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### Bio-Heat and Mass Transfer

J. Heat Transfer. 2012;134(7):071101-071101-7. doi:10.1115/1.4006100.

This paper discusses the effects of magnetic field and heat and mass transfer on the peristaltic flow of an incompressible fluid in a channel with compliant walls. Mathematical formulation for the fourth grade fluid is presented. Relations of stream function, temperature, concentration field, and heat transfer coefficient are derived. The variations of the interesting parameters entering into the problem are carefully analyzed.

Commentary by Dr. Valentin Fuster

### Conduction

J. Heat Transfer. 2012;134(7):071301-071301-6. doi:10.1115/1.4006103.

This paper considers the numerical optimization of the shape of cavities that intrude into a cylindrical solid body. The objective is to minimize the global thermal resistance between the solid body and the cavities. Internal heat generating is distributed uniformly throughout the solid body. The cavities are isothermal, while the solid body has adiabatic conditions on the outer surface. The total volume is fixed. The cavities are rectangular, with fixed volume and variable aspect ratio. The number of cavities of the conducting body, N, is a design parameter. The optimized geometry and performance are reported graphically as functions of the ratio between the volume of the cavities and the total volume, $φ0$, and N. The paper shows an example of the application of optimal distribution of imperfections principle. The results indicate that the optimal distribution of the hot spots is affected not only by the complexity of the configuration (larger N) but also by the area of cavities fraction φ0 .

Commentary by Dr. Valentin Fuster

### Evaporation, Boiling, and Condensation

J. Heat Transfer. 2012;134(7):071501-071501-9. doi:10.1115/1.4006164.

Metallic porous structures have proved to be effective in enhancing heat transfer due to the inherent characteristics such as high specific surface area and large pore densities. In this study, structured-porous fins were built from plain weaved copper wire mesh screens. Seven test articles were made, with pore hydraulic diameter varying from 214 μm to 48 μm. Boiling experiments were conducted with Isopentane, a highly wetting fluid, flowing through the porous fin. The tested system pressure varies from 2 bars to 5 bars, and the channel Reynolds number from 2000 to 10,000. Influences of system pressure, flow rate, and pore sizes (mesh number) on flow boiling performance were investigated. The mechanisms for the influences were discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071502-071502-11. doi:10.1115/1.4006097.

Heat transfer coefficients and bubble motion characteristics are reported for two-phase water flow in an array of 13 equally spaced microchannels over an area of 1 cm2 . Each channel has Dh  = 451 ± 38 μm, W/H = 0.8, and L/Dh  = 22.2. Uniform heat flux is applied through the base, and wall temperatures are determined from the thermocouple readings corrected for heat conduction effects. The upper surface is insulated and transparent. Single-phase heat transfer coefficients are in a good agreement with comparable trends of existing correlations for developing flow and heat transfer, although a difference is seen due to the insulated upper surface. Two-phase heat transfer coefficients and flow characteristics are determined for 221 < G < 466 kg/m2 s and 250 < q < 1780 kW/m2 . Heat transfer coefficients normalized with mass flux exhibit a trend comparable to that of available studies that use similar thermal boundary conditions. Flow visualization shows expanding vapor slug flow as the primary flow regime with nucleation and bubbly flow as the precursors. Analysis of bubble dynamics reveals ∼t1/3 dependence for bubble growth. Flow reversal is observed and quantified, and different speeds of the vapor phase fronts are quantified at the leading and trailing edges of vapor slugs once the bubble diameter equals the channel width. Bubble formation, growth, coalescence, and detachment at the outlet of the array are best characterized by the Weber number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071503-071503-7. doi:10.1115/1.4006099.

The thermophysical properties pertaining to the impingement of a nano-droplet onto a solid surface were investigated using molecular dynamics (MD) simulations. The MD simulations used data collection for an entire group of molecules to investigate the propagation of energy in the system. Simulations of a moving nano-droplet colliding with a stationary solid were performed to determine the heat transfer between the droplet and the surface. It was discovered that the droplet-substrate collision caused the droplet temperature to rise significantly upon impact. The substrate also experiences a temperature jump with a slower response time. A theoretical relation for the substrate temperature jump is also developed that shows reasonable agreement with the MD simulations for small droplet diameters. Increasing the diameter of the droplet from 2.0 nm to 4.5 nm showed a gain in the total added substrate kinetic energy. Varying the initial speed of the droplet from 10 m/s to 40 m/s showed no significant difference in the applied kinetic energy onto the substrate, suggesting that the acceleration of the droplet toward the surface due to intermolecular interactions produces an impact speed relatively independent of the initial droplet bulk speed. These trends were also reflected in a thermodynamically based simple theoretical prediction of collision energy, which was shown to be accurate for droplet diameters up to 3.5 nm. The collision energy was estimated to be on the order of 1–10 eV, and the applied heat flux is on the order of GW/m2 .

