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### Research Papers: Conduction

J. Heat Transfer. 2017;139(7):071301-071301-10. doi:10.1115/1.4035713.

The finite difference (FD), finite element (FE), and finite volume (FV) methods are critically assessed by comparing the solutions produced by the three methods for a simple one-dimensional steady-state heat conduction problem with heat generation. Three issues are assessed: (1) accuracy of temperature, (2) accuracy of heat flux, and (3) satisfaction of global energy conservation. It is found that if the order of accuracy of the numerical discretization schemes is the same (central difference for FD and FV, linear basis functions for FE), the accuracy of the temperature produced by the three methods is similar, except close to the boundaries where the FV method outshines the other two methods. Consequently, the FV method is found to predict more accurate heat fluxes at the boundaries compared to the other two methods and is found to be the only method that guarantees both local and global conservation of energy irrespective of mesh size. The FD and FE methods both violate energy conservation, and the degree to which energy conservation is violated is found to be mesh size dependent. Furthermore, it is shown that in the case of prescribed heat flux (Neumann) and Newton cooling (Robin) boundary conditions, the accuracy of the FD method depends in large part on how the boundary condition is implemented. If the boundary condition and the governing equation are both satisfied at the boundary, the predicted temperatures are more accurate than in the case where only the boundary condition is satisfied.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):071302-071302-11. doi:10.1115/1.4036003.

This paper presents a new approach of meshless local B-spline based finite difference (FD) method for transient 2D heat conduction problems with nonhomogenous and time-dependent heat sources. In this method, any governing equations are discretized by B-spline approximation which is implemented as a generalized FD technique using local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighboring nodal values based on B-spline interpolants. The set of neighboring nodes is allowed to be randomly distributed. This allows enhanced flexibility to be obtained in the simulation. The method is truly meshless as no mesh connectivity is required for field variable approximation or integration. Galerkin implicit scheme is employed for time integration. Several transient 2D heat conduction problems with nonuniform heat sources in arbitrary complex geometries are examined to show the efficacy of the method. Comparison of the simulation results with solutions from other numerical methods in the literature is given. Good agreement with reference numerical methods is obtained. The method is shown to be simple and accurate for the time-dependent problems.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):071303-071303-7. doi:10.1115/1.4036086.

Minimum entropy production principle (MEPP) is an important variational principle for the evolution of systems to nonequilibrium stationary state. However, its restricted validity in the domain of Onsager's linear theory requires an inverse temperature square-dependent thermal conductivity for heat conduction problems. A previous derivative principle of MEPP still limits to constant thermal conductivity case. Therefore, the present work aims to generalize the MEPP to remove these nonphysical limitations. A new dissipation potential is proposed, the minimum of which thus corresponds to the stationary state with no restriction on thermal conductivity. We give both rigorous theoretical verification of the new extremum principle and systematic numerical demonstration through 1D transient heat conduction with different kinds of temperature dependence of the thermal conductivity. The results show that the new principle remains always valid while MEPP and its derivative principle fail beyond their scopes of validity. The present work promotes a clear understanding of the existing thermodynamic extremum principles and proposes a new one for stationary state in nonlinear heat transport.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2017;139(7):071701-071701-10. doi:10.1115/1.4035855.

The Chilton–Colburn analogy is very helpful for evaluating the heat transfer in internal forced flows. The Chilton–Colburn analogy between the Chilton–Colburn j-factor for heat transfer, jH (St·Pr2/3) and the Fanning friction factor (cf) is popularly considered to hold when St·Pr2/3 equals to cf/2, for constant fluid properties. The physical fluid properties, namely, viscosity and thermal conductivity, are generally a function of temperature for microconvective water flow due to a quite steep temperature gradient. Therefore, in present investigation, the validity of Chilton–Colburn analogy between St·Pr2/3 and cf is re-examined for laminar microconvective flow with variable thermophysical fluid properties. It is observed that the Chilton–Colburn analogy is valid only for that portion of the flow regime, where St·Pr2/3 decreases with decreasing cf. The validity of Chilton–Colburn analogy is also verified by the inverse dependence of Reynolds number (Re) with cf. Two modified nondimensional parameters “Π and ΠSk” are emerged from the nondimensional form of 2D, steady-state, incompressible, pure continuum-based, laminar conservation of momentum and energy equations, respectively. These modified nondimensional parameters show the significance of variable fluid properties in momentum transport and energy transport. Additionally, the role of Π and ΠSk in flow friction is also investigated. The higher values of Π and ΠSk indicate the stronger influence on microconvection due to large variations in fluid properties.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Transfer Enhancement

