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### IN APPRECIATION

J. Heat Transfer. 2011;133(9):090401-090401-1. doi:10.1115/1.4004329.
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On behalf of the ASME Heat Transfer Division, I wish to express our deepest appreciation to Yogesh Jaluria for his dedicated service and excellent leadership as Editor of the ASME Journal of Heat Transfer from 2005 to 2010. Since he started as an Associate Technical Editor of the JHT beginning in 1993, his high standards, attention to detail, and creative ideas were readily recognized by his peers. When he assumed the role as Editor of the JHT in 2005, his dedication, vision, and leadership has helped the Journal to become one of the most renowned ASME Journals and widely read heat transfer publications worldwide. The impact and visibility of the JHT has grown significantly under his leadership, and as representative of the ASME heat transfer community, I cannot express enough gratitude and appreciation to Yogesh Jaluria for his dedicated service to the ASME Heat Transfer Division throughout his professional career.

Commentary by Dr. Valentin Fuster

### Research Papers: Conduction

J. Heat Transfer. 2011;133(9):091301-091301-9. doi:10.1115/1.4003814.

In this work, transient heat transport in a flat layered system, with interface thermal resistance, is analyzed, under the approach of the Cattaneo–Vernotte hyperbolic heat conduction model using the thermal quadrupole method. For a single semi-infinite layer, analytical formulas useful in the determination of its thermal relaxation time as well as its thermal effusivity are obtained. For a composite-layered system, in the long time regime and under a Dirichlet boundary condition, the well-known effective thermal resistance formula and a novel expression for the effective thermal relaxation time are derived, while for a Neumann problem, only a heat capacity identity is found. In contrast in the short time regime, under both Dirichlet and Neumann conditions, an expression that involves the effective thermal diffusivity and relaxation time as a function of the time is derived. In this time regime and under the Fourier approach, a formula for the effective thermal diffusivity in terms of the time, the thermal properties of the individual layers and its interface thermal resistance is obtained. It is shown that these results can be useful in the development of experimental methodologies to perform the thermal characterization of materials in the time domain.

Commentary by Dr. Valentin Fuster

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

J. Heat Transfer. 2011;133(9):091501-091501-10. doi:10.1115/1.4003901.

The objectives of this study are (i) to determine the transient phase redistributions of a two-phase flow in a smooth horizontal annular channel by applying high voltage pulses to induce electric fields and (ii) to quantify the resultant changes in the condensation heat transfer. The experiments were performed using refrigerant R-134a flowing in the annular channel that was cooled on the outside by a counter-current flow of water. The electric fields are established by applying high voltage to a concentric rod electrode inside a grounded tube. The effect of the electrohydrodynamic (EHD) forces on the changes to the initial stratified/stratified wavy flow pattern was visualized using a high speed camera. The EHD effect results in the redistribution of the liquid–vapor phase within the channel and unique flow structures, such as twisted liquid cones and entrained droplets, are observed. These structures only appear during the initial application of EHD and are absent in the steady state. Experiments were performed using a 8 kV pulse width modulated (PWM) signal with duty cycles ranging from 0% to 100% to evaluate the heat transfer and pressure drop characteristics of the transient EHD flow patterns. The resultant heat transfer increased with the duty cycle to approximately 2.7-fold at a mass flux of 45–55 kg/m2 s and 1.2-fold at a mass flux of 110 kg/m2 s. The enhancement was higher as the pulse width was increased.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):091502-091502-9. doi:10.1115/1.4003924.

The behavior of cryogenic nitrogen in a room-temperature evaporator six meters long is analyzed. Trapezoid fins are employed to enhance the heat flux supplied by the environment. The steady-state governing equations specified by the mixed parameters are derived from the conservations of momentum and energy. The initial value problem is solved by space integration. The fixed ambient conditions are confirmed by way of the meltback effect. An integrated model is utilized to analyze the convective effect of two-phase flow, which dominates the evaporation behavior. Another integrated model is employed to determine the total heat flux from the environment to the wet surface of the evaporator. The foundation of the formation of an ice layer surrounding the evaporator is presented. If the fin height is shorter than 0.5 $m$, the whole evaporator is surrounded by ice layer. If the fin height is longer than 0.5 $m$, the total pressure drop of nitrogen in the tube is negligible. The outlet temperature is always within the range between −12 °C and 16 °C for the evaporator with the fin height of 1.0 $m$. For the evaporator with dry surface, the nitrogen has the outlet temperature less than the ambient temperature at least by 5 °C.