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071504-071504-13. doi:10.1115/1.4006113.

Dynamic wetting behaviors of water droplet on the modified surface were investigated experimentally. Dynamic contact angles were measured as a characterization method to explain the extraordinary pool boiling critical heat flux (CHF) enhancement on the zirconium surface by anodic oxidation modification. The sample surface is rectangular zirconium alloy plates (20 × 25 × 0.7 mm), and 12 μl of deionized water droplets were fallen from 40 mm of height over the surface. Dynamic wetting movement of water on the surface showed different characteristics depending on static contact angle (49.3 deg–0 deg) and surface temperature (120 °C–280 °C). Compared with bare surface, wettable and spreading surface had no-receding contact angle jump and seemed stable evaporating meniscus of liquid droplet in dynamic wetting condition on hot surface. This phenomenon could be explained by the interaction between the evaporation recoil and the surface tension forces. The surface tension force increased by micro/nanostructure of the modified zirconium surface suppresses the vapor recoil force by evaporation which makes the water layer unstable on the heated surface. Thus, such increased surface force could sustain the water layer stable in pool boiling CHF condition so that the extraordinary CHF enhancement could be possible.

Commentary by Dr. Valentin Fuster

### Forced Convection

J. Heat Transfer. 2012;134(7):071701-071701-9. doi:10.1115/1.4006165.

This paper focuses on the magnetohydrodynamic (MHD) slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physically pure exponential type solution ceases to exist. In the case of the presence of multiple solutions, closed-form formulae for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walter’s liquid B fluids. Heat transfer analyzes are also carried out for two general types of boundary heating processes, either by a prescribed quadratic power law surface temperature or by a prescribed quadratic power law surface heat flux. The flow field is affected by the presence of several physical parameters, whose influences on the unique/multiple solutions of velocity and temperature profiles, and Nusselt numbers are examined and discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071702-071702-9. doi:10.1115/1.4006014.

This paper reports on the prediction of heat transfer in a fully developed turbulent flow in a straight rotating channel with blowing and suction through opposite walls. The channel is rotated about its spanwise axis; a mode of rotation that amplifies the turbulent activity on one wall and suppresses it on the opposite wall leading to reverse transition at high rotation rates. The present predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using a differential Reynolds-stress transport closure. A number of alternative formulations for the difficult fluctuating pressure–strain correlations term were assessed. These included a high turbulence Reynolds-number formulation that required a “wall-function” to bridge the near-wall region as well as three alternative low Reynolds-number formulations that permitted integration through the viscous sublayer, directly to the walls. The models were assessed by comparisons with experimental data for flows in channels at Reynolds-numbers spanning the range of laminar, transitional, and turbulent regimes. The turbulent heat fluxes were modeled via two very different approaches: one involved the solution of a modeled differential transport equation for each of the three heat-flux components, while in the other, the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. The results for rotating channels with wall suction and blowing show that the algebraic model, when properly extended to incorporate the effects of rotation, yields results that are essentially identically to those obtained with the far more complex and computationally intensive heat-flux transport closure. This outcome argues in favor of incorporation of the algebraic model in industry-standard turbomachinery codes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071703-071703-10. doi:10.1115/1.4006110.

A numerical study has been carried out to understand and highlight the effects of axial wall conduction in a conjugate heat transfer situation involving simultaneously developing laminar flow and heat transfer in a square microchannel with constant flux boundary condition imposed on bottom of the substrate wall. All the remaining walls of the substrate exposed to the surroundings are kept adiabatic. Simulations have been carried out for a wide range of substrate wall to fluid conductivity ratio (ksf  ∼ 0.17–703), substrate thickness to channel depth (δsf  ∼ 1–24), and flow rate (Re ∼ 100–1000). These parametric variations cover the typical range of applications encountered in microfluids/microscale heat transfer domains. The results show that the conductivity ratio, ksf is the key factor in affecting the extent of axial conduction on the heat transport characteristics at the fluid–solid interface. Higher ksf leads to severe axial back conduction, thus decreasing the average Nusselt number ($Nu¯$). Very low ksf leads to a situation which is qualitatively similar to the case of zero-thickness substrate with constant heat flux applied to only one side, all the three remaining sides being kept adiabatic; this again leads to lower the average Nusselt number ($Nu¯$). Between these two asymptotic limits of ksf , it is shown that, all other parameters remaining the same (δsf and Re), there exists an optimum value of ksf which maximizes the average Nusselt number ($Nu¯$). Such a phenomenon also exists for the case of circular microtubes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071704-071704-13. doi:10.1115/1.4006114.