J. Heat Transfer. 2017;139(7):071901-071901-8. doi:10.1115/1.4035712.

The present study aims at explaining why heat transfer is enhanced in turbulent ribbed-pipe flow, based on our previous large eddy simulation (LES) database (Kang and Yang, 2016, “Characterization of Turbulent Heat Transfer in Ribbed Pipe Flow,” ASME J. Heat Transfer, 138(4), p. 041901) obtained for Re = 24,000, Pr = 0.71, pitch ratio (PR) = 2, 4, 6, 8, 10, and 18, and blockage ratio (BR) = 0.0625. Here, the bulk velocity and the pipe diameter were used as the velocity and length scales, respectively. The ribs were implemented in the cylindrical coordinate system by means of an immersed boundary method. In particular, we focus on the cases of PR ≥ 4 for which heat transfer turns out to be significantly enhanced. Instantaneous flow fields reveal that the vortices shed from the ribs are entrained into the main recirculating region behind the ribs, inducing velocity fluctuations in the vicinity of the pipe wall. In order to identify the turbulence structures responsible for heat transfer enhancement in turbulent ribbed-pipe flow, various correlations among the fluctuations of temperature and velocity components have been computed and analyzed. The cross-correlation coefficient and joint probability density distributions of velocity and temperature fluctuations, obtained for PR = 10, confirm that temperature fluctuation is highly correlated with velocity-component fluctuation, but which component depends upon the axial location of interest between two neighboring ribs. Furthermore, it was found via the octant analysis performed for the same PR that at the axial point of the maximum heat transfer rate, O3 (cold wallward interaction) and O5 (hot outward interaction) events most contribute to turbulent heat flux and most frequently occur.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2017;139(7):072001-072001-12. doi:10.1115/1.4035714.

Considerable recent research has focused on the ability of microstructured fibers to exhibit diverse optical functionalities. However, accurately preserving the structure imposed at the preform stage after drawing it down to fiber, while avoiding Rayleigh–Plateau style instabilities, has proven to be a major fabrication challenge. This modeling/analytical study was carried out in support of an experimental program into possible fabrication options for various microstructured optical fibers and considers the generic case of the nonisothermal drawing of a capillary preform to fiber. Model development was carried out in two stages. Initially, a fully conjugate multiphase model, which includes all heat transfer modes within an operational fiber drawing furnace, was validated against available experimental data. To evaluate the external radiative heat flux using the net-radiation method, a Monte Carlo ray-tracing (MC-RT) method was coupled to the commercial polyflow package to obtain all view factors between the various furnace walls and the deforming preform/fiber. A simplified model was also developed (to shorten simulation run times) by explicitly calculating the convective heat transfer between the air within the furnace and the preform/fiber surface using a heat transfer coefficient determined by matching predicted results with those obtained from the multiphase model.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):072002-072002-11. doi:10.1115/1.4036079.

High porosity open-cell metal foams have captured the interest of thermal industry due to their high surface area density, low weight, and ability to create tortuous mixing of fluid. In this work, application of metal foams as heat sinks has been explored. The foam has been represented as a simple cubic structure and heat transfer from a heated base has been treated analogous to that of solid fins. Based on this model, three performance parameters namely, foam efficiency, overall foam efficiency, and foam effectiveness have been evaluated for metal foam heat sinks. Parametric studies with varying foam length, porosity, pore density, material, and fluid velocity have been conducted. It has been observed that geometric mean of foam efficiency and foam effectiveness can be a useful parameter to exactly determine the optimum foam length. Additionally, the variation in temperature profile of different foams heated from one end has been determined experimentally by cooling these with atmospheric air. The experimental results have been presented for open-cell metal foams (10 and 30 PPI) made of copper/aluminium/Fe–Ni–Cr alloy with porosity in the range of 0.908–0.964.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):072003-072003-9. doi:10.1115/1.4036077.

