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# Current Issue

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

J. Heat Transfer 136, 112201 (2014) (11 pages);   Paper No: HT-13-1542;   doi:10.1115/1.4028081

This paper numerically and experimentally investigated the effect of weak crossflow on the heat transfer characteristics of a short-distance impinging jet. The Reynolds number of the impinging jet ranged from 6000 to 15,000, and the mass velocity ratio (M) between the crossflow and the jet varied from 0 to 0.15. The separation distance (H) between the exit of the jet nozzle and the impingement surface equals to the exit diameter (D) of the impinging jet. In the experiments, the temperature distribution on the impingement target surface was measured using a transient liquid crystal method. In the numerical simulation, a multiblock hexahedral mesh was applied to discrete the computational domain, and a commercial CFD package (Ansys cfx-12.0) with a standard $k-ɛ$ turbulence model was used for computation. It was found that compared to the impinging cooling without crossflow, the heat transfer characteristics near the impinging stagnation point remained almost constant. At the same time, the presence of crossflow decreased the heat transfer rate in the upstream region of the impinging stagnation point, while increased that in the downstream of the impinging stagnation point. Taken together, crossflow has a complex influence on the impinging cooling, which is highly dependent on the mass velocity ratio between the crossflow and the jet.

J. Heat Transfer 136, 112202 (2014) (10 pages);   Paper No: HT-13-1337;   doi:10.1115/1.4028242

A numerical investigation using unsteady three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations with the k-ω SST (shear stress transport) turbulent model was conducted to determine the flow and thermal characteristics of an unsubmerged axisymmetric oil jet in air, impinging normally on to a heated flat disk with finite radius, bounded by cylindrical walls kept at constant temperature. A 10 mm thick disk subjected to a high uniform heat flux was located at impingement distances ranging from 40 to 80 mm from the nozzle exit, for nozzle exit diameters of d = 1.0, 2.0, and 4.0 mm. The volume of fluid (VOF) method with a high-resolution interface-capturing (HRIC) scheme was implemented in STAR-CCM+. A new methodology was developed to predict the stagnation zone and local heat transfer coefficients. Contrary to previous research, it is shown that the radial extent of the stagnation zone is not fixed but depends on the gradient of radial velocity along the disk. The normalized local Nusselt number profile along the disk radius is found to be weakly dependent on Reynolds number for a given nozzle size. It is also shown that the local Nusselt number is not uniform in the stagnation region as reported by experimental studies but depends on the distribution of the near-wall radial velocity gradient. Using the computational results, new correlations to predict the dimensionless radial velocity gradient and Nusselt number have been developed. The present correlations are dimensionally balanced, eliminating a deficiency in earlier correlations noted in the literature.

### Research Papers: Porous Media

J. Heat Transfer 136, 112601 (2014) (10 pages);   Paper No: HT-13-1655;   doi:10.1115/1.4028113

Because of their light weight, open porosity, high surface area per unit volume, and thermal characteristics, metal foams are a promising material for many industrial applications involving fluid flow and heat transfer. The pressure drop and heat transfer in porous media have inspired a number of experimental and numerical studies, and many models have been proposed in the literature that correlate the pressure gradient and the heat transfer coefficient with the mean cell size and porosity. However, large differences exist among results predicted by different models, and most studies are based on idealized periodic cell structures. In this study, the true three-dimensional microstructure of the metal foam is obtained by employing x-ray computed microtomography (XCT). This is the “real” structure. For comparison, ideal Kelvin foam structures are developed in the free-to-use software “surface evolver” surface energy minimization program. These are “ideal” structures. Pressure drop and heat transfer are then investigated in each structure using the CFD module of COMSOL® Multiphysics code. A comparison between the numerical predictions from the real and ideal geometries is carried out. The predictions showed that heat transfer characteristics are very close for low values of Reynolds number, but larger Reynolds numbers create larger differences between the results of the ideal and real structures. Conversely, the differences in pressure drop at any Reynolds number are nearly 100%. Results from the models are then validated by comparing them with experimental results taken from the literature. The validation suggests that the ideal structure poorly predicts the heat transfer and pressure drops.

J. Heat Transfer 136, 112602 (2014) (8 pages);   Paper No: HT-13-1532;   doi:10.1115/1.4028177

This paper presents an analysis of forced convection flow and heat transfer in triangular ducts containing a porous medium. The porous medium is isotropic and the flow is laminar, fully developed with constant properties. Numerical results for velocity and temperature distribution (in dimensionless format) in the channel are presented for a wide range of porosity, permeability, and apex angles. The effects of apex angle and porous media properties (porosity and permeability) are demonstrated on the velocity and temperature distribution, as well as the friction factor (fRe) and Nusselt numbers in the channel for both Isoflux (NuH) and Isothermal (NuT) boundary conditions. The consistency of our findings has been verified with earlier results in the literature on empty triangular ducts, when the porosity in our models is made to approach one.

### Research Papers: Experimental Techniques

J. Heat Transfer 136, 112701 (2014) (11 pages);   Paper No: HT-11-1549;   doi:10.1115/1.4024666

In this paper, the steady magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous electrically conducting fluid over a stretching sheet has been investigated. Velocity and thermal slip conditions have been incorporated in the study. The effects of induced magnetic field and thermal radiation have also been duly taken into account. The nonlinear partial differential equations arising out of the mathematical analysis of the problem are transformed into a system of nonlinear ordinary differential equations by using similarity transformation and boundary layer approximation. These equations are solved by developing an appropriate numerical method. Considering an illustrative example, numerical results are obtained for velocity, temperature, skin friction, and Nusselt number by considering a chosen set of values of various parameters involved in the study. The results are presented graphically/in tabular form.

