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### RESEARCH PAPERS: Forced Convection

J. Heat Transfer. 2005;128(3):217-225. doi:10.1115/1.2150836.

An integral analysis of hydrodynamics and heat transfer in a thin liquid film flowing over a rotating disk surface is presented for both constant temperature and constant heat flux boundary conditions. The model is found to capture the correct trends of the liquid film thickness variation over the disk surface and compare reasonably well with experimental results over the range of Reynolds and Rossby numbers covering both inertia and rotation dominated regimes. Nusselt number variation over the disk surface shows two types of behavior. At low rotation rates, the Nusselt number exhibits a radial decay with Nusselt number magnitudes increasing with higher inlet Reynolds number for both constant wall temperature and heat flux cases. At high rotation rates, the Nusselt number profiles exhibit a peak whose location advances radially outward with increasing film Reynolds number or inertia. The results also compare favorably with the full numerical simulation results from an earlier study as well as with the reported experimental results.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):226-233. doi:10.1115/1.2150832.

A rod was positioned upstream of a circular cylinder to enhance its heat transfer in an air stream. The diameter of the cylinder was $40mm$ and the diameter of the rod ranged from $1to12mm$. The distance between the axes of the cylinder and the rod was varied between 40 and $120mm$ and the Reynolds number ranged from $1.5×104$ to $6.2×104$. In the optimum configuration, the heat transfer on the front face of the cylinder increases remarkably relative to a single circular cylinder, and results in a 40% overall increase in heat transfer.

Commentary by Dr. Valentin Fuster

### RESEARCH PAPERS: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2005;128(3):234-239. doi:10.1115/1.2150833.

We have measured the thermal resistance of a $152‐nm$-diameter carbon nanofiber before and after a platinum layer was deposited on the contacts between the nanofiber and the measurement device. The contact resistance was reduced by the platinum coating for about 9–13% of the total thermal resistance of the nanofiber sample before the platinum coating. At a temperature of $300K$, the axial thermal conductivity of the carbon nanofiber is about three times smaller than that of graphite fibers grown by pyrolysis of natural gas prior to high-temperature heat treatment, and increases with temperature in the temperature range between $150K$ and $310K$. The phonon mean free path was found to be about $1.5nm$ and approximately temperature-independent. This feature and the absence of a peak in the thermal conductivity curve indicate that phonon-boundary and phonon-defect scattering dominate over phonon-phonon Umklapp scattering for the temperature range.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):240-250. doi:10.1115/1.2150834.

Nanofluids are engineered colloids made of a base fluid and nanoparticles $(1–100nm)$. Nanofluids have higher thermal conductivity and single-phase heat transfer coefficients than their base fluids. In particular, the heat transfer coefficient increases appear to go beyond the mere thermal-conductivity effect, and cannot be predicted by traditional pure-fluid correlations such as Dittus-Boelter’s. In the nanofluid literature this behavior is generally attributed to thermal dispersion and intensified turbulence, brought about by nanoparticle motion. To test the validity of this assumption, we have considered seven slip mechanisms that can produce a relative velocity between the nanoparticles and the base fluid. These are inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage, and gravity. We concluded that, of these seven, only Brownian diffusion and thermophoresis are important slip mechanisms in nanofluids. Based on this finding, we developed a two-component four-equation nonhomogeneous equilibrium model for mass, momentum, and heat transport in nanofluids. A nondimensional analysis of the equations suggests that energy transfer by nanoparticle dispersion is negligible, and thus cannot explain the abnormal heat transfer coefficient increases. Furthermore, a comparison of the nanoparticle and turbulent eddy time and length scales clearly indicates that the nanoparticles move homogeneously with the fluid in the presence of turbulent eddies, so an effect on turbulence intensity is also doubtful. Thus, we propose an alternative explanation for the abnormal heat transfer coefficient increases: the nanofluid properties may vary significantly within the boundary layer because of the effect of the temperature gradient and thermophoresis. For a heated fluid, these effects can result in a significant decrease of viscosity within the boundary layer, thus leading to heat transfer enhancement. A correlation structure that captures these effects is proposed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):251-260. doi:10.1115/1.2150837.

Geometrical effects of MEMS-based microfabricated inlet orifices on the suppression of parallel channel and upstream compressible volume instabilities commonly exhibited during flow boiling in parallel microchannels have been investigated. The heat fluxes at the onset of unstable boiling have been obtained over effective heat fluxes ranging from 9 to $614W∕cm2$ and mass fluxes from $115to389kg∕m2s$. A dimensionless parameter $M$, which accounts for the pressure drop increase imposed by the inlet restrictors, has been used to correlate the extent of flow instability suppression. It has been shown that the onset of unstable boiling asymptotically increases with $M$. At sufficiently high $M$ values, parallel channels and upstream compressible volume instabilities are completely eradicated although it gives way to another instability to develop, namely, the critical heat flux conditions. A correlation has been developed in terms of $M$ to predict the conditions leading to unstable boiling.