This work is devoted to the numerical investigation of heat and fluid flow past a sphere with a centric, cylindrical bore. Such spherical rings are of interest in many technological processes. In chemical reactors, for example, spherical rings are used as a catalyst with an increased reacting surface. Motivated by this fact, we considered spherical rings with different bores and different orientations in flow regimes corresponding to Reynolds numbers from 10 up to 300. The results show a significant influence of the bore diameter on the symmetry and hence the steadiness of the flow field. The Nusselt number can be increased, which leads to a moderate rise in the drag coefficient. Thereby, the effect of the borehole depends on the Reynolds number, the bore diameter, and the angle of attack. For that reason, drag forces and total heat transfers do not simply follow the heat exchanging surface area. Based on the presented results, new correlations are given for both the drag coefficient and the Nusselt number; correlations which incorporate the bore geometry and the bore orientation in the flow field.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071705-071705-7. doi:10.1115/1.4006112.

We introduce a new method of solution for the convective heat transfer under forced laminar flow that is confined by two parallel plates with a distance of 2a or by a circular tube with a radius of a. The advection–conduction equation is first mapped onto the boundary. The original problem of solving the unknown field $T(x,r,t)$ is reduced to seek the solutions of T at the boundary (r = a or r = 0, r is the distance from the centerline shown in Fig. 1), i.e., the boundary functions $Ta(x,t)≡T(x,r=a,t)$ and/or $T0(x,t)≡T(x,r=0,t)$. In this manner, the original problem is significantly simplified by reducing the problem dimensionality from 3 to 2. The unknown field $T(x,r,t)$ can be eventually solved in terms of these boundary functions. The method is applied to the convective heat transfer with uniform wall temperature boundary condition and with heat exchange between flowing fluids and its surroundings that is relevant to the geothermal applications. Analytical solutions are presented and validated for the steady-state problem using the proposed method.

Commentary by Dr. Valentin Fuster

### Heat Exchangers

J. Heat Transfer. 2012;134(7):071801-071801-8. doi:10.1115/1.4006102.

This paper presents a double-tube once-through steam generator (DOTSG) consisting of the outer straight tube and the inner helical tube. The tube length and pressure drop of are important parameters in optimal design of DOTSG. For optimal design of such a system, it was modeled to estimate its tube length and pressure drop. Pitch of inner helical tube, flow distribution ratio of the primary fluid, and tube assemblage are considered as design parameters. Then fast and elitist nondominated sorting genetic algorithm-II (NSGA-II) method was applied to find the optimum values of design parameters. In the presented optimal design approach, the tube length and the total pressure drop are two objective functions. The results of optimal designs were a set of multiple optimum solutions, called “Pareto optimal solutions.” The sensitivity analysis of change in optimum tube length and pressure drop with change in design parameters of the DOTSG is also performed and the results are reported.

Commentary by Dr. Valentin Fuster

### Heat Transfer Enhancement

J. Heat Transfer. 2012;134(7):071901-071901-10. doi:10.1115/1.4006008.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):071902-071902-9. doi:10.1115/1.4006098.

A numerical study was conducted to investigate the effects of dimple depth on the flow and heat transfer characteristics in a pin fin-dimple channel, where dimples are located spanwisely between the pin fins. The study aimed at promoting the understanding of the underlying convective heat transfer mechanisms in the pin fin-dimple channels and improving the cooling design for the gas turbine components. The flow structure, friction factor, and heat transfer performance of the pin fin-dimple channels with various dimple depths have been obtained and compared with each other for the Reynolds number range of 8200–80,800. The study showed that, compared to the pin fin channel, the pin fin-dimple channels have further improved convective heat transfer performance, and the pin fin-dimple channel with deeper dimples shows relatively higher Nusselt number values. The study still showed a dimple depth-dependent flow friction performance for the pin fin-dimple channels compared to the pin fin channel, and the pin fin-dimple channel with shallower dimples shows relatively lower friction factors over the studied Reynolds number range. Furthermore, the computations showed the detailed characteristics in the distribution of the velocity and turbulence level in the flow, which revealed the underlying mechanisms for the heat transfer enhancement and flow friction reduction phenomenon in the pin fin-dimple channels.

Commentary by Dr. Valentin Fuster

### Porous Media

J. Heat Transfer. 2012;134(7):072601-072601-8. doi:10.1115/1.4006035.

Predicting the thermal conductivity of loose-fill fibrous thermal insulation is a complex problem, when considering the combined conduction, convection, and radiation heat transfer within a scattering, emitting, and absorbing medium. A piecewise model for predicting