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### Research Papers: Conduction

J. Heat Transfer. 2010;132(7):071301-071301-11. doi:10.1115/1.4000947.

A one-dimensional, steady-state model of a triangular microheat pipe (MHP) is developed, with the main purpose of investigating the thermal effects of the solid wall on the heat transport capacity of an MHP. The energy equation of the solid wall is solved analytically to obtain the axial temperature distribution, the average of which over the entire length of the MHP is simply its operating temperature. Next, the liquid phase is coupled with the solid wall by a heat transfer coefficient. Then, the continuity, momentum, and energy equations of the liquid and vapor phases are, together with the Young–Laplace equation, solved numerically to yield the heat and fluid flow characteristics of the MHP. The heat transport capacity and the associated optimal charge level of the working fluid are predicted for different operating conditions. Comparison between the models with and without a solid wall reveals that the presence of the solid wall induces a change in the phase change heat transport by the working fluid, besides facilitating axial heat conduction in the solid wall. The analysis also highlights the effects of the thickness and thermal conductivity of the solid wall on its axial temperature distribution. Finally, while the contribution of the thermal effects of the solid wall on the heat transport capacity of the MHP is usually not dominant, it is, nevertheless, not negligible either.

Commentary by Dr. Valentin Fuster

### Research Papers: Electronic Cooling

J. Heat Transfer. 2010;132(7):071401-071401-9. doi:10.1115/1.4000951.

A numerical analysis of forced convective heat transfer from an elliptical pin fin heat sink with and without metal foam inserts is conducted using three-dimensional conjugate heat transfer model. The pin fin heat sink model consists of six elliptical pin rows with 3 mm major diameter, 2 mm minor diameter, and 20 mm height. The Darcy–Brinkman–Forchheimer and classical Navier–Stokes equations, together with corresponding energy equations are used in the numerical analysis of flow field and heat transfer in the heat sink with and without metal foam inserts, respectively. A finite volume code with point implicit Gauss–Seidel solver in conjunction with algebraic multigrid method is used to solve the governing equations. The code is validated by comparing the numerical results with available experimental results for a pin fin heat sink without porous metal foam insert. Different metallic foams with various porosities and permeabilities are used in the numerical analysis. The effects of air flow Reynolds number and metal foam porosity and permeability on the overall Nusselt number, pressure drop, and the efficiency of heat sink are investigated. The results indicate that structural properties of metal foam insert can significantly influence on both flow and heat transfer in a pin fin heat sink. The Nusselt number is shown to increase more than 400% in some cases with a decrease in porosity and an increase in Reynolds number. However, the pressure drop increases with decreasing permeability and increasing Reynolds number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):071402-071402-14. doi:10.1115/1.4000978.

Computational fluid dynamics/heat transfer (CFD/HT) methods are too time consuming and costly to examine the effect of multiple design variables on the system thermal performance, especially for systems with multiple components and interacting physical phenomena. In this paper, a proper orthogonal decomposition (POD) based reduced order thermal modeling approach is presented for complex convective systems. The basic POD technique is used with energy balance equations, and heat flux and/or surface temperature matching to generate a computationally efficient thermal model in terms of the system design variables. The effectiveness of the presented approach is studied through application to an air-cooled data center cell with a floor area of $23.2 m2$ and a total power dissipation of 240 kW, with multiple turbulent convective components and five design variables. The method results in average temperature rise prediction error of $1.24°C$ (4.9%) for different sets of design variables, while it is $∼150$ times faster than CFD/HT simulation. Also, the effects of the number of available algebraic equations and retained POD modes on the accuracy of the obtained thermal field are studied.

Commentary by Dr. Valentin Fuster

### Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2010;132(7):071501-071501-9. doi:10.1115/1.4000975.

Experiments are performed to investigate saturation boiling of degassed PF-5060 dielectric liquid on microporous copper dendrite surface layers deposited on $10×10 mm2$ Cu substrates. The electrochemically deposited surface layers are of different thicknesses ($145.6 μm$, $46.3 μm$, and $33.1 μm$). The thickest layer gives the best results: the saturation CHF of $25.27 W/cm2$ occurs at a surface superheat of only 2.9 K and the maximum nucleate boiling heat transfer coefficient, $hMNB$, near the end of the fully developed nucleate boiling region, is $8.76 W/cm2 K$. In addition, nucleate boiling ensues at a surface temperature slightly above saturation $(<0.5 K)$, with no temperature excursion. The temperature excursions before initiating boiling on the $46.3 μm$ and $33.1 μm$ thick Cu nanodendrite surface layers are small (3.7 K and 6 K), corresponding to surface temperatures of $∼55.1°C$ and $57.4°C$, respectively. These temperatures are much lower than recommended $(85°C)$ for reliable operation of most silicon electronics and central processor units.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2010;132(7):071701-071701-10. doi:10.1115/1.4000061.