Commentary by Dr. Valentin Fuster

### RESEARCH PAPERS: Radiative Heat Transfer

J. Heat Transfer. 2005;128(3):261-268. doi:10.1115/1.2151196.

An exact analytical method is presented for determination of emissive as well as absorptive performance of spherical cavities having diffuse-specular reflective walls. The method presented utilizes a novel coordinate transformation technique, which provides convenient means for setting up the governing radiant exchange integral equations. These equations are then solved by the usual iterative method devized for the Fredholm integral equation of the second kind. The suggested coordinate transformation is also utilized for determination of directional absorptivity of a fully specular spherical cavity when collimated radiation enters through its mouth from a specified direction. Results show that for a spherical cavity the dependence of the apparent emissivity on the degree of specularity is high when the emissivity of the cavity wall is low, but this dependence decreases as the emissivity of the cavity wall increases. Also there are situations, unlike cases of cylindrical and conical cavities, for which the purely diffuse spherical cavity is a more efficient emitter than the purely specular cavity having an identical geometry and wall emissivity. Moreover, it is shown that the apparent directional absorptivity of specular spherical cavities having small openings becomes highly fluctuating as the direction of the incident radiation changes

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):269-282. doi:10.1115/1.2151198.

A particular inverse design problem is proposed as a benchmark for comparison of five solution techniques used in design of enclosures with radiating sources. The enclosure is three-dimensional and includes some surfaces that are diffuse and others that are specular diffuse. Two aspect ratios are treated. The problem is completely described, and solutions are presented as obtained by the Tikhonov method, truncated singular value decomposition, conjugate gradient regularization, quasi-Newton minimization, and simulated annealing. All of the solutions use a common set of exchange factors computed by Monte Carlo, and smoothed by a constrained maximum likelihood estimation technique that imposes conservation, reciprocity, and non-negativity. Solutions obtained by the various methods are presented and compared, and the relative advantages and disadvantages of these methods are summarized.

Commentary by Dr. Valentin Fuster

### RESEARCH PAPERS: Heat Transfer Enhancement

J. Heat Transfer. 2005;128(3):283-289. doi:10.1115/1.2150838.

The thermofluid-dynamic effects of ion injection from sharp metallic points added perpendicularly to the inner wire of a short horizontal annulus were experimentally investigated. A dielectric liquid (FC-72 by 3M) was weakly forced to flow in the duct, which was uniformly heated on the outer wall. A dc voltage as high as $22kV$ was applied to the inner electrode, while the heated wall was grounded. Both the laminar and the turbulent mixed-convection regimes were obtained, varying the imposed flow rate. Once an electric field is applied, the flow is dramatically modified by the jets of charged particles, which transfer their momentum to the neutral adjacent ones. Different injection strengths were obtained on the emitters, because the shape of the point tips was not controlled at the microscale. Nusselt number distributions were obtained azimuthally and longitudinally, monitoring the wall temperatures. In all cases, heat transfer turned out greatly enhanced in the proximity of the emitters, without a significant increase in pressure drop through the test section and with a negligible Joule heating, making this technique very attractive for application in compact heat exchangers.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Heat Transfer. 2005;128(3):290-294. doi:10.1115/1.2151197.

Modeling of a multicomponent droplet evaporation is investigated based on the film theory in both low- and high-pressure environments. Unlike the classical film theory, effects of blowing due to evaporation on gas-side heat and mass transfer are included through the film thicknesses. The corresponding gas-side heat and mass transfer equations are derived in terms of film thicknesses. In a high-pressure situation, the real gas behavior is considered. Based on the derived equations, a new model for multicomponent droplet evaporation is formulated and validated against the published data.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):295-301. doi:10.1115/1.2150839.

A formula is derived for the dependence of heat exchanger effectiveness on the number of transfer units for a spiral-plate heat exchanger with equal capacitance rates. The difference-differential equations that describe the temperature distributions of the two counter-flowing fluids, neglecting the effects of thermal radiation, are solved symbolically to close approximation. Provision is made for the offset inlet and exit of the hot and cold fluids at the outer periphery and for large heat transfer coefficients in the entrance regions. The peak effectiveness and the number of transfer units at which it occurs are linear functions of the maximum angle of the Archimedean spiral that describes the ducts; entrance region effects reduce both.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):302-306. doi:10.1115/1.2150840.

An apparatus for the measurement of the total hemispherical emittance and specific heat of metals has been developed. The measurement principle is based on the calorimetric technique: the sample, heated by Joule effect and placed in a vacuum chamber, exchanges radiative heat transfer with the walls of the container, kept at a relatively low temperature. Emittance is deduced from the radiative heat transfer laws at the steady state. When the heating power is switched off, the specific heat of the sample can be recovered from the time history of the sample temperature during the cooling transient. Measurements have been performed on samples of aluminum Anticorodal alloy and Inconel 718 alloy under different surface conditions in the $350–635K$ range.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):307-310. doi:10.1115/1.2150841.