Commentary by Dr. Valentin Fuster

### Research Papers: Experimental Techniques

J. Heat Transfer. 2011;133(9):091601-091601-9. doi:10.1115/1.4003827.

A confined jet impingement configuration has been investigated in which the matter of interest is the convective heat transfer from the air flow to the passage walls. The geometry is similar to gas turbine blade cooling applications. The setup is distinct from usual cooling passages by the fact that no crossflow and no bulk flow directions are present. The flow exhausts through two staggered rows of holes opposing the impingement wall. Hence, a complex 3-D vortex system arises, which entails a complex heat transfer situation. The transient thermochromic liquid crystal (TLC) method was used in previous studies to measure the heat transfer on the passage walls. Due to the nature of these experiments, the fluid as well as the wall temperature vary with location and time. As a prerequisite of the transient TLC technique, the heat transfer coefficient is assumed to be constant over the transient experiment. Therefore, it is the scope of this article to qualify this assumption and to validate the results at discrete locations. For this purpose, fast response surface thermocouples and heat flux sensors were applied, in order to gain information on the temporal evolution of the wall heat fluxes. The linear relation between heat flux and temperature difference could be verified for all measurement sites. This validates the assumption of a constant heat transfer coefficient. Nusselt number evaluations from independent techniques show a good agreement, considering the respective uncertainty ranges. For all investigated sites, the Nusselt numbers range within ±9% of the values gained from the TLC measurement.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2011;133(9):091701-091701-10. doi:10.1115/1.4003968.

The present investigation considers the fully developed electro-osmotic flow of power-law fluids in a planar microchannel subject to constant wall heat fluxes. Using an approximate velocity distribution, closed form expressions are obtained for the transverse distribution of temperature and Nusselt number. The approximate solution is found to be quite accurate, especially for the values of higher than ten for the dimensionless Debye-Huckel parameter where the exact values of Nusselt number are predicted. The results demonstrate that a higher value of the dimensionless Debye-Huckel parameter is accompanied by a higher Nusselt number for wall cooling, whereas the opposite is true for wall heating case. Although to increase the dimensionless Joule heating term is to decrease Nusselt number for both pseudoplastic and dilatant fluids, nevertheless its effect on Nusselt number is more pronounced for dilatants. Furthermore, to increase the flow behavior index is to decrease the Nusselt number for wall cooling, whereas the contrary is right for the wall heating case. Depending on the value of flow parameters, a singularity is observed in the Nusselt number values of the wall heating case.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):091702-091702-13. doi:10.1115/1.4003828.

We investigate the effectiveness of the optimal homotopy asymptotic method (OHAM) in solving nonlinear systems of differential equations. In particular we consider the heat transfer flow of a third grade fluid between two heated parallel plates separated by a finite distance. The method is successfully applied to study the constant viscosity models, namely plane Couette flow, plane Poiseuille flow, and plane Couette–Poiseuille flow for velocity fields and the temperature distributions. Numerical solutions of the systems are also obtained using a finite element method (FEM). A comparative analysis between the semianalytical solutions of OHAM and numerical solutions by FEM are presented. The semianalytical results are found to be in good agreement with numerical solutions. The results reveal that the OHAM is precise, effective, and easy to use for such systems of nonlinear differential equations.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Transfer Enhancement

J. Heat Transfer. 2011;133(9):091901-091901-6. doi:10.1115/1.4003829.

Heat transfer characteristics of baffled channel flow, where thin baffles are mounted on both channel walls periodically in the direction of the main flow, have been numerically investigated in a laminar range. The main objectives of the present study are to find the physical reason responsible for the heat transfer enhancement in finned heat exchangers, and to identify the optimal configurations of the baffles to achieve the most efficient heat removal from the channel walls. Two key parameters are considered, namely ratio of baffle interval to channel height (RB ) and Reynolds number (Re). We performed a parametric study and found that the large-scale vortices travelling along the channel walls between the neighboring baffles, which are generated by flow separation at the tips of the baffles and become unsteady due to a Hopf bifurcation from steady to a time-periodic flow, play the key role in the heat transfer enhancement by inducing strong vertical velocity fluctuation in the vicinity of the channel walls. We also propose a contour diagram (“map”) of averaged Nusselt number on the channel walls as a function of the two parameters. The results shed light on understanding and controlling heat transfer mechanism in a finned heat exchanger, being quite beneficial to its design.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2011;133(9):092001-092001-8. doi:10.1115/1.4003900.

