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### Research Papers: Bio-Heat and Mass Transfer

J. Heat Transfer. 2016;139(3):031101-031101-11. doi:10.1115/1.4034937.

This paper presents a mathematical analysis of bioconvection heat, mass, and motile microorganisms transfer over a stretching sheet in a medium filled with a fluid containing gyrotactic microorganisms. Cross-diffusion is taken into account in the medium. Using the boundary layer approximations, the set of unsteady partial differential equations governing the fluid flow is transformed into nonlinear PDEs form and then solved numerically using bivariate spectral relaxation method (BSRM) and bivariate spectral quasi-linearization method (BSQLM). A comparison between BSRM and BSQLM is made for the first time in this work. The accuracy and convergence analysis of the methods are also discussed. The methods are found to be convergent and give very accurate results with very few grid points in the numerical discretization procedure. A parametric study of the entire flow regime is carried out to illustrate the effects of various governing parameters on the fluid properties and flow characteristics. The results obtained show a significant effect of cross-diffusion on the fluid properties and flow characteristics. The Dufour number was found to increase the local Sherwood number and density number of motile microorganisms while decreasing the Nusselt number, and the reverse effect is true for the Soret number. Furthermore, the Nusselt number, Sherwood number, and density number of motile microorganisms are highly influenced by buoyancy and bioconvection parameters.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;139(3):031102-031102-10. doi:10.1115/1.4034962.

Heat stress experienced by firefighters is a common consequence of extreme firefighting activity. In order to avoid the adverse health conditions due to uncompensable heat stress, the prediction and monitoring of the thermal response of firefighters is critical. Tissue properties, among other parameters, are known to vary between individuals and influence the prediction of thermal response. Further, measurement of tissue properties of each firefighter is not practical. Therefore, in this study, we developed a whole body computational model to evaluate the effect of variability (uncertainty) in tissue parameters on the thermal response of a firefighter during firefighting. Modifications were made to an existing human whole body computational model, developed in our lab, for conducting transient thermal analysis for a firefighting scenario. In conjunction with nominal (baseline) tissue parameters obtained from literature, and physiologic conditions from a firefighting drill, the Pennes' bioheat and energy balance equations were solved to obtain the core body temperature of a firefighter. Subsequently, the uncertainty in core body temperature due to variability in the tissue parameters (input parameters), metabolic rate, specific heat, density, and thermal conductivity was computed using the sensitivity coefficient method. On comparing the individual effect of tissue parameters on the uncertainty in core body temperature, the metabolic rate had the highest contribution (within ±0.20 °C) followed by specific heat (within ±0.10 °C), density (within ±0.07 °C), and finally thermal conductivity (within ±0.01 °C). A maximum overall uncertainty of ±0.23 °C in the core body temperature was observed due to the combined uncertainty in the tissue parameters. Thus, the model results can be used to effectively predict a realistic range of thermal response of the firefighters during firefighting or similar activities.

Commentary by Dr. Valentin Fuster

### Research Papers: Conduction

J. Heat Transfer. 2016;139(3):031301-031301-5. doi:10.1115/1.4034938.

At the microscale length and smaller, solid–solid interfaces pose a significant contribution to resistance, resulting in a build-up of energy carriers, in turn leading to extreme temperature gradients within a single electronic component. These localized temperature gradients, or “hot spots,” are known to promote degradation, thus reducing device longevity and performance. To mitigate thermal management issues, it is crucial to both measure and understand conductance at interfaces in technologically relevant thin film systems. Recent trends in photonic devices have been pushing the consumption of indium in the U.S. to grow exponentially each year. Thus, we report on the temperature-dependent thermal boundary conductances at a series of metal/In-based III–V semiconductor interfaces. These measurements were made using time-domain thermoreflectance (TDTR) from 80 to 350 K. The high-temperature thermal boundary conductance results indicate, for these interfaces, that interfacial transport is dominated by elastic transmission, despite varying levels of acoustic mismatch. There is a strong direct correlation between the interfacial bond strength, approximated by the picosecond acoustics, and the thermal boundary conductance values. Both the interfacial bond strength and the overlap in the phonon density of states (PDOS) play significant roles in the magnitude of the thermal boundary conductance values. Measurements are compared against two separate predictive models, one for a perfect interface and one which accounts for disorder, such as interfacial mixing and finite grain sizes.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Transfer Enhancement

