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Research Papers: Conduction

J. Heat Transfer. 2016;138(8):081301-081301-11. doi:10.1115/1.4033326.

Thermoelectric coolers (TECs) are solid-state cooling devices which can be used in certain applications to reduce the operating temperature of electronics or increase their heat dissipation. However, the performance of the cooler is strongly influenced by the thermal system into which it is placed, and the cooler design should be optimized for a given system. In this work, the possible benefits of a TEC implemented within a realistic thermal system are quantified. Finite thermal conductances between the cooled device and the TEC and between the TEC and the heat sink are considered. The entire problem is treated using dimensionless parameters, which reduces the number of independent parameters and enables generalized performance maps which clearly show the maximum benefit (in terms of a reduced device temperature or increased device heat dissipation) that a prescribed TEC can deliver to a particular application. The use of these dimensionless parameters also allows for optimization of TEC parameters without considering the cooler detailed design geometry.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2016;138(8):081501-081501-9. doi:10.1115/1.4033347.

Falling film type condensers/reboilers applied to cryogenic air separation units (ASUs) have drawn more attentions in recent years. This paper presents and analyzes a mathematical model for the falling film plate-fin condensers/reboilers (FPCR). In the modeling, both the laminar falling film evaporation and condensation processes, incorporating with interference of mass transfer and interfacial shear stress, are considered, and related to a plate-fin heat exchanger (PHX). The liquid film flow and heat transfer characteristics of oxygen and nitrogen fluids in the PHX are analyzed under given conditions by solving the model with a numerical iteration method. The variations of liquid film thicknesses and local heat transfer coefficients of oxygen and nitrogen as well as the total local heat transfer coefficient have been obtained. Furthermore, the effects of the inlet mass flow rate allocation ratio (i.e., the ratio of inlet mass flow rate of oxygen liquid over the base plate to that over the fin surfaces) on the wetted length of the heat transfer surfaces, the heat transfer performance, and the oxygen liquid circulation ratio (i.e., the ratio of the inlet liquid mass flow rate to the generated vapor mass flow rate) are also discussed. A proper inlet mass flow rate allocation ratio of oxygen liquid is presented. The wave effects are further considered and analyzed through the inclusion of a model for the wave factor.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;138(8):081502-081502-7. doi:10.1115/1.4033210.

Smooth DLC (diamond-like carbon) coated surfaces can profoundly mitigate scaling during pool boiling of calcium sulphate solutions. Previous investigations though carried out mostly for the smooth surfaces rather than structured, i.e., finned tubes. This study compares experimental results of DLC coated smooth and finned tubes at clean and fouling conditions. Fouling runs were conducted during pool boiling of saturated CaSO4 solution of 1.6 g/L at 300 kW/m2. The substrate of the attempted tubes was stainless steel and finned tubes of 19 and 40 fins per inch were used. The DLC coated smooth tube showed an enhanced clean heat transfer up to 50% and reduced fouling resistance compared to the uncoated smooth tube. After a short operating time, though, the coated smooth tube reached an asymptotic fouling resistance of 0.00005 m2 K/W whereas for the uncoated smooth tube, it was 4.8 times higher. DLC coating of the finned tubes with the physical vapor deposition (PVD) technique implicated difficulties. The base surface of the finned tubes was defectively coated. The defectiveness of the coating was attributed to the limitation of the PVD for coating of structured surfaces.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2016;138(8):081701-081701-9. doi:10.1115/1.4033137.

Numerical results show that at supercritical pressures, once the buoyancy force increases, the effect of the turbulent Prandtl number, Prt, on convective heat transfer becomes considerable. This phenomenon has not been adequately addressed in the literature. In this study, the effect of the turbulent Prandtl number on the rate of heat transfer in both enhanced and deteriorated regimes of heat transfer to supercritical fluid flows has been extensively investigated. Having realized that variations of the turbulent Prandtl number can affect the model predictions so greatly, a new correlation to express the changes of Prt with respect to flow conditions in a supercritical environment is developed. Effects of various important parameters such as heat flux, mass flux, and fluid pressure are included in the proposed correlation. This correlation has been modified to be applicable for different supercritical fluids. The comparison with various experimental data shows that by implementing the new correlation of Prt in the numerical code, it is possible to significantly improve the simulation results. Such a correlation seems to be the first one introduced in the literature for a supercritical fluid flow.