Hollow fiber membrane contactors are used in air dehumidification. The benefit of this technology is that the liquid desiccant is not in a direct contact with the process air; therefore, the problem of liquid droplets crossover is prevented. The equations governing the heat and moisture transfer from the air to the liquid, through the membranes, are described. An analytical solution is obtained for the dimensionless differential equations, with which the dehumidification effectiveness could be estimated by simple algebraic calculations. It provides a convenient yet accurate tool for the component design and system optimization. The model is validated by experiments. The effects of varying operating conditions on system performance are investigated. It is found that the total number of transfer units for sensible heat and the overall Lewis number are the most dominant parameters influencing heat and mass transfer.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2011;133(9):092401-092401-6. doi:10.1115/1.4003960.

Thermal rectification is a phenomenon in which transport is preferred in one direction over the opposite. Although observations of thermal rectification have been elusive, it could be useful in many applications such as thermal management of electronics and improvement of thermoelectric devices. The current work explores the possibility of thermally rectifying devices with the use of nanostructured interfaces. Interfaces can theoretically result in thermally rectifying behavior because of the difference in phonon frequency content between two dissimilar materials. The current work shows an effective rectification of greater than 25% in a device composed of two different materials divided equally by a single planar interface.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):092402-092402-11. doi:10.1115/1.4003961.

A generalized form of the ballistic-diffusive equations (BDEs) for approximate solution of the Boltzmann Transport equation (BTE) for phonons is formulated. The formulation presented here is new and general in the sense that, unlike previously published formulations of the BDE, it does not require a priori knowledge of the specific heat capacity of the material. Furthermore, it does not introduce artifacts such as media and ballistic temperatures. As a consequence, the boundary conditions have clear physical meaning. In formulating the BDE, the phonon intensity is split into two components: ballistic and diffusive. The ballistic component is traditionally determined using a viewfactor formulation, while the diffusive component is solved by invoking spherical harmonics expansions. Use of the viewfactor approach for the ballistic component is prohibitive for complex large-scale geometries. Instead, in this work, the ballistic equation is solved using two different established methods that are appropriate for use in complex geometries, namely the discrete ordinates method (DOM) and the control angle discrete ordinates method (CADOM). Results of each method for solving the BDE are compared against benchmark Monte Carlo results, as well as solutions of the BTE using standalone DOM and CADOM for two different two-dimensional transient heat conduction problems at various Knudsen numbers. It is found that standalone CADOM (for BTE) and hybrid CADOM-P1 (for BDE) yield the best accuracy. The hybrid CADOM-P1 is found to be the best method in terms of computational efficiency.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2011;133(9):092501-092501-12. doi:10.1115/1.4003902.

This paper considers the unsteady MHD free convective Couette flow of a viscous incompressible electrically conducting fluid between two parallel vertical porous plates. Both cases of the applied magnetic field being fixed either to the fluid or to the moving porous plate are considered. The solution of the governing equations has been obtained by using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert the Laplace domain to the time domain. The unified solution obtained for the velocity have been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as Prandtl number, Grashof number, and the suction/injection parameter are discussed with the aid of line graphs. The skin friction have been seen to decrease with both suction and injection on the surface of the moving plate when the channel is being cooled, while on the stationary plate, the magnitude of the skin friction increases with injection.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):092502-092502-8. doi:10.1115/1.4003925.

The present work is concerned with the modeling of buoyancy-modified mixed convection flows, such flows being representative of low-flow-rate flows in the cores of Gas-cooled Reactors. Three different eddy viscosity models (EVMs) are examined using the in-house code, “CONVERT. ” All fluid properties are assumed to be constant, and buoyancy is accounted for within the Boussinesq approximation. Comparison is made against experimental measurements and the direct numerical simulations (DNS). The effects of three physical parameters including the heat loading, Reynolds number, and pipe length on heat transfer have been examined. It is found that by increasing the heat loading, three thermal-hydraulic regimes of “early onset of mixed convection,” “laminarization,” and “recovery” were present. At different Reynolds numbers, the three thermal-hydraulic regimes are also evident. The k-ε model of Launder and Sharma was found to be in the closest agreement with consistently normalized DNS results for the ratio of mixed-to-forced convection Nusselt number (Nu/Nu0 ). It was also shown that for the “laminarization” case, the pipe length should be at least “500× diameter” in order to reach a fully developed solution. In addition, the effects of two numerical parameters namely buoyancy production and Yap length-scale correction terms have also been investigated and their effects were found to be negligible on heat transfer and friction coefficient in ascending flows.