Heat transfer in jet impingement is a complicated phenomenon and a general analytical solution is not available. Typical jet impingement studies are conducted experimentally and best-fit correlations are proposed (Beitelmal, Saad, and Patel [2]; Beitelmal [3]; Beitelmal, Saad, and Patel [4]; Schauer and Eustis [7]; McMurray, Myers, and Uyehara [8], Gardon and Akfirat [9]). Separate solutions for the stagnation region and the wall jet region are then combined to determine the overall heat transfer solution for the impinging jet. In this paper, stagnation and wall jet region solutions for a two-dimensional jet normally impinging on a flat surface are developed using heat transfer relations available in the literature. These solutions are analyzed and compared to previous experimental results (Beitelmal, Saad, and Patel [2]; Beitelmal [3]). The potential flow assumption is used for the fluid dynamics analysis at the stagnation region. For the wall jet region, a comparison was achieved through consideration of the classical analytical solution for parallel flow over a flat plate. Analytical solutions as well as semiempirical solutions for the stagnation region and the wall jet reported by previous investigators were also considered. Predictions for heat transfer in the stagnation region using potential flow assumptions were found to be accurate to within 20%. For the wall jet region, previous correlations predicted by McMurray, Myers, and Uyehara [8] and Nizou [10] were found to be the most accurate. At large values of $x∕D$, the heat transfer properties in the wall jet are shown to be very similar to those of a turbulent boundary layer over a flat plate. Such a simplified analysis in different regions of an impinging jet using some basic fluid dynamics assumptions can greatly facilitate a prediction of the local Nusselt number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):311-317. doi:10.1115/1.2150842.

The critical heat fluxes (CHFs) and the heat transfer coefficients (HTCs) in subcooled flow boiling were applied to a thermal analysis of the flat-plate-type divertor of a helical-type fusion experimental device, which is a Large Helical Device (LHD) located in the National Institute for Fusion Science (NIFS), Japan. The incident CHF, $qcr,inc$, for the divertor plate with the cooling tube diameter, $d$, of $10mm$ and the plate width, $w$, ranging from 16 to $30mm$ were numerically analyzed based on the measured CHFs, $qcr,sub$, and HTCs for the test tube inner diameter, $d$, of $9mm$ and the heated length, $L$, of 48 to $149mm$. The peripheral distributions of the surface heat flux and the surface temperature in the cooling tube were obtained. Numerical solutions of $qcr,inc$ become larger with a decrease in $w∕d$ at a fixed $L$. It is confirmed that the ratio of the one-side heat loading data, $qcr,inc$, to the uniform heat loading data, $qcr,sub$, can be represented as the simple equation based on the numerical solutions. The values of the $qcr,inc$ for the tube length of 50, 100, and $150mm$ were estimated with various $w∕d$ at a higher pressure.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2005;128(3):318-323. doi:10.1115/1.2098862.

The enhancement in the rate of the heat transfer resulting from rotating smooth and rough vertical cylinders, of 1.28 and $21.75μm$ average roughness, respectively, are experimentally studied. Experiments were carried out for cooling fluid Reynolds numbers from 3300 to 7800 with varying the rotational speed up to $280rpm$. Experimental runs at the stationary case showed an acceptable agreement with the theoretical values. The experimental Nusselt number values at various rotational speeds are correlated as functions of Reynolds, Weber, and Prandtl numbers for smooth and rough surfaces. The correlated equations were compared with the correlation obtained by another author. The results show that the enhancement of the heat transfer rate becomes more appreciable for low Reynolds numbers at high rotational speeds and for high Reynolds numbers at low rotational speeds. The rotation causes an enhancement in the overall heat transfer coefficient of $∼89%$ at $Re=7800$, $We=1084$, and $Pr=1.48$ for smooth surface and of $∼13.7%$ at $Re=4700$, $We=4891$, and $Pr=1.696$ for rough surface. Also, the enhancement in the heat transfer rates utilizing rotary surface becomes more pronounced for the smooth surface compared with the rough one, therefore the choice of the heat transfer surface is very important. The present work shows a reduction in the heat transfer rate below its peak value depending on the type of the heat transfer surface. It is shown that the enhancement in the heat transfer, i.e., enhancement in the Nusselt number, depends on the Weber number value and the surface type while the Nusselt number value mainly depends on the Reynolds and Prandtl numbers. Correlated equation have been developed to represent the Nusselt number values as functions of the Weber and Reynolds numbers within the stated ranges of the parameters.

Commentary by Dr. Valentin Fuster

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