J. Heat Transfer. 2016;139(3):031901-031901-12. doi:10.1115/1.4035068.

This paper focuses on the study of an innovative manifold microchannel design for air-side heat transfer enhancement that uses additive manufacturing (AM) technology. A numerical-based multi-objective optimization was performed to maximize the coefficient of performance and gravimetric heat transfer density ($Q/MΔT$) of air–water heat exchanger designs that incorporate either manifold-microchannel or conventional surfaces for air-side heat transfer enhancement. Performance comparisons between the manifold-microchannel and conventional heat exchangers studied under the current work show that the design based on the manifold-microchannel in conjunction with additive manufacturing promises to push the performance substantially beyond that of conventional technologies. Different scenarios based on manufacturing constraints were considered to study the effect of such constraints on the heat exchanger performance. The results clearly demonstrate that the AM-enabled complex design of the fins and manifolds can significantly improve the overall performance, based on the criteria described in this paper. Based on the current manufacturing limit, up to nearly 60% increase in gravimetric heat transfer density is possible for the manifold-microchannel heat exchanger compared to a wavy-fin heat exchanger. If the manufacturing limit (fin thickness and manifold width) can be reduced even further, an even larger improvement is possible.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2016;139(3):032001-032001-10. doi:10.1115/1.4034900.

The movement and distribution of each phase in annular flow can be considered as random events at a microscopic level. Hence, a probability analysis is appropriate to estimate the morphological features and mechanical characteristics of annular flow from a macroscopic scale. In the present work, three characteristic parameters including the film thickness, interfacial shear stress, and characteristic droplet size are predicted by a probability model as the statistical results of abundant samples. The film thickness can be directly calculated as one of the solutions to the basic equations of annular flow. The interfacial shear stress is estimated as a combination of the frictional and dragging components. The droplet size distribution is obtained using a method of undetermined coefficients. These characteristic parameters are well verified by comparing with the experimental data available in the literature. It is demonstrated that the probability model can accurately calculate the film thickness and maximum droplet size, but the predictions of the interfacial shear stress and mean droplet size are relatively coarse. Furthermore, the effects on the film thickness and Sauter mean diameter of other parameters are discussed in detail. Finally, some important phenomena observed in experiments are interpreted by the probability model.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;139(3):032002-032002-10. doi:10.1115/1.4035042.

A Monte Carlo rejection technique for numerically solving the complete, nonlinear phonon Boltzmann transport equation (BTE) is presented in this work, including three particles interactions. The technique has been developed to explicitly model population-dependent scattering within a full-band cellular Monte Carlo (CMC) framework, to simulate phonon transport in semiconductors, while ensuring conservation of energy and momentum for each scattering event within gridding error. The scattering algorithm directly solves the many-body problem accounting for the instantaneous distribution of the phonons. Our general approach is capable of simulating any nonequilibrium phase space distribution of phonons using the full phonon dispersion without the need of approximations used in previous Monte Carlo simulations. In particular, no assumptions are made on the dominant modes responsible for anharmonic decay, while normal and umklapp scattering are treated on the same footing. In this work, we discuss details of the algorithmic implementation of both the three-particle scattering for the treatment of the anharmonic interactions between phonons, as well as treating isotope and impurity scattering within the same framework. The simulation code was validated by comparison with both analytical and experimental results; in particular, the simulation results show close agreement with a wide range of experimental data such as thermal conductivity as function of the isotopic composition, the temperature, and the thin-film thickness.

Commentary by Dr. Valentin Fuster

### Research Papers: Melting and Solidification

J. Heat Transfer. 2016;139(3):032301-032301-11. doi:10.1115/1.4034813.

The nonisothermal phase-change behavior of droplet deposition on a substrate has been studied. The governing equation for the flow field is solved using a finite-volume scheme with a two-step projection method on a fixed computational grid. The volume-of-fluid (VOF) method is used to track the free surface, and the continuum surface force (CSF) method is used to model the surface tension. An enthalpy formulation with a porosity model is adopted for solving the energy equation. A comparison with published experimental findings has been done to validate the numerical model. The effects of convection terms in the energy equation are examined, and droplet spreading and solidification along with substrate remelting have been analyzed. A parametric study relating the effects of substrate preheating and impact velocity on remelting, cooling rate, spreading, and solidification has also been carried out. It has been observed that the flow field within the droplet has a significant effect on the overall deposition process.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2016;139(3):032401-032401-14. doi:10.1115/1.4035040.