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2011;133(9):092601-092601-7. doi:10.1115/1.4003813.

This study examines the influence of Soret and Dufour effects on double diffusive free convection due to wavy vertical surface immersed in a fluid saturated semi-infinite porous medium under Darcian assumptions. A wavy to flat surface transformation is applied, and the resulting coupled nonlinear partial differential equations under Boussinesq approximation are reduced to boundary layer equations. A finite difference scheme based on the Keller-Box approach has been used in conjunction with block-tridiagonal solver for obtaining the solution for boundary layer equations. Results from the current study are compared with those available in literature. The effect of various parameters such as wave amplitude (a), Lewis number (Le), buoyancy ratio (B), and Soret (Sr) and Dufour (Df) numbers are analyzed through local and average Nusselt number, and local and average Sherwood number plots.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):092602-092602-11. doi:10.1115/1.4003969.

In this paper, combined forced and natural convection in a vertical channel containing both porous and viscous regions taking into account the influences of inertial force and viscous dissipation has been studied. In this regard, fully developed fluid flow in the porous region was modeled using the Brinkman–Forchheimer extended Darcy model. To solve governing equations of both the porous and viscous regions including thermal energy and momentum equations, a two-parameter perturbation method was applied. The velocity and temperature distributions of both the regions were obtained in terms of various parameters such as inertial force, Grashof, Reynolds, and Brinkman numbers, as well as various types of viscous dissipation models. In addition, numerical solution was conducted using finite difference method to compare the results. The predicted results clearly indicate that the type of viscous dissipation model has significant effect on the temperature and velocity distributions. The acquired knowledge in this study can be used by designers to control channel flow as suitable for a certain application.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):092603-092603-9. doi:10.1115/1.4004209.

Fully developed forced convective heat transfer in a parallel-plate channel partially filled with highly porous, open-celled metallic foam is analytically investigated. The Navier–Stokes equation for the hollow region is connected with the Brinkman–Darcy equation in the foam region by the flow coupling conditions at the porous–fluid interface. The energy equation for the hollow region and the two energy equations of solid and fluid for the foam region are linked by the heat transfer coupling conditions. The normalized closed-form analytical solutions for velocity and temperature are also obtained to predict the flow and temperature fields. The explicit expression for Nusselt number is also obtained through integration. A parametric study is conducted to investigate the influence of different factors on the flow resistance and heat transfer performance. The analytical solution can provide useful information for related heat transfer enhancement with metallic foams and establish a benchmark for similar work.

Commentary by Dr. Valentin Fuster

### Research Papers: Two-Phase Flow and Heat Transfer

J. Heat Transfer. 2011;133(9):092901-092901-7. doi:10.1115/1.4003904.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Heat Transfer. 2011;133(9):094501-094501-4. doi:10.1115/1.4003834.

A similarity solution is presented for the steady free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with nanofluids. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. For the porous medium the Darcy-Boussinesq model is employed. This solution depends on a Lewis number $Le$, a buoyancy-ratio parameter $Nr$, a Brownian motion parameter $Nb$, and a thermophoresis parameter $Nt$. The effects of these parameters on the velocity, temperature and nanoparticle fraction profiles are discussed. The dependency of the local Nusselt and Sherwood numbers on these four parameters is also investigated.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):094502-094502-6. doi:10.1115/1.4003905.

