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Research Papers: Conduction

J. Heat Transfer. 2017;140(3):031301-031301-22. doi:10.1115/1.4037775.

Finite integral transform techniques are applied to solve the one-dimensional (1D) dual-phase heat conduction problem, and a comprehensive analysis is provided for general time-dependent heat generation and arbitrary combinations of various boundary conditions (Dirichlet, Neumann, and Robin). Through the dependence on the relative differences in heat flux and temperature relaxation times, this analytical solution effectively models both parabolic and hyperbolic heat conduction. In order to demonstrate several exemplary physical phenomena, four distinct cases that illustrate the wavelike heat conduction behavior are presented. In the first model, following an initial temperature spike in a slab, the thermal evolution portrays immediate dissipation in parabolic systems, whereas the dual-phase solution depicts wavelike temperature propagation—the intensity of which depends on the relaxation times. Next, the analysis of periodic surface heat flux at the slab boundaries provides evidence of interference patterns formed by temperature waves. In following, the study of Joule heating driven periodic generation inside the slab demonstrates that the steady-periodic parabolic temperature response depends on the ratio of pulsatile electrical excitation and the electrical resistivity of the slab. As for the dual-phase model, thermal resonance conditions are observed at distinct excitation frequencies. Building on findings of the other models, the case of moving constant-amplitude heat generation is considered, and the occurrences of thermal shock and thermal expansion waves are demonstrated at particular conditions.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2017;140(3):031701-031701-9. doi:10.1115/1.4037208.

Both experimental and numerical studies of a turbulent flow in a bifurcating channel are performed to characterize the dynamical behavior of the flow and its impact on the convective heat transfer on the sides of the branch. This configuration corresponds to the radial vents placed in the stator vertically to the rotor–stator air gap in the electrical machines. Indeed, our analysis focuses on the local convective heat transfer on the vents internal surface under a turbulent mass flow rate. The flow field measurements were carried out with two components particle image velocimetry (PIV) system, and the local heat transfer on the sides of the bifurcation branch was measured using an infrared thermography device. The convective heat transfer and the flow dynamics through the geometry are investigated numerically considering a three-dimensional (3D) flow. The closure system of the Navier–Stokes equations for steady and incompressible flow is based on the low-Reynolds numbers Reynolds stress model (RSM) (RSM-stress-ω). The comparison of the 3D computed results with the measurements in the xy symmetry plane is satisfactory in the vertical and horizontal channels. The numerical prediction of the secondary flow in the vertical branch was analyzed and complements the experimental results. It was particularly noticed that the accelerated flow observed at the right side of the branch's inlet allows more pronounced heat transfer comparatively to the left side. Beyond approximately 7 hydraulic diameters from the entrance of the branch, the Nusselt number curves on the two sides of the branch tend to be the same developed Nusselt number, Nud.

Commentary by Dr. Valentin Fuster

Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2017;140(3):032201-032201-12. doi:10.1115/1.4037786.

Liquid microjets are emerging as candidate primary or secondary heat exchangers for the thermal management of next generation photonic integrated circuits (PICs). However, the thermal and hydrodynamic behavior of confined, low Reynolds number liquid slot jets is not yet comprehensively understood. This investigation experimentally examined jet outlet modifications—in the form of tabs and chevrons—as techniques for passive control and enhancement of single-phase convective heat transfer. The investigation was carried out for slot jets in the laminar flow regime, with a Reynolds number range, based on the slot jet hydraulic diameter, of 100–500. A slot jet with an aspect ratio of 4 and a fixed confinement height to hydraulic diameter ratio (H/Dh) of 1 was considered. The local surface heat transfer and velocity field characteristics were measured using infrared (IR) thermography and particle image velocimetry (PIV) techniques. It was found that increases in area-averaged Nusselt number of up to 29% compared to the baseline case could be achieved without incurring additional hydrodynamic losses. It was also determined that the location and magnitude of Nusselt number and velocity peaks within the slot jet stagnation region could be passively controlled and enhanced through the application of outlet tabs of varying geometries and locations.

Commentary by Dr. Valentin Fuster

Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2017;140(3):032501-032501-14. doi:10.1115/1.4037875.

The continuity, momentum, and the energy conservation equation for air around a hollow cylinder with inline or staggered holes have been solved in three dimensions to assess the buoyancy driven flow and temperature field around the cylinder. From the thermal field, the average surface Nu could be computed for hollow cylinders with inline or staggered holes and the heat loss from the cylinder could be compared with that of a hollow cylinder without holes. Interesting flow and thermal plume around the hollow cylinder with holes could be seen, which could help to explain why there is more heat loss from a cylinder with staggered holes compared to a cylinder with inline holes at lower Ra of 105, whereas for higher Ra of 106 or more, there exists an optimum d/D where the heat loss from the perforated cylinder has a maximum value and thereafter it reduces. There are interesting comparisons on Nu for the hollow cylinder with inline or staggered holes and new correlations for Nu versus many different pertinent input parameters have been developed for many cases, which can be used practically in industry for designing perforated cylinder with heat loss.

