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Research Papers: Conduction

J. Heat Transfer. 2015;137(7):071301-071301-11. doi:10.1115/1.4029774.

In order to better manage computational requirements in the study of thermal conduction with short-scale heterogeneous materials, one is motivated to arrange the thermal energy equation into an accurate and efficient form with averaged properties. This should then allow an averaged temperature solution to be determined with a moderate computational effort. That is the topic of this paper as it describes the development using multiple-scale analysis of an averaged thermal energy equation based on Fourier heat conduction for a heterogeneous material with isotropic properties. The averaged energy equation to be reported is appropriate for a stationary or moving solid and three-dimensional heat flow. Restrictions are that the solid must display its heterogeneous properties over short spatial and time scales that allow averages of its properties to be determined. One distinction of the approach taken is that all short-scale effects, both moving and stationary, are combined into a single function during the analytical development. The result is a self-contained form of the averaged energy equation. By eliminating the need for coupling the averaged energy equation with external local problem solutions, numerical solutions are simplified and made more efficient. Also, as a result of the approach taken, nine effective averaged thermal conductivity terms are identified for three-dimensional conduction (and four effective terms for two-dimensional conduction). These conductivity terms are defined with two types of averaging for the component material conductivities over the short-scales and in terms of the relative proportions of the short-scales. Numerical results are included and discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(7):071302-071302-7. doi:10.1115/1.4029775.

We develop a computational framework, based on the Boltzmann transport equation (BTE), with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path (MFP) distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with the frequency-dependent (FD) approach. Second, when the MFP distribution is available from theoretical models, our approach allows one to include easily the material dispersion in the calculations without discretizing the phonon frequencies for all polarizations thereby reducing considerably computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multiscale method that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon MFP distributions length. After validating our model against the FD approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has the potential to advance high-efficiency thermoelectric devices.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(7):071303-071303-9. doi:10.1115/1.4029820.

Silicon films of submicrometer thickness play a central role in many advanced technologies for computation and energy conversion. Numerous thermal conductivity data for silicon films are available in the literature, but they are mainly for the lateral, or in-plane, direction for both polycrystalline and single crystalline films. Here, we use time-domain thermoreflectance (TDTR), transmission electron microscopy, and semiclassical phonon transport theory to investigate thermal conduction normal to polycrystalline silicon (polysilicon) films of thickness 79, 176, and 630 nm on a diamond substrate. The data agree with theoretical predictions accounting for the coupled effects of phonon scattering on film boundaries and defects related to grain boundaries. Using the data and the phonon transport model, we extract the normal, or cross-plane thermal conductivity of the polysilicon (11.3 ± 3.5, 14.2 ± 3.5, and 25.6 ± 5.8 W m−1 K−1 for the 79, 176, and 630 nm films, respectively), as well as the thermal boundary resistance between polysilicon and diamond (6.5–8 m2 K GW−1) at room temperature. The nonuniformity in the extracted thermal conductivities is due to spatially varying distributions of imperfections in the direction normal to the film associated with nucleation and coalescence of grains and their subsequent columnar growth.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2015;137(7):071501-071501-9. doi:10.1115/1.4029969.

The effect of a variety of surface enhancements on the heat transfer achieved with an array of impinging jets is experimentally investigated using the dielectric fluid HFE-7100 at different volumetric flow rates. The performance of a 5 × 5 array of jets, each 0.75 mm in diameter, is compared to that of a single 3.75 mm diameter jet with the same total open orifice area, in single-and two-phase operation. Four different target copper surfaces are evaluated: a baseline smooth flat surface, a flat surface coated with a microporous layer, a surface with macroscale area enhancement (extended square pin–fins), and a hybrid surface on which the pin–fins are coated with the microporous layer; area-averaged heat transfer and pressure drop measurements are reported. The array of jets enhances the single-phase heat transfer coefficients by 1.13–1.29 times and extends the critical heat flux (CHF) on all surfaces compared to the single jet at the same volumetric flow rates. Additionally, the array greatly enhances the heat flux dissipation capability of the hybrid coated pin–fin surface, extending CHF by 1.89–2.33 times compared to the single jet on this surface, with a minimal increase in pressure drop. The jet array coupled with the hybrid enhancement dissipates a maximum heat flux of 205.8 W/cm2 (heat input of 1.33 kW) at a flow rate of 1800 ml/min (corresponding to a jet diameter-based Reynolds number of 7800) with a pressure drop incurred of only 10.9 kPa. Compared to the single jet impinging on the smooth flat surface, the array of jets on the coated pin–fin enhanced surface increased CHF by a factor of over four at all flow rates.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(7):071502-071502-7. doi:10.1115/1.4029818.