A numerical study of steady burning of spherical ethanol particles in a spray environment is presented. A spray environment is modeled as a high temperature oxidizer stream where the major products of combustion such as carbon dioxide and water vapor will be present along with reduced amounts of oxygen and nitrogen. The numerical model, which employs variable thermophysical properties, a global single-step reaction mechanism, and an optically thin radiation model, has been first validated against published experimental results for quasi-steady combustion of spherical ethanol particles. The validated model has been employed to predict the burning behavior of the ethanol particle in high temperature modified oxidizer environment. Results show that based on the amount of oxygen present in the oxidizer the burning rate constant is affected. The ambient temperature affects the burning rate constant only after a sufficient decrease in the oxygen content occurs. In pure air stream, ambient temperature variation does not affect the evaporation constant. Results in terms of burning rates, maximum temperature around the particle, and the evaporation rate constants are presented for all the cases. The variation of normalized Damköhler number is also presented to show the cases where combustion or pure evaporation would occur.

Commentary by Dr. Valentin Fuster

### Errata

J. Heat Transfer. 2011;133(9):097001-097001-1. doi:10.1115/1.4003835.
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Some corrections on citation/reference are needed in this paper, as follows:
• Page 040801-1, the citation in Line 6 from bottom (right column) should read “Refs. [5, 17, 19],” rather than “Refs. [5, 17, 18].”
• Page 040801-3, the citation in Row 5 of Table 1 should read “Wang et al.  [22],” rather than “Wang et al.  [37].”
• Page 040801-4, the citation in Row 2 of Table 2 should read “Beck et al.  [50],” rather than “Beck et al.  [52].”
• Page 040801-4, the citation in Row 3 of Table 2 should read “Chon et al.  [47],” rather than “Chon et al.  [49].”
• Page 040801-9, the citation in Line 3 above Eq. (12) should read “Refs. [22, 64, 85],” rather than “Refs. [37, 64, 85].”
• Page 040801-13, the authors of Ref. [85] should read “Prasher, R., Bhattacharya, P., and Phelan, P. E.,” rather than “Prasher, R.,”
• Figures 6(a)–6(d) should be replaced with the following ones, with some citation errors corrected:
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):097002-097002-1. doi:10.1115/1.4003836.
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The typographical errors in this paper occur in Eqs. 13,14,15 in which the Hankel function of the second kind was inadvertently denoted as the integer Bessel function. The correct notations in these equations are Display Formula

$Ψkjs~Zk∑s,n=-∞∞Fn(-i)s-nexp[i(s-n)γkj]Hs-n(ℓiRjk)Jn(ℓiRjp)$
(13)
Display Formula
$Ψj~∑nFn{ɛj+∑k≠j∑sZkexp[i(s-n)γkj+π]Hs-n(ℓiRjk)}Jn(ℓiRjp)+Ψjs$
(14)
Display Formula
$limkiRjk→∞Hs-n(kiRjk)~1/kiRjk→0$
(15)

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):097003-097003-1. doi:10.1115/1.4004210.
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There are three mistakes in typing the formula which are as follows:
• On the right hand of Eq. 4, the radiative heat flux ($∇·qr$) must be negative, but in the paper, it is positive. The correct form of Eq. 4 is as follows:Display Formula
$∂∂x(ρucpT)+∂∂y(ρvcpT)=κ(∂2T∂x2+∂2T∂y2)-∇·qr$
(4)
• In Eq. 15, Spi must be multiply by $β∀$ (Beta · Volume). Equation 15 is a well known equation in radiative heat transfer and can be found in Ref. [13]. The correct form of this equation is as follows:Display Formula
$Ipi=|ξi|AxIxii+|ηi|AyIyii+β∀Spiβ∀+|ξi|Ax+|ηi|Ay$
(15)
• In Eq. 23, in the second term on the right hand, $τ$ (Tau) must be omitted which is related to the radiative Nusselt number. The correct form of this equation is as follows:Display Formula
$Nut=Nuc+Nur=-1Θw-Θb∂Θ∂Y|Y=0+RC·θ1·θ2Θw-Θbqr*$
(23)
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(9):097004-097004-1. doi:10.1115/1.4004211.
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There are some errors in Eq. 22, Table 1, and nomenclature. The corrections of these errors are shown below:
• Display Formula
$S2z=0.5(B-Sp/cosβ)[D1-Ds+Ds-dott(tt-do)]$
(22)
• $Do/Di$ in Table 1 should be $Do/D1$.
• $Dctl$ in the nomenclature should be deleted and following revisions should be made:
• $D1$ = inside diameter of the shell, m.
• $Do$ = outside diameter of the shell, m.
• $Ds$ = diameter of the tube bundle, m.
Commentary by Dr. Valentin Fuster