The entropy generation due to steady, incompressible micropolar fluid flow in a rectangular duct with slip and convective boundary conditions (CBCs) is calculated. An external uniform magnetic field is applied which is directed arbitrarily in a plane perpendicular to the flow direction. The governing partial differential equations of momentum, angular momentum, and energy are solved numerically using finite-difference method. The obtained velocity, microrotation, and temperature distributions are then used to evaluate the entropy generation and Bejan number. The effects of various parameters on the entropy generation and Bejan number are discussed through graphs.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Transfer in Manufacturing

J. Heat Transfer. 2017;139(7):072101-072101-10. doi:10.1115/1.4035889.

A major challenge in maintaining quality and reliability in today's microelectronics chips comes from the ever increasing levels of integration in the device fabrication, as well as from the high current densities. Transient Joule heating in the on-chip interconnect metal lines with characteristic sizes of tens of nanometer, can lead to thermomechanical fatigue and failure due to the thermal expansion coefficient mismatch between different materials. Full-field simulations of nearly a billion interconnects in a modern microprocessor are infeasible due to the grid size requirements. To prevent premature device failures, a rapid predictive capability for the thermal response of on-chip interconnects is essential. This work develops a two-dimensional (2D) transient heat conduction framework to analyze inhomogeneous domains, using a reduced-order modeling approach based on proper orthogonal decomposition (POD) and Galerkin projection. POD modes are generated by using a representative step function as the heat source. The model rapidly predicted the transient thermal behavior of the system for several cases, without generating any new observations, and using just a few POD modes.

Commentary by Dr. Valentin Fuster

### Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2017;139(7):072201-072201-13. doi:10.1115/1.4035651.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2017;139(7):072401-072401-12. doi:10.1115/1.4035890.

Improvement of the effectiveness of heat exchanger is the demand of compact and efficient cooling devices. In that respect, a numerical study of fluid flow and heat transfer has been conducted with different arrangements of simple vortex generator (VG) in a rectangular microchannel Reynolds number (Re) in the range between 200 and 1100. The combined effect of spanwise and pitchwise distance of VG on heat transfer is investigated rigorously to observe the dependence of heat transfer on both. By processing the numerical predictions through gene expression programing and genetic algorithm optimization, the output variations in heat transfer, or Nusselt number, and friction factor with Re and locations of VGs in the channel are predicted in the form of explicit equations. The predicted monotonic increase of the outputs with Re shows heat transfer enhancement of 40–135% at the cost of increased pressure drop by 62–186.7% with respect to channels without VGs.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):072402-072402-7. doi:10.1115/1.4036076.

The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and substantial derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):072403-072403-6. doi:10.1115/1.4036082.

A relatively simple theory of annular laminar film condensation in microchannels, based on the Nusselt approximations for the condensate film and a theoretically based approximation for the vapor shear stress, has no empirical input and gives the local heat transfer coefficient and local quality for given vapor mass flux and vapor–surface temperature difference distribution along the channel. As well as streamwise vapor shear stress and gravity, the theory includes transverse (to the flow direction) surface tension-driven motion of the condensate film and gives a differential equation for the local (transverse and streamwise) condensate film thickness. As well as four transverse direction boundary conditions due to condensate surface curvature, a streamwise boundary condition is required as in the Nusselt theory. When the vapor is saturated or superheated at inlet, this is provided by the fact that the film thickness is zero around the channel perimeter at the position of onset on condensation. Most experimental investigations have been conducted with quality less than one at inlet and only approximate comparisons, discussed in earlier papers, can be made. The present paper is devoted to comparisons between theory and measurements in investigations where local heat flux and channel surface temperature were measured and the vapor at inlet was superheated. Measured and calculated heat transfer coefficients and their dependence on distance along the channel and on local quality are in surprisingly good agreement and suggest that the mode of condensation is, in fact, annular and laminar, at least where the quality is high.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2017;139(7):072501-072501-13. doi:10.1115/1.4035919.