We semi-analytically capture the effects of evaporation and condensation at menisci on apparent thermal slip lengths for liquids suspended in the Cassie state on ridge-type structured surfaces using a conformal map and convolution. An isoflux boundary condition is prescribed at solid–liquid interfaces and a constant heat transfer coefficient or isothermal one at menisci. We assume that the gaps between ridges, where the vapor phase resides, are closed systems; therefore, the net rates of heat and mass transfer across menisci are zero. The reduction in apparent thermal slip length due to evaporation and condensation relative to the limiting case of an adiabatic meniscus as a function of solid fraction and interfacial heat transfer coefficient is quantified in a single plot. The semi-analytical solution method is verified by numerical simulation. Results suggest that interfacial evaporation and condensation need to be considered in the design of microchannels lined with structured surfaces for direct liquid cooling of electronics applications and a quantitative means to do so is elucidated. The result is a decrease in thermal resistance relative to the predictions of existing analyses which neglect them.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2015;137(7):071701-071701-12. doi:10.1115/1.4029817.

The overall film cooling performance of three novel film cooling holes has been numerically investigated in this paper, including adiabatic film cooling effectiveness, heat transfer coefficients as well as discharge coefficients. The novel holes were proposed to help cooling injection spread laterally on a cooled endwall surface. Three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations with shear stress transport (SST) k-ω turbulence model were solved to perform the simulation based on turbulence model validation by using the relevant experimental data. Additionally, the grid independent test was also carried out. With a mainstream Mach number of 0.3, flow conditions applied in the simulation vary in a wide range of blowing ratio from 0.5 to 2.5. The coolant-to-mainstream density ratio (DR) is fixed at 1.75, which can be more approximate to real typical gas turbine applications. The numerical results for the cylindrical hole are in good agreement with the experimental data. It is found that the flow structures and temperature distributions downstream of the cooling injection are significantly changed by shaping the cooling hole exit. For a low blowing ratio of 0.5, the three novel shaped cooling holes present similar film cooling performances with the traditional cylindrical hole, while with the blowing ratio increasing, all the three novel cooling holes perform better, of which the bean-shaped hole is considered to be the best one in terms of the overall film cooling performance.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(7):071702-071702-8. doi:10.1115/1.4029821.

This paper presents an experimental study of the heat transfer and pressure drop characteristics of a single phase high heat flux microchannel cooling system with spiraling radial inflow. The heat sink provides enhanced heat transfer with a simple inlet and outlet design while providing uniform flow distribution. The system is heated from one conducting wall made of copper and uses water as a working fluid. The microchannel has a 1 cm radius and a 300 μm gap height. Experimental results show, on average, a 76% larger pressure drop compared to an analytic model for laminar flow in a parallel disk system with spiral radial inflow. The mean heat transfer coefficients measured are up to four times the heat transfer coefficient for unidirectional laminar fully developed flow between parallel plates with the same gap height. Flow visualization studies indicate the presence of secondary flows and the onset of turbulence at higher flow rates. Combined with the thermally developing nature of the flow, these characteristics lead to enhanced heat transfer coefficients relative to the laminar parallel plate values. Another beneficial feature of this device, for high heat flux cooling applications, is that the thermal gradients on the surface are small. The average variation in surface temperature is 18% of the total bulk fluid temperature gain across the device. The system showed promising cooling characteristics for electronics and concentrated photovoltaics applications with a heat flux of 113 W/cm2 at a surface temperature of 77 °C and a ratio of pumping power to heat rate of 0.03%.

Commentary by Dr. Valentin Fuster

Research Papers: Heat Exchangers

J. Heat Transfer. 2015;137(7):071801-071801-8. doi:10.1115/1.4029819.

An experimental study has been carried out to investigate the convective heat transfer and pressure drop characteristics of microencapsulated phase change material (MPCM) slurry in a coil heat exchanger (CHX). The thermal and fluid properties of the MPCM slurries were determined using a differential scanning calorimeter (DSC) and a rotating drum viscometer, respectively. The overall heat transfer coefficient and pressure drop of slurries at 4.6% and 8.7% mass fractions were measured using an instrumented CHX. A friction factor correlation for MPCM slurry in the CHX has been developed in terms of Dean number and mass fraction of the MPCM. The effects of flow velocity and mass fraction of MPCM slurry on thermal performance have been analyzed by taking into account heat exchanger effectiveness and the performance efficiency coefficient (PEC). The experimental results showed that using MPCM slurry should improve the overall performance of a conventional CHX, even though the MPCM slurries are characterized by having high viscosity.

Commentary by Dr. Valentin Fuster

Research Papers: Melting and Solidification

J. Heat Transfer. 2015;137(7):072301-072301-10. doi:10.1115/1.4029035.

Development of the solid–liquid interface, distribution of the particle concentration field, as well as the development of thermosolutal convection during solidification of colloidal suspensions in a differentially heated cavity are investigated. The numerical model is based on the one-fluid mixture approach combined with the single-domain enthalpy porosity model for phase change, and it is implemented in fluent software package. The linear dependence of the liquidus and solidus temperatures with the concentration of the nanoparticles was assumed. A colloidal suspension consisting of water and copper or alumina nanoparticles were considered. In the current investigation, the nanoparticle size selected was 5 and 2 nm. The suspension was solidified unidirectionally inside a square differentially heated cavity that was cooled from the left side. It was found that the solid–liquid interface changed its morphology from a planar shape to a dendritic one as the solidification process proceeds in time, due to the constitutional supercooling that resulted from the increased concentration of particles at the solid–liquid interface rejected from the crystalline phase. Initially, the flow consisted of two vortices rotating in opposite directions. However, at later times, only one counter clockwise rotating cell survived. Changing the material of the particle to alumina resulted in crystallized phase with a higher concentration of particles. If it is compared to that of the solid phase resulted from freezing the copper–water colloidal suspension. Decreasing the segregation coefficient destabilizes the solid–liquid interface and increases the intensity of the convection cell with respect to that of the case of no particle rejection. At slow freezing rates, the resulting crystal phase consisted of lower particle content compared to the case of higher freezing rate.