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

J. Heat Transfer 136, 112901 (2014) (8 pages);   Paper No: HT-14-1004;   doi:10.1115/1.4028086

Thermal ground planes (TGPs) are flat, thin (external thickness of 2 mm) heat pipes which utilize two-phase cooling. The goal is to utilize TGPs as thermal spreaders in a variety of microelectronic cooling applications. In addition to TGPs and flat heat pipes, some investigators refer to similar devices as vapor chambers. TGPs are novel high-performance, integrated systems able to operate at a high power density with a reduced weight and temperature gradient. In addition to being able to dissipate large amounts of heat, they have very high effective axial thermal conductivities and (because of nanoporous wicks) can operate in high adverse gravitational fields. A three-dimensional (3D) finite element model is used to predict the thermal performance of the TGP. The 3D thermal model predicts the temperature field in the TGP, the effective axial thermal conductivity, and the evaporation and the condensation rates. A key feature of this model is that it relies on empirical interfacial heat transfer coefficient data to very accurately model the interfacial energy balance at the vapor–liquid saturated wick interface. Wick samples for a TGP are tested in an experimental setup to measure the interfacial heat transfer coefficient. Then the experimental heat transfer coefficient data are used for the interfacial energy balance. Another key feature of this model is that it demonstrates that for the Jakob numbers of interest, the thermal and flow fields can be decoupled except at the vapor–liquid saturated wick interface. This model can be used to predict the performance of a TGP for different geometries and implementation structures. This paper will describe the model and how it incorporates empirical interfacial heat transfer coefficient data. It will then show theoretical predictions for the thermal performance of TGP's, and compare with experimental results.

### Research Papers: Conduction

J. Heat Transfer 136, 111301 (2014) (10 pages);   Paper No: HT-13-1190;   doi:10.1115/1.4027348

In recent years, there has been interest in employing atomistic computations to inform macroscale thermal transport analyses. In heat conduction simulations in semiconductors and dielectrics, for example, classical molecular dynamics (MD) is used to compute phonon relaxation times, from which material thermal conductivity may be inferred and used at the macroscale. A drawback of this method is the noise associated with MD simulation (here after referred to as MD noise), which is generated due to the possibility of multiple initial configurations corresponding to the same system temperature. When MD is used to compute phonon relaxation times, the spread may be as high as 20%. In this work, we propose a method to quantify the uncertainty in thermal conductivity computations due to MD noise, and its effect on the computation of the temperature distribution in heat conduction simulations. Bayesian inference is used to construct a probabilistic surrogate model for thermal conductivity as a function of temperature, accounting for the statistical spread in MD relaxation times. The surrogate model is used in probabilistic computations of the temperature field in macroscale Fourier conduction simulations. These simulations yield probability density functions (PDFs) of the spatial temperature distribution resulting from the PDFs of thermal conductivity. To allay the cost of probabilistic computations, a stochastic collocation technique based on generalized polynomial chaos (gPC) is used to construct a response surface for the variation of temperature (at each physical location in the domain) as a function of the random variables in the thermal conductivity model. Results are presented for the spatial variation of the probability density function of temperature as a function of spatial location in a typical heat conduction problem to establish the viability of the method.

J. Heat Transfer 136, 111302 (2014) (7 pages);   Paper No: HT-13-1580;   doi:10.1115/1.4028082

The transversal method of lines (TMOL) is a general hybrid technique for determining approximate, semi-analytic solutions of parabolic partial differential equations. When applied to a one-dimensional (1D) parabolic partial differential equation, TMOL engenders a sequence of adjoint second-order ordinary differential equations, where in the space coordinate is the independent variable and the time appears as an embedded parameter. Essentially, the adjoint second-order ordinary differential equations that result are of quasi-stationary nature, and depending on the coordinate system may have constant or variable coefficients. In this work, TMOL is applied to the unsteady 1D heat equation in simple bodies (large plate, long cylinder, and sphere) with temperature-invariant thermophysical properties, constant initial temperature and uniform heat flux at the surface. In engineering applications, the surface heat flux is customarily provided by electrical heating or radiative heating. Using the first adjoint quasi-stationary heat equation for each simple body with one time jump, it is demonstrated that approximate, semi-analytic TMOL temperature solutions with good quality are easily obtainable, regardless of time. As a consequence, usage of the more involved second adjoint quasi-stationary heat equation accounting for two consecutive time jumps come to be unnecessary.

### Research Papers: Heat Exchangers

J. Heat Transfer 136, 111801 (2014) (8 pages);   Paper No: HT-13-1028;   doi:10.1115/1.4028176

Within a Marnoch heat engine (MHE), a water/glycol mixture transfers heat from the heat source into a set of variable flow heat exchangers and removes heat from adjoining cold heat exchangers. The compressed dry air is used as the working medium in this heat engine. The MHE has four shell and tube heat exchangers, which operate transient and variable flow conditions. A new transient heat transfer model is developed to predict this transient behavior of the heat exchangers for different flow regimes and temperatures. The results from the model are validated against experimental results from an MHE prototype. The heat transfer model shows 85% agreement with measured data from the MHE prototype for the individual heat exchangers. This model can be used for similar shell and tube heat exchangers with straight or U-shaped tubes. The heat transfer model predicts the gas temperature on the shell side, when a step change is imposed on the liquid entering the tubes.