Numerical simulations have been conducted to study natural convection heat transfer from solid or hollow cylinders in the laminar range of Ra spanning from 104 to 108 for L/D in the range of $0.05≤(L/D)≤20$. Interesting flow structures around the thin hollow cylinder have been observed for small and large L/D. It has been found that the average Nu for solid or hollow horizontal cylinders in air is marginally higher than when they are on ground for the entire range of L/D and Ra limited up to 107. Up to a Ra of 107 Nu for a solid cylinder in air is higher than that of Nu for a hollow cylinder in air but when Ra exceeds 107 Nu for a hollow cylinder is marginally higher than that of the solid cylinder until an L/D of 0.2. When, L/D rises beyond 0.2 the situation reveres causing Nu for a solid cylinder to be again higher than that of the hollow cylinder when suspended in air. A solid cylinder on ground has higher Nu compared to that of a hollow cylinder on ground up to a Ra of 106. However, for higher Ra of 108 a hollow cylinder on ground has higher Nu compared to that of a solid cylinder on ground until an L/D of 5 and after that the situation reverses again.

Topics: Cylinders
Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2017;139(7):072701-072701-6. doi:10.1115/1.4035732.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2017;139(7):074501-074501-10. doi:10.1115/1.4035805.

Modeling subcooled boiling flows in vertical channels has relied heavily on the utilization of empirical correlations for the active nucleation site density, bubble departure diameter, and bubble departure frequency. Following the development and application of mechanistic modeling at low pressures, the capability of the model to resolve flow conditions at elevated pressure up to 10 bar is thoroughly assessed and compared with selected empirical models. Predictions of the mechanistic and selected empirical models are validated against two experimental data at low to elevated pressures. The results demonstrate that the mechanistic model is capable of predicting the heat and mass transfer processes. In spite of some drawbacks of the currently adopted force balance model, the results still point to the great potential of the mechanistic model to predict a wide range of flow conditions in subcooled boiling flows.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):074502-074502-5. doi:10.1115/1.4036005.

This paper presents research for a class of recombination reaction and diffusion problems in which the Cattaneo relaxation, n-diffusion flux, and p-Fisher–Kolmogorov–Petrovsky–Piscounov (KPP) reaction are considered. Approximate analytical solutions are obtained by Adomian decomposition method (ADM) and shown graphically. Some interesting results for spatial variable and temporal variable evolution are obtained. For specified spatial variable, the temperature profiles decrease with respect to the increase of relaxation parameter and power-law index n but decrease with respect to Fisher–KPP reaction parameter p. For specified temporal variable, the temperature profiles are seem oscillating with values of the relaxation parameter and power-law index n.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):074503-074503-4. doi:10.1115/1.4036085.

In this paper, the new optimal perturbation iteration method (OPIM) is introduced and applied for solving nonlinear differential equations arising in heat transfer. The effectiveness of the proposed method will be tested by considering two specific applications: the temperature distribution equation in a thick rectangular fin radiation to free space and cooling of a lumped system with variable specific heat. Comparing different methods shows that the results obtained by optimal perturbation iteration method are very good agreement with the numerical solutions and perform better than the most existing analytic methods.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):074504-074504-4. doi:10.1115/1.4036006.

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):074505-074505-5. doi:10.1115/1.4036078.

A numerical thermal elastohydrodynamic lubrication (EHL) model is developed for coated line contacts by considering both the mechanical properties and the thermal properties of the coating and the substrate. The temperature fields within the oil film and within the solids are solved by deriving the energy equations for the solids and the oil film. Heat continuity conditions are satisfied at the interfaces between the solids and the oil film, and the coating/substrate interfaces. Effects of the slide-to-roll ratio (SR), the thermal conductivities of the coating bodies, and the oil film on temperature fields are studied.

Commentary by Dr. Valentin Fuster