Commentary by Dr. Valentin Fuster

Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2015;137(7):072401-072401-8. doi:10.1115/1.4029913.

Atomistic simulations of carbon nanotubes (CNTs) in a liquid environment are performed to better understand thermal transport in CNT-based nanofluids. Thermal conductivity is studied using nonequilibrium molecular dynamics (MD) methods to understand the effective conductivity of a solvated CNT combined with a novel application of Hamilton–Crosser (HC) theory to estimate the conductivity of a fluid suspension of CNTs. Simulation results show how the presence of the fluid affects the CNTs ability to transport heat by disrupting the low-frequency acoustic phonons of the CNT. A spatially dependent use of the Irving–Kirkwood relations reveals the localized heat flux, illuminating the heat transfer pathways in the composite material. Model results can be consistently incorporated into HC theory by considering ensembles of CNTs and their surrounding fluid as being present in the liquid. The simulation-informed theory is shown to be consistent with existing experimental results.

Commentary by Dr. Valentin Fuster

Research Papers: Porous Media

J. Heat Transfer. 2015;137(7):072601-072601-8. doi:10.1115/1.4029816.

A numerical study of the natural convection flow in a porous cavity with wavy bottom and top walls having sinusoidal temperature distributions on vertical walls filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation and the Buongiorno's nanofluid model. The boundary-value problem has been solved numerically on the basis of a second-order accurate finite difference method. Efforts have been focused on the effects of five types of influential factors such as the Rayleigh (Ra = 10–300) and Lewis (Le = 1–1000) numbers, the buoyancy-ratio parameter (Nr = 0.1–0.4), the Brownian motion parameter (Nb = 0.1–0.4), and the thermophoresis parameter (Nt = 0.1–0.4) on the fluid flow and heat transfer characteristics. It has been found that the average Nusselt and Sherwood numbers are increasing functions of the Rayleigh number, buoyancy- ratio parameter, and thermophoresis parameter, and decreasing functions of the Lewis number and Brownian motion parameter.

Commentary by Dr. Valentin Fuster

Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2015;137(7):072701-072701-7. doi:10.1115/1.4029814.

The spherical harmonics (PN) method, especially its lowest order, i.e., the P1 or differential approximation, enjoys great popularity because of its relative simplicity and compatibility with standard models for the solution of the (overall) energy equation. Low-order PN approximations perform poorly in the presence of strongly nonisotropic intensity distributions, especially in optically thin situations within nonisothermal enclosures (due to variation in surface radiosities across the enclosure surface, causing rapid change of irradiation over incoming directions). A previous modification of the PN approximation, i.e., the modified differential approximation (MDA), separates wall emission from medium emission to reduce the nonisotropy of intensity. Although successful, the major drawback of this method is that the intensity at the walls is set to zero into outward directions, while incoming intensity is nonzero, resulting in a discontinuity at grazing angles. To alleviate this problem, a new approach, termed here the “advanced differential approximation (ADA),” is developed, in which the directional gradient of the intensity at the wall is minimized. This makes the intensity distribution continuous for the P1 method and mostly continuous for higher-order PN methods. The new method is tested for a 1D slab and concentric spheres and for a 2D medium. Results are compared with the exact analytical solutions for the 1D slab as well as the Monte Carlo-based simulations for 2D media.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Heat Transfer. 2015;137(7):074501-074501-7. doi:10.1115/1.4029878.

This paper aims to present numerical solutions for the problem of steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous media exposed to constant uniform temperature and concentration in the cylinder and in the media surface. A square finite domain 3 × 3 and acceptance criterion converged solution with an absolute error under 1 × 10−3 were considered to obtain results presented. The Patankar's power law for approaching of variables calculated T, C, and ϕ also was adopted. In order of method validation, an investigation of mesh points number as function of Ra, Le, and N was done. A finite volume scheme has been used to predict the flow, temperature, and concentration distributions at any space from a heat cylinder buried into a fluid-saturated porous medium for a bipolar coordinates system. Examples presented show that the differences in the flow distribution caused not only when Rayleigh number range is considered but also when Lewis number range is considered. Further, increase in the Rayleigh number has a significant influence in the flow distribution when the concentration distribution is considered. Steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous medium is studied numerically using the finite volume method. To model fluid flow inside the porous medium, the Darcy equation is used. Numerical results are obtained in the form of streamlines, isotherms, and isoconcentrations. The Rayleigh number values range from 0 to 1000, the Lewis number values range from 0 to 100, and the buoyancy ratio number is equal to zero. Calculated values of average heat transfer rates agree reasonably well with values reported in the literature.

Commentary by Dr. Valentin Fuster

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