The steady-state fully developed laminar flow of non-Newtonian power-law fluids is analytically studied in a circular microchannel under an imposed uniform and constant wall heat flux. Increasing the flow behavior index results in broadening the dimensionless temperature distribution, i.e., in enlarging the wall and bulk fluid temperature difference. Similar behavior may also be observed when heating or cooling flux is reduced. For any particular value of the flow behavior index, a critical Brinkman number exists in which the bulk mean fluid temperature equals the wall temperature; in this special case of surface cooling, the Nusselt number tends to infinity. Dilatants (shear-thickening fluids) demonstrate more tangible reactions than pseudoplastics (shear-thinning fluids) to changes in the Brinkman number. Entropy generation increases with the flow behavior index as well as the Brinkman number. For shear-thickening fluids, the entropy generation rate from heat transfer is more than the entropy generation rate from fluid friction, while an opposite trend is observed for shear-thinning fluids.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2016;139(3):032501-032501-8. doi:10.1115/1.4035041.

This work studies numerically the combined heat and mass transfer of uniform blowing/suction, non-Newtonian power-law fluid, and thermal radiation effects on free convection adjacent to a vertical cone within a porous medium in the presence of Soret/Dufour effects. The surface of the vertical cone has a uniform wall temperature and uniform wall concentration (UWT/UWC). The Rosseland diffusion approximation is employed to describe the radiative heat flux. A nonsimilarity analysis is performed, and the transformed governing equations are solved by Keller box method (KBM). The effects of these major parameters of the Dufour parameter, Soret parameter, Lewis number, buoyancy ratio, power-law index of the non-Newtonian fluids, blowing/suction parameter, and thermal radiation parameter on the heat and mass transfer characteristics have been carried out. In general, for the case of blowing, both the local Nusselt number and the local Sherwood number decrease. This trend reversed for suction of fluid. The physical aspects of the problem are discussed in detail.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(3):032502-032502-11. doi:10.1115/1.4035069.

Natural convection heat transfer from vertical 5 × 5 rod bundles in liquid sodium was numerically analyzed for two types of the bundle geometry (equilateral square array (ESA) and equilateral triangle array (ETA)). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The phoenics code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 5 × 5 test rods for diameter (D = 7.6 mm), heated length (L = 200 mm), and L/d (=26.32) were used in this work. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, (Rf,L)ij and (Rf,L)5×5,S/D, ranging from 3.08 × 104 to 4.19 × 107 (q = 1 × 104–7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of S/D, which are ratios of the diameter of flow channel for bundle geometry to the rod diameter, for vertical 5 × 5 rod bundles were ranged from 1.8 to 6 on each bundle geometry. The spatial distribution of local and average Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, on vertical rods of a bundle was clarified. The average value of Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, for the two types of the bundle geometry with various values of S/D were calculated to examine the effect of the bundle geometry, S/D, (Rf,L)ij, and (Rf,L)5×5,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)5×5,S/D value under the condition of S/D = constant was examined. The correlations for (Nuav,B)5×5,S/D for two types of bundle geometry above mentioned including the effects of (Rf,L)5×5,S/D and S/D were developed. The correlations can describe the theoretical values of (Nuav,B)5×5,S/D for the two types of the bundle geometry at S/D ranging from 1.8 to 6 within −12.64% to 7.73% difference.

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2016;139(3):032601-032601-7. doi:10.1115/1.4034936.

In this study, the performance of a heat sink embedded with a porous medium and nanofluids as coolants is analyzed experimentally. The nanofluid is a mixture of de-ionized water and nanoscale Al2O3 particles with three different volumetric concentrations: ζ = 0.41%, 0.58%, and 0.83%. The experimental test section is a rectangular minichannel filled with metal foam, which is electrically heated to provide a constant heat flux. The porous medium is assumed to be homogeneous and the flow regime is laminar. The result of heat transfer enhancement by slurry of Al2O3 nanofluid in porous media is studied under various flow velocities, heat flux, porous media structure, and particle concentration of nanofluid. The effect of particles volume fraction on heat transfer coefficient is also studied. This experimental study discovers and/or confirms the following hypotheses: (1) nanoparticle slurry in conjunction with metal foam has a significant effect on heat transfer rate; (2) there is an optimum permeability for the foam resulting in maximal heat transfer rate; (3) for a fixed particle concentration, smaller particles are more effective in enhancing heat transfer; and (4) increasing particle concentration results in some gains, but this trend weakens after a threshold.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2016;139(3):032701-032701-9. doi:10.1115/1.4034814.

This work gives a brief description of the statistical model that takes into account when calculating the physical, in particular, the optical properties of some ultraporous nonmetallic high-temperature materials, the real regularities of the material structure, and the physical properties of substances constituting the material. For the spectral part of the model, some tests are presented, confirming its adequacy. The simulation of the spectra and the scattering of monochromatic radiation pattern by using the representative elements of the model and the material as a whole are carried out. It is found that despite the fact that the scattering pattern based on the use of representative elements of a material can be approximated by the classical distributions, this is not true for the material as a whole. Calculations of the angular scattering probability density of the materials are carried out, and the approximations of obtained distributions that extend the class of modeling scattering phase functions (SPF) are proposed.