Commentary by Dr. Valentin Fuster

Research Papers: Porous Media

J. Heat Transfer. 2017;140(3):032601-032601-11. doi:10.1115/1.4038006.

The interstitial heat transfer coefficient (IHTC) is a key parameter in the two-energy equation model usually employed to investigate the thermal performance of high porosity open-cell metal foam/paraffin composite phase change material. Due to the existence of weak convection of liquid paraffin through metal foam during phase change process, the IHTC should be carefully determined for a low Reynolds number range (Re = 0–1), which however has been rarely addressed in the literature. In this paper, a direct simulation at foam pore scale is carried out to determine the IHTC between paraffin and metal foam at Re = 0–1. For this purpose, the cell structures reflecting realistic metal foams are first constructed based on the three-dimensional (3D) Weaire–Phelan foam cell to serve as the representative elementary volume (REV) of metal foam for direct simulation. Then, by solving the Navier–Stokes equations and energy equation for the REV, the influences of Reynolds number (Re), Prandtl number (Pr), foam porosity (ε), and pore density (PPI) on the dimensionless IHTC, i.e., the Nusselt number Nuv, are investigated. According to the numerical results, a correlation of Nuv at Re = 0–1 is proposed for metal foam/paraffin composite material, which covers both diffusion-dominated interstitial heat transfer region (Re ≤ 0.1) and convection-dominated interstitial heat transfer region (0.1 < Re ≤ 1). Finally, the applicability of this correlation in the two-energy equation model for solid–liquid phase change of paraffin in metal foam is validated by comparing the model predicted melting front with that of experimental observations made in this study. It is found that the IHTC correlation proposed in this study can be used in the two-energy equation model for well predicting the phase change process of paraffin in metal foam.

Commentary by Dr. Valentin Fuster

Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2017;140(3):032701-032701-11. doi:10.1115/1.4037823.

In this study, a new model for intumescent coatings is developed including the radiation transfer equation. So, one of the important features of this model is to give the insight of the radiative heat transfer in intumescent coating during expansion. In addition, the model equations are derived into a new coordinate system by introducing the expansion effect into the corresponding parameters. Consequently, the numerical results can be carried out by using a fixed grid system. The numerical results show that the radiative heat transfer near the exposed coating surface cannot be well simulated by the model of thermal radiation conductivity, which is widely used in the previous studies. So, it is suggested that the radiative heat transfer in the expanded char region should be formulated by a more considerate model. In addition, several parameters of coating thermal properties (thermal conductivity, extinction coefficient, and albedo) are tested and investigated under a radiant heat source. In addition to the transient response, the effects of these coating properties on the quasi steady results are also discussed. It is found that the thermal conductivity and the extinction coefficient in the expanded char region both dominate the coating performance. For the thermal properties of virgin coating, the thermal conductivity may have significant effect when the coating has large incomplete pyrolysis (expansion) region, while the extinction coefficient has little influence. Besides, the thermal conductivity and the albedo of virgin coating both alter the heating time to initial expansion but in different mechanisms.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;140(3):032702-032702-12. doi:10.1115/1.4038004.

In the present work, strategies for the grouping of the spectral absorption coefficients used in multiscale (MS) multigroup (MG) full-spectrum k-distribution models were improved by considering the effects of variations in both temperature and species molar ratio on the correlated-k characteristics of the spectra of H2O–CO2-soot mixtures. The improvements in the accuracy of predictions of radiation heat transfer characteristics resulting from these new grouping strategies were evaluated using a series of semi-one-dimensional (1D) cases with significant temperature, participating species molar ratio, and pressure inhomogeneities. Finally, evaluations of grouping strategies were presented on calculation of the full-spectrum thermal images of an actual aeroengine combustor.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Heat Transfer. 2017;140(3):034501-034501-6. doi:10.1115/1.4037874.

The separation of variables (SOV) can be used for all Fourier, single-phase lag (SPL), and dual-phase lag (DPL) heat conduction problems with time-independent source and/or boundary conditions (BCs). The Laplace transform (LT) can be used for problems with time-dependent BCs and sources but requires large computational time for inverse LT. In this work, the orthogonal eigenfunction expansion (OEEM) has been proposed as an alternate method for non-Fourier (SPL and DPL) heat conduction problem. However, the OEEM is applicable only for cases where BCs are homogeneous. Therefore, BCs of the original problem are homogenized by subtracting an auxiliary function from the temperature to get a modified problem in terms of a modified temperature. It is shown that the auxiliary function has to satisfy a set of conditions. However, these conditions do not lead to a unique auxiliary function. Therefore, an additional condition, which simplifies the modified problem, is proposed to evaluate the auxiliary function. The methodology is verified with SOV for time-independent BCs. The implementation of the methodology is demonstrated with illustrative example, which shows that this approach leads to an accurate solution with reasonable number of terms in the expansion.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;140(3):034502-034502-4. doi:10.1115/1.4038001.

The constant flux forced convection in a rectangular duct with two highly conductive (H1) walls and two poorly conductive (H2) walls is studied for the first time. This mixed problem is solved analytically using a modified single series method. The Nusselt number is determined for various duct aspect ratios. Depending on the aspect ratio, hot spots and cold spots may occur either on the H1 walls or on the H2 walls.

Commentary by Dr. Valentin Fuster

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