Laminar forced convection flow past an in-line elliptical cylinder array with inclination is simulated using the finite element method. The inclination of the elliptical cylinders is increased with the number of the cylinder in the array, 0 deg for the first cylinder and 90 deg for the last cylinder. The global objective of this research is to enhance the heat transfer out of the cylinders. A parametric study of heat exchanges between the cylinders and flow (expressed by the Nusselt number) is reported for Reynolds numbers between 125 and 1000, while the Prandtl number is fixed at 0.71. The results are compared with an elliptical cylinder array without inclination to assess the heat transfer enhancement. The problem is solved as transient, and a vortex shedding phenomenon is reported. The results indicated that the Reynolds number has a significant effect on the heat transfer out of the cylinders, and the inclination of the elliptical cylinders enhances heat transfer rate up to 238.59%, but pressure drop is increased as high as 700%. Also, skin-friction coefficient along the five cylinders’ perimeter, plots of the velocity flow field, and temperature contours are presented.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):071702-071702-10. doi:10.1115/1.4000986.

Heat transfer and pressure drop have been experimentally investigated in an equilateral triangular channel $(Dh=1.83 cm)$, which can be used to simulate the internal cooling passage near the leading edge of a gas turbine blade. Three different rib configurations (45 deg, inverted 45 deg, and 90 deg) were tested at four different Reynolds numbers (10,000–40,000), each with five different rotational speeds (0–400 rpm). The rib pitch-to-height $(P/e)$ ratio is 8 and the height-to-hydraulic diameter $(e/Dh)$ ratio is 0.087 for every rib configuration. The rotation number and buoyancy parameter achieved in this study were 0–0.58 and 0–2.3, respectively. Both the rotation number and buoyancy parameter have been correlated with predict the rotational heat transfer in the ribbed equilateral triangular channel. For the stationary condition, staggered 45 deg angled ribs show the highest heat transfer enhancement. However, staggered 45 deg angled ribs and 90 deg ribs have the higher comparable heat transfer enhancement at rotating condition near the blade leading edge region.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Exchangers

J. Heat Transfer. 2010;132(7):071801-071801-9. doi:10.1115/1.4000988.

The impact of a vortex-generation technique for air-side heat-transfer improvement is experimentally investigated through full-scale wind-tunnel testing of a plain-fin round-tube heat exchanger under dry-surface conditions. Inspired by the formation locomotion of animals in nature, a new vortex generator (VG) array deployed in a “V” is proposed in the present work, aiming to create constructive interference between vortices. The array is composed of two delta-winglet pairs and placed at an attack angle of 10 deg or 30 deg. Its effectiveness is compared with a baseline configuration and two conventional single-pair designs placed at 30 deg, a small pair with half the area of the array and a large pair with the same area as the array. The frontal air velocity considered ranges from 2.3 m/s to 5.5 m/s, corresponding to a Reynolds number range based on the hydraulic diameter of 1400–3400. The experimental results show little impact of the 10 deg array and a moderate heat-transfer improvement of up to 32% for the small pair, both introducing additional pressure loss of approximately 20–40%. For the 30 deg array and the large pair, similar augmentation of 25–55% in air-side heat-transfer coefficient is obtained accompanied by average pressure drop penalties of 90% and 140%, respectively. Performance evaluation using the criteria of the modified area goodness factor and the volume goodness factor indicates the superiority of the heat exchanger enhanced by the 30 deg array among all the investigated VGs. The VG array is found more effective at comparatively low Reynolds numbers, representative of many heating, ventilation, air-conditioning, and refrigeration applications and compact heat-exchanger designs.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2010;132(7):072401-072401-12. doi:10.1115/1.4001100.

Fluid flow in microchannels has some characteristics, which one of them is rarefaction effect related with gas flow. In the present work, hydrodynamically and thermally fully developed laminar forced convection heat transfer of a rarefied gas flow in two microgeometries is studied, namely, microannulus and parallel plate microchannel. The rarefaction effects are taken into consideration using first-order slip velocity and temperature jump boundary conditions. Viscous heating is also included for either the wall heating or the wall cooling case. Closed form expressions are obtained for dimensionless temperature distribution and Nusselt number. The results demonstrate that for both geometries, as Brinkman number increases, the Nusselt number decreases. However, the effect of viscous heating on the Nusselt number at greater values of Knudsen number becomes insignificant. In the absence of viscous heating, increasing values of Knudsen number lead to smaller values of Nusselt number. Furthermore, it is observed that viscous heating causes singularities in Nusselt number values. Also, asymmetry causes singularities in Nusselt numbers of both microannulus walls and the parallel plate wall having lower heat flux, even in the absence of viscous heating. For parallel plate microchannel, in the absence of viscous heating, Nusselt number of the wall having larger heat flux is an increasing function of the wall heat fluxes ratio.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):072402-072402-9. doi:10.1115/1.4000965.