Commentary by Dr. Valentin Fuster

### Research Papers: Max Jakob Award Paper

J. Heat Transfer. 2016;139(3):033001-033001-9. doi:10.1115/1.4035006.

Traditionally, the numerical computation of particle motion in a fluid is resolved through computational fluid dynamics (CFD). However, resolving the motion of nanoparticles poses additional challenges due to the coupling between the Brownian and hydrodynamic forces. Here, we focus on the Brownian motion of a nanoparticle coupled to adhesive interactions and confining-wall-mediated hydrodynamic interactions. We discuss several techniques that are founded on the basis of combining CFD methods with the theory of nonequilibrium statistical mechanics in order to simultaneously conserve thermal equipartition and to show correct hydrodynamic correlations. These include the fluctuating hydrodynamics (FHD) method, the generalized Langevin method, the hybrid method, and the deterministic method. Through the examples discussed, we also show a top-down multiscale progression of temporal dynamics from the colloidal scales to the molecular scales, and the associated fluctuations, hydrodynamic correlations. While the motivation and the examples discussed here pertain to nanoscale fluid dynamics and mass transport, the methodologies presented are rather general and can be easily adopted to applications in convective heat transfer.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2016;139(3):034501-034501-4. doi:10.1115/1.4034796.
OPEN ACCESS

A generalized enhanced Fourier law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables is derived from the Boltzmann transport equation. It generalizes the previously reported EFL from a gray phonon population to an arbitrary quasi-ballistic phonon mode population, the chief advantage being its formulation in terms of observables like the heat flux and temperature, in a manner akin to the Fourier law albeit rigorous enough to describe quasi-ballistic phonon transport.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;139(3):034502-034502-4. doi:10.1115/1.4034902.

A mathematical model describing the homogeneous–heterogeneous reactions in the vicinity of the forward stagnation point of a cylinder immerged in a nanofluid is established. We assume that the homogeneous reaction is given by isothermal cubic autocatalator kinetics, while the heterogeneous reaction is chosen as first-order kinetics. The existence of multiple solutions through hysteresis bifurcations is discussed in detail for the various diffusion coefficients of reactant and autocatalyst.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;139(3):034503-034503-5. doi:10.1115/1.4035039.

A boundary layer analysis is laid out for the steady, laminar, mixed convection flow past an isothermal vertical cone embedded in a porous medium filled with a nanofluid. The model used for the nanofluid is one which includes the effects of Brownian motion and thermophoresis. A parametric study is performed for different physical parameters, such as magnetic (M), cone angle (m), mixed convection (χ), Brownian motion (Nt), and thermophoresis (Nb), on the velocity, temperature, and nanoparticle concentration profiles. The local Nusselt, Sherwood, and nanoparticle Sherwood number have been laid out in a graphical way. The dependency of the rate of heat and mass transfer on the governing parameters has been discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;139(3):034504-034504-6. doi:10.1115/1.4035016.

The results of a numerical investigation on the effects of the temperature dependence of viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight ducts of constant cross sections are used to obtain new correlations for the axial distributions of the peripherally averaged local Nusselt number. Three different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (square) ducts. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. A superposition method is applied to obtain the values of the peripherally averaged local Nusselt number by separately considering the effects of temperature-dependent viscosity and those of temperature-dependent thermal conductivity.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;139(3):034505-034505-6. doi:10.1115/1.4035017.

In this technical brief, the application of infrared thermal imaging to investigate melting of a phase-change material (PCM) filled in an open-cell metal foam was proposed. Melting experiments in a rectangular cell were performed with paraffin/copper foam composite samples having a single pore size of 15 ppi. The visualized study at the pore-scale was enabled using an infrared video camera equipped with a macrolens, offering a resolution of 50 μm. The transient thermal imaging results were first validated against the temperature readings by a pre-installed thermocouple. A relative deviation below 4% was observed between the two methods over the entire course of melting. The local thermal nonequilibrium between a copper ligament and its surrounding paraffin was found to become more pronounced as melting proceeds, which could reach up to the order of 10 °C during the late stage of melting. The quantitative observation of the local thermal nonequilibrium effect may facilitate improvement of the existing two-temperature models for numerical simulations on melting of PCM enhanced by embedding metal foams.

Commentary by Dr. Valentin Fuster