Commentary by Dr. Valentin Fuster

Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2016;138(8):082001-082001-10. doi:10.1115/1.4033350.

In this work, convection heat transfer for combined electro-osmotic and pressure driven flow of power-law fluid through a microtube has been analyzed. Typical results for velocity and temperature distributions, friction coefficient, and Nusselt number are illustrated for various values of key parameters such as flow behavior index, length scale ratio (ratio of Debye length to tube radius), dimensionless pressure gradient, and dimensionless Joule heating parameter. The results reveal that friction coefficient decreases with increasing dimensionless pressure gradient, and classical Poiseuille solutions can be retrieved as the dimensionless pressure gradient approaches to infinite. To increase the length scale ratio has the effect to reduce Nusselt number, while the influence of this ratio on Nusselt number diminishes as the pressure gradient increases. With the same magnitude of dimensionless Joule heating parameter, Nusselt number can be increased by increasing both the flow behavior index and dimensionless pressure gradient for surface cooling, while the opposite behavior is observed for surface heating. Also, singularities occurs in the Nusselt number variations for surface cooling as the ratio of Joule heating to wall heat flux is sufficiently large with negative sign.

Commentary by Dr. Valentin Fuster

Research Papers: Thermal Systems

J. Heat Transfer. 2016;138(8):082801-082801-9. doi:10.1115/1.4033346.

An entropic wall with circulating water inside could be a solution for acclimatizing a new building with high-energy efficiency and high levels of internal comfort. If circulating water is thermally stabilized by exchanging in the ground such has it happens in geothermal plants, a thermal shield could be realized keeping walls in comfort conditions and minimizing energy needs for further temperature regulations. This paper presents optimization guidelines of such a wall with the objective of maximizing the performances of the wall for reaching optimal internal wellness conditions. Optimization has been realized by a constructal law based method, which has been personalized by a step-by-step process and has been named constructal design for efficiency (CDE). The optimization of the system has been produced at different levels. It starts from a preliminary analysis at system levels, which allow defining the best objectives that could be reached. After this preliminary process, the system has been divided into modules, and the critical ones which have higher influence on the performances of the system have been evaluated. This analysis has been coupled also with an industrial analysis with the goal of defining an effective layout, which could be also manufactured with acceptable costs. The result has produced a final solution with a very good compromise between energetic performances and minimization of costs at industrial level. The results open interesting perspectives for the constructal law to become the core of an effective methodology of an industrial design which can couple perfectly with the modular approach which is currently the major part of industrial companies.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;138(8):082802-082802-12. doi:10.1115/1.4033209.

Optimal material utilization in metal-matrix heat sink is investigated using constructal design (CD) in combination with fin theory to develop a constructal tree of optimally shaped convective fins. The structure is developed through systematic growth of constructs, consisting initially of a single convective fin enveloped in a convective medium. Increasingly complex convective fin structures are created and optimized at each level of complexity to determine optimal fin shapes, aspect ratios, and fin-base thickness ratios. One result of the optimized structures is a functional grading of porosity. The porosity increases as a function of distance from the heated surface in a manner ranging from linear to a power function of distance with exponent of about 2. The degree of nonlinearity in this distribution varies depending on the volume of the heat sink and average packing density and approaches a parabolic shape for large volume. For small volume, porosity approaches a linear function of distance. Thus, a parabolic (or least-material) fin shape at each construct level would not necessarily be optimal. Significant improvements in total heat transfer, up to 55% for the cases considered in this work, were observed when the fin shape is part of the optimization in a constructal tree of convective fins. The results of this work will lead to better understanding of the role played by the porosity distribution in a metal-matrix heat sink and may be applied to the analysis, optimization, and design of more effective heat sinks for electronics cooling and related areas.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Heat Transfer. 2016;138(8):084501-084501-7. doi:10.1115/1.4033164.

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

Commentary by Dr. Valentin Fuster

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