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### Research Papers: Conduction

J. Heat Transfer. 2016;138(9):091301-091301-6. doi:10.1115/1.4033461.

This paper presents a numerical study for predicting the optimal spacing (OS) of decaying heat sources/sinks in a conducting medium. The optimal configuration that minimizes the overall thermal resistance between the cylinder array and surrounding medium is tracked using interpolation technique. Consequently, the dimensionless OS obtained is of the order of 0.442th power of the Fourier number (Fo) defined as a function of the decaying time constant, which differs from the 0.5th value reported in previous study. In addition, the overall thermal resistance is shown to be highly dependent on the dimensionless spacing and Fo, while the OS also depends on the array type of the cylinders. Based on the extensive numerical study, closed-form correlations are proposed for predicting the OS of decaying heat sources/sinks in both quadratic and hexagonal arrangements. These results can be widely utilized for optimally positioning heat sources/sinks with two dimensional configurations.

Commentary by Dr. Valentin Fuster

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

J. Heat Transfer. 2016;138(9):091501-091501-13. doi:10.1115/1.4033497.

We investigated the role of surface microstructures in two-phase microchannels on suppressing flow instabilities and enhancing heat transfer. We designed and fabricated microchannels with well-defined silicon micropillar arrays on the bottom heated microchannel wall to promote capillary flow for thin film evaporation while facilitating nucleation only from the sidewalls. Our experimental results show significantly reduced temperature and pressure drop fluctuation especially at high heat fluxes. A critical heat flux (CHF) of 969 W/cm2 was achieved with a structured surface, a 57% enhancement compared to a smooth surface. We explain the experimental trends for the CHF enhancement with a liquid wicking model. The results suggest that capillary flow can be maximized to enhance heat transfer via optimizing the microstructure geometry for the development of high performance two-phase microchannel heat sinks.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;138(9):091502-091502-7. doi:10.1115/1.4033352.

Studies in the literature have shown that zeotropic mixture condensation rates are lower than those predicted using a pure-fluid approach. This has been attributed to the decrease in fluid temperature that occurs with zeotropic mixtures and to the development of concentration gradients in the vapor-phase that limit the condensation heat transfer. The decrease in the apparent heat transfer coefficient is not consistent across mass fluxes, tube diameters, fluid combinations, saturation pressures, and concentrations. Several modeling techniques exist, which allow engineers to model the decrease in heat transfer rates. This study provides guidelines on when the mass transfer effects can be neglected and when it is appropriate to apply established models in the literature. A condensation database containing fluid combinations of pairs of hydrocarbons, ammonia and water, and synthetic refrigerants across large changes in operating conditions, tube diameters, and concentrations is used to validate the approach. The proposed framework predicts that the Bell and Ghaly (1973, “An Approximate Generalized Design Method for Multicomponent/Partial Condensers,” AIChE Symp. Ser., 69, pp. 72–79) approach is valid for mid- and high-reduced pressures, i.e., above 0.40, while explicitly accounting for mass transfer is necessary at lower reduced pressures, i.e., below 0.40, where the influence of the temperature glide in the Bell and Ghaly method is weighted too strongly.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;138(9):091503-091503-11. doi:10.1115/1.4033496.

Condensation enhancement was investigated for flow condensation in mini-channels. Simultaneous flow visualization and heat transfer experiments were conducted in 0.952-mm diameter mini-gaps. An open loop steam apparatus was constructed for a mass flux range of 50–100 kg/m2s and steam quality range of 0.2–0.8, and validated with single-phase experiments. Filmwise condensation was observed in the hydrophilic mini-gap; pressure drop and heat transfer coefficients were compared to the (Kim and Mudawar, 2013, “Universal Approach to Predicting Heat Transfer Coefficient for Condensing Mini/Micro-Channel Flow,” Int. J. Heat Mass Transfer, 56(1–2), pp. 238–250) correlation and prediction was very good; the mean absolute error (MAE) was 20.2%. Dropwise condensation was observed in the hydrophobic mini-gap, and periodic cycles of droplet nucleation, coalescence, and departure were found at all mass fluxes. Snapshots of six typical sweeping cycles were presented, including integrated flow visualization quantitative and qualitative results combined with heat transfer coefficients. With a fixed average steam quality ($x¯$ = 0.42), increasing mass flux from 50 to 75 to 100 kg/m2s consequently reduced average sweeping periods from 28 to 23 to 17 ms and reduced droplet departure diameters from 13.7 to 12.9 to 10.3 μm, respectively. For these cases, condensation heat transfer coefficients increased from 154,700 to 176,500 to 194,800 W/m2 K at mass fluxes of 50, 75, and 100 kg/m2 s, respectively. Increased mass fluxes and steam quality reduced sweeping periods and droplet departure diameters, thereby reducing liquid thickness and increasing heat transfer coefficients.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2016;138(9):092001-092001-12. doi:10.1115/1.4033418.

