause of temperature gradient in the medium (over diffused or flux precedence (FP) heat flow), the DPL model is compatible with the traditional second law without any constraints. Otherwise, when the temperature gradient is the cause of heat flux (gradient precedence (GP) heat flow), the conditions of stable solution of the DPL heat transfer equation should be considered to obtain compatible solution with the local equilibrium thermodynamics. Finally, an insight inspection has been presented to declare precisely the influence of high-order terms on the EPRs.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2018;140(8):082401-082401-12. doi:10.1115/1.4039217.

Numerical investigation of natural convective heat transfer and fluid flow in a differentially heated square cavity filled with a CuO-water nanofluid having variable properties is performed. Governing partial differential equations formulated in nondimensional stream function, vorticity, temperature, and nanoparticles volume fraction are solved by the second-order accurate finite difference method and taking into account the Brownian diffusion and thermophoresis. The effects of Rayleigh number (Ra = 104–106), initial nanoparticles volume fraction (C0 = 0–0.09), location of the heater (Δ = 0.0–0.9), and dimensionless time (τ = 0–300) on flow patterns, isotherms, and concentration fields as well as the local and average Nusselt numbers at the heater surface are studied. The isoconcentrations reveal that for most of the cavity domain the nanoparticle concentration is around the initial average concentration of nanoparticles except for a very limited variation in a region close to the cavity walls that experiences minor deviation from the initial concentration. It was found that the flow strength within the cavity (i.e., $ψmaxRa⋅Pr$) is inversely proportional to the heater location Δ and is directly proportional to the Rayleigh number. Also, it was found that the best location of the heater, from a heat transfer perspective, is placing it entirely at the left wall of the cavity where a maximum average Nusselt number is registered. This study revealed that for all heater locations there is always an adverse impact of nanoparticles on the heat transfer and the worst case is registered for the Δ = 0 and the least deterioration is noticed for Δ = 0.9.

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2018;140(8):082601-082601-16. doi:10.1115/1.4038909.

Convective heat transfer in a channel partially filled with porous medium has received a lot of attention due to its wide engineering applications. However, most researches focused on a channel partially filled with single layer porous medium. In this paper, we will analyze the heat transfer and entropy generation inside a channel partially filled with N-layer porous media. The flow and the heat transfer in the porous region are described by the Darcy–Brinkman model and the local thermal nonequilibrium model, respectively. At the porous-free fluid interface, the momentum and the heat transfer are described by the stress jump boundary condition and the heat flux jump boundary condition, respectively; while at the interface between two different porous layers, the momentum and the heat transfer are described by the stress continuity boundary condition and the heat flux continuity boundary condition, respectively. The analytical solutions for the velocity and temperature in the channel are derived and used to calculate the overall Nusselt number, the total entropy generation rate, the Bejan number, and the friction factor. Furthermore, the performances of the flow and heat transfer of a channel partially filled with third-layer porous media are studied.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2018;140(8):082701-082701-11. doi:10.1115/1.4039305.

Combined with the light-field imaging technique, the Landweber method is applied to the reconstruction of three-dimensional (3D) temperature distribution in absorbing media theoretically and experimentally. In the theoretical research, simulated exit radiation intensities on the boundary of absorbing media according to the computing model of light field are employed as inputs for inverse analysis. Compared with the commonly used iterative methods, i.e., the least-square QR decomposition method and algebraic reconstruction technique (ART), the Landweber method can produce reconstruction results with better quality and less computational time. Based on the numerical study, an experimental investigation is conducted to validate the suitability of the proposed method. The temperature distribution of the ethylene diffusion flame is reconstructed by using the Landweber method from the flame image captured by a light-field camera. Good agreement was found between the reconstructed temperature distribution and the measured temperature data obtained by a thermocouple. All the experimental results demonstrate that the temperature distribution of ethylene flame can be reconstructed reasonably by using the Landweber method combined with the light-field imaging technique, which is proven to have potential for the use in noncontract measurement of temperature distribution in practical engineering applications.

Commentary by Dr. Valentin Fuster

### Research Papers: Thermal Systems

J. Heat Transfer. 2018;140(8):082801-082801-13. doi:10.1115/1.4039215.

The aim of the study is the analysis of a uniform magnetic field effect on fluid flow, heat transfer, and entropy generation through the operation of a pulsating heat pipe (PHP). An open loop PHP with three neighboring vapor plugs and two liquid slugs has been considered. The governing equations such as momentum, energy, and mass equations are solved using an explicit method except for the energy equation of liquid slugs. For each case study, Bejan number has been derived to find the heat transfer share in entropy generation. According to the results, the performance of the oscillating heat pipe decreases by applying uniform magnetic field. Moreover, the obtained results illustrate the effects of the applied magnetic field position on the heat transfer and the entropy generation. The latent and sensible heat transfer into the PHP enhance as a result of increase in the pipe diameter, so that the liquid slugs oscillate with high amplitudes. In addition, the entropy generation value increases with an augmentation in the value of the pipe diameter. The evaluated Bejan numbers indicate that the viscous effects in entropy generation decrease as the pipe diameter increases. Furthermore, the results depict that the heat transfer performance of PHP improves by increasing temperature difference between evaporator and condenser sections. With an increase in the value of the evaporator temperature, the Bejan number will increase, as a result, this phenomenon reveals the inconsiderable role of viscous impacts in high evaporator temperatures. In order to validate the calculations, the calculated results have been compared with the previous studies which show good agreement.

Commentary by Dr. Valentin Fuster

### Research Papers: Two-Phase Flow and Heat Transfer

J. Heat Transfer. 2018;140(8):082901-082901-17. doi:10.1115/1.4039686.

This paper presents a numerical method for high-speed compressible cavitating flows. The method is derived from one-fluid formulation in a sense that the two phases are well mixed and the mixture is considered as a locally homogeneous media. Energy equation is solved to predict the temperature evolution which is then used together with pressure to update the density field. A volume of fluid (VOF) phase-fraction based interface capturing approach is used to capture the phase front between the two immiscible fluids. The derived formulations have been implemented into a pressure-based, segregated algebraic semi-implicit compressible solver in Openfoam, which can be used to solve for high-speed compressible two-phase flows involving phase changing. Numerical examples include the cavitating flows induced by an ultrasonic oscillating horn with and without a counter sample. The numerical results by the proposed method are validated against the published experimental data as well as numerical results and good agreements have been obtained. Our calculation demonstrates that the proposed numerical method is applicable to the study of high-speed two phase flows with phase transition and wave propagation, such as shock waves induced by the collapse of the cavitation bubbles.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2018;140(8):084501-084501-8. doi:10.1115/1.4039219.

This study establishes an image-based approach to determine the thermal conductivity of a metal material as a function of temperature using isotherm movement. The thermal conductivity within a range of temperature can be derived from a combined experimental and theoretical study based on Wiedemann–Franz law. A cubic relation between heating time and distance from heat source has been observed, proved, and used to determine the thermal conductivity at different temperature. The temporal and spatial information provided by infrared imaging allow continuous temperature dependence of thermal conductivity to be derived with high accuracy. This method has the potential to determine thermal conductivities of multiple samples at high throughput, and to derive thermal conductivity along different crystal orientation in a thermally anisotropic system.

Commentary by Dr. Valentin Fuster

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