This paper reports on experimental and computational investigations into the thermal performance of microelectromechanical systems (MEMS) as a function of the pressure of the surrounding gas. High spatial resolution Raman thermometry was used to measure the temperature profiles on electrically heated, polycrystalline silicon bridges that are nominally $10 μm$ wide, $2.25 μm$ thick, and either $200 μm$ or $400 μm$ long in nitrogen atmospheres with pressures ranging from 0.05 Torr to 625 Torr (6.67 Pa–83.3 kPa). Finite element modeling of the thermal behavior of the MEMS bridges is performed and compared with the experimental results. Noncontinuum gas effects are incorporated into the continuum finite element model by imposing temperature discontinuities at gas-solid interfaces that are determined from noncontinuum simulations. The results indicate that gas-phase heat transfer is significant for devices of this size at ambient pressures but becomes minimal as the pressure is reduced below 5 Torr. The model and experimental results are in qualitative agreement, and better quantitative agreement requires increased accuracy in the geometrical and material property values.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):072403-072403-6. doi:10.1115/1.4000987.

In times comparable to the characteristic time of the energy carriers, Fourier’s law of heat conduction breaks down and heat may propagate as waves. Based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics, according to the Einstein’s mass-energy relation, the phonon gas in the dielectrics is described as a weighty, compressible fluid. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, because the drift velocity of a phonon gas is normally much less than the speed of light. The propagation velocity of the thermal wave in the phonon gas is derived directly from the equation of state for the phonon gas, rather than from the relaxation time in the Cattaneo–Vernotte (CV) model (Cattaneo, C., 1948, “Sulla Conduzione Del Calore,” Atti Semin. Mat. Fis. Univ. Modena, 3, pp. 83–101; Vernotte, P., 1958, “Paradoxes in the Continuous Theory of the Heat Equation,” C. R. Acad. Bulg. Sci., 246, pp. 3154–3155). The equation of motion for the phonon gas gives rise to the thermomass model, which depicts the general relation between the temperature gradient and heat flux. The linearized conservation equations for the phonon gas lead to a damped thermal wave equation, which is similar to the CV-wave equation, but with different characteristic time. The lagging time in the resulting thermal wave equation is related to the wave velocity in the phonon gas, which is approximately two orders of magnitude larger than the relaxation time adopted in the CV-wave model for the lattices. A numerical example for fast transient heat conduction in a silicon film is presented to show that the temperature peaks resulting from the thermomass model are much higher than those resulting from the CV-wave model. Due to the slower thermal wave velocity in the phonon gas, by as much as one order of magnitude, the damage due to temperature overshooting may be more severe than that expected from the CV-wave model.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2010;132(7):072701-072701-12. doi:10.1115/1.4000948.

A detailed theoretical analysis has been carried out to study efficient microwave assisted heating of thermoplastic (Nylon 66) slabs via polymer-ceramic-polymer composite attached with ceramic plate at one side. The ceramic layer or plate is chosen as $Al2O3$ or SiC. The detailed spatial distributions of power and temperature are obtained via finite element simulation. It is found that uniform heating with enhanced processing rate may occur with specific thickness of $Al2O3$ composite, whereas SiC composite leads to enhanced processing rate with higher thermal runaway for thick Nylon samples attached with $Al2O3$ plate. SiC composite is effective due to enhanced processing rate, whereas $Al2O3$ is not effective due to reduced processing rate for thin samples attached with $Al2O3$ plate. For samples attached with SiC plate, thermal runaway is reduced by SiC composite, whereas that is not reduced by Alumina composite. Current study recommends efficient heating methodologies for thermoplastic substances with ceramic composite to achieve a higher processing rate with uniform temperature distribution.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):072702-072702-6. doi:10.1115/1.4000974.

A ray-tracing method is presented for numerically determining radiative view factors in complex three-dimensional geometries. This method uses a set of “primitive” shapes to approximate the required geometry together with a Monte Carlo simulation to track the fate of randomized rays leaving each surface. View factors were calculated for an operational fiber drawing furnace using both numerical integration and ray-tracing methods. Calculated view factor profiles were essentially identical above a ray density of $105$ per unit area. Run times for the ray-tracing method were considerable longer, although the setup time to describe a new geometry is very short and essentially independent of system complexity.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):072703-072703-8. doi:10.1115/1.4000994.

Reduced models for radiative heat transfer analysis through anisotropic medium are presented and evaluated. The models include two equivalent heat transfer models through isotropic medium using isotropic or Henyey–Greenstein scattering phase functions with arithmetic or weighted means radiative properties calculated over all incident direction and an anisotropic model with directional radiative properties coupled to an isotropic scattering phase function or directional anisotropically scattering phase function. The pertinence of the models is investigated by solving coupled conduction/radiation heat transfer through a slab of anisotropic fibrous medium with fiber randomly oriented in the plan parallel to the boundaries. Good agreements on heat fluxes and thermal conductivity are obtained for reduced anisotropic models and for reduced equivalent isotropic models with weighted mean radiative properties.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):072704-072704-7. doi:10.1115/1.4000995.

A methodology is proposed, which is capable of determining the near field thermal radiation based on the Wiener chaos expansion. The approach has no explicit constraints on the geometry and temperature distributions of the system and can be easily included with classical electrodynamics simulations. A specific application is made for the near field thermal radiation between two plates and the results are in very good agreement with the classical solutions obtained from Green’s function method. Also, by comparing the resulting solutions with the solutions from Green’s function method, a new point of view for interpreting the results for the near field thermal radiation in terms of a chaos expansion is provided.

Commentary by Dr. Valentin Fuster

### Max Jakob Award Paper

J. Heat Transfer. 2010;132(7):073001-073001-17. doi:10.1115/1.4000703.
FREE TO VIEW

This paper deals with the distribution of airflow and the resulting cooling in a data center. First, the cooling challenge is described and the concept of a raised-floor data center is introduced. In this arrangement, cooling air is supplied through perforated tiles. The flow rates of the cooling air must meet the cooling requirements of the computer servers placed next to the tiles. These airflow rates are governed primarily by the pressure distribution under the raised floor. Thus, the key to modifying the flow rates is to influence the flow field in the under-floor plenum. Computational fluid dynamics (CFD) is used to provide insight into various factors affecting the airflow distribution and the corresponding cooling. A number of ways of controlling the airflow distribution are explored. Then attention is turned to the above-floor space, where the focus is on preventing the hot air from entering the inlets of computer serves. Different strategies for doing this are considered. The paper includes a number of comparisons of measurements with the results of CFD simulations.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Heat Transfer. 2010;132(7):074501-074501-3. doi:10.1115/1.4000710.

Preliminary experimental results of forced convection by octadecane paraffin (encapsulating phase-change material (EPCM)) particles, acrylonitrile butadiene styrene plastic particles, or by clear (of particulates) water flowing through a heated parallel-plates channel are reported. The objective is to investigate the mixing effect of the particles vis-à-vis the latent heat effect. The particle concentration is kept at 3% in volume. The results, in terms of surface-averaged channel temperature and heat transfer coefficient for different fluid speed and heat-flux, indicate the mixing effect to account from 19% to 68% of the heat transfer enhancement produced by using EPCM particles. Hence particle mixing, even at a very low particle concentration, is an effective convection mechanism.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):074502-074502-4. doi:10.1115/1.4000950.

A new neural network modeling approach to the evaporator performance under dry and wet conditions has been developed. Not only the total cooling capacity but also the sensible heat ratio and pressure drops on both air and refrigerant sides are modeled. Since the evaporator performance under dry and wet conditions is, respectively, dominated by the dry-bulb temperature and the web-bulb temperature, two neural networks are used together for capturing the characteristics. Training of a multi-input multi-output neural network is separated into training of multi-input single-output neural networks for improving the modeling flexibility and training efficiency. Compared with a well-developed physics-based model, the standard deviations of trained neural networks under dry and wet conditions are less than 1% and 2%, respectively. Compared with the experimental data, errors fall into $±5%$.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2010;132(7):074503-074503-4. doi:10.1115/1.4001125.

The onset of convection in a horizontal layer of a cellular porous material heated from below is investigated. The problem is formulated as a combined conductive-convective-radiative problem in which radiative heat transfer is treated as a diffusion process. The problem is relevant to cellular foams formed from plastics, ceramics, and metals. It is shown that the variation of conductivity with temperature above that of the cold boundary leads to an increase in the critical Rayleigh number (based on the conductivity of the fluid at that boundary temperature) and an increase in the critical wave number. On the other hand, the critical Rayleigh number based on the conductivity at the mean temperature decreases with increase in the thermal variation parameter if the radiative contribution to the effective conductivity is sufficiently large compared with the nonradiative component.

Commentary by Dr. Valentin Fuster