The underlying concept of the standard effectiveness-number of transfer units (NTU) model is that the effectiveness of an exchanger can be correlated to two dimensionless parameters, namely, heat capacity ratio (Cr) and NTU. However, a limitation of this model is that it cannot account for the changes in effectiveness due to changes in operating temperature and humidity of simultaneous heat and moisture exchangers, specifically liquid-to-air membrane energy exchangers (LAMEEs). The purpose of this paper is to explain the reason for this limitation and also to explore the extension of the aforementioned concept of the effectiveness-NTU model to LAMEEs. The first contribution of this paper is to demonstrate that the reason for this limitation is that one of the simplifying assumptions of the standard effectiveness-NTU model, i.e., that Cr represents the ratio between the changes in the temperatures of the two fluid streams across an exchanger, is not applicable to LAMEEs. Further analysis in this paper yields two new fundamental dimensionless parameters that are analogous to Cr, termed effective Cr and effective m*, which represent the actual ratios between the changes in the temperatures and humidity ratios of the fluid streams. Then, it is shown that models analogous to the standard effectiveness-NTU model can be used to correlate the dependency of the effectiveness of LAMEEs on the operating temperature and humidity to effective Cr and effective m*.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2016;138(9):092401-092401-7. doi:10.1115/1.4033538.

Vertically aligned carbon nanotube (CNT) arrays are promising candidates for advanced thermal interface materials (TIMs) since they possess high mechanical compliance and high intrinsic thermal conductivity. However, the overall thermal performance of CNT arrays often falls short of expectations when used as TIMs, and the underlying reasons have yet to be fully understood. In this work, the volume fraction of CNT arrays is demonstrated to be the key factor in determining the CNT array thermal transport properties. By increasing the array volume fraction, both the CNT array effective thermal conductivity and the CNT array–glass thermal contact conductance were experimentally found to increase monotonically. One interesting phenomenon is that the increasing rate of thermal conductivity is larger than that of array volume fraction. Compressive experiments verified that the CNT arrays with lower volume fractions suffer from severe buckling, which results in a further decreasing trend. By understanding the underlying reasons behind this trend, the overall thermal performance of vertically aligned CNT arrays can be further increased.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2016;138(9):094501-094501-4. doi:10.1115/1.4033460.

Forced flow of an electrically conducting Newtonian fluid due to an exponentially stretching sheet is studied numerically. Free stream velocity is present and so is suction at the sheet. The governing coupled, nonlinear, partial differential equations of flow and heat transfer are converted into coupled, nonlinear, ordinary differential equations by similarity transformation and are solved numerically using shooting method, and curve fitting on the data is done by differential transform method together with Padé approximation. Prescribed exponential order surface temperature (PEST) and prescribed exponential order surface heat flux are considered for investigation of heat transfer related quantities. The influence of Chandrasekhar number, suction/injection parameter, and freestream parameter on heat transport is presented and discussed. Coefficient of friction and heat transport is also evaluated in the study. The results are of interest in extrusions and such other processes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;138(9):094502-094502-6. doi:10.1115/1.4033419.

Peristaltic motion of couple-stress fluid with Joule heating through asymmetric channel under the effect of magnetic field is investigated. Robin-type (convective) boundary conditions are employed. The basic equations of couple-stress fluid are modeled in wave frame of reference by utilizing long wavelength and low Reynolds number approximation. Numerical solution of the resulting problem is analyzed. The effects of various parameters of interest on the velocity, pressure rise, and temperature are discussed and illustrated graphically.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2016;138(9):094503-094503-6. doi:10.1115/1.4033567.

In this paper, the control volume finite element method (CVFEM) is coupled with the weighted sum of gray gases model (WSGGM) to study the radiative heat transfer in a nongray medium. To the best of our knowledge, the CVFEM–WSGGM is applied for the first time to simulate real-gas. The accuracy of the proposed method is tested through one- and two-dimensional radiative heat transfer within an enclosure filled with a single composition (water vapor or carbon dioxide) or a mixture of H2O, CO2, and N2. Compared to the discrete ordinates method (DOM)–statistical narrow band model (SNBM), the proposed method, using the WSGG model parameters due to Smith or Farag, yields much accurate results than the zonal method (ZM)–WSGGM and DOM–WSGGM. In addition, the present method needs very less control volumes and angles, and consequently computational time, compared to the DOM and ZM coupled with WSGGM.

Commentary by Dr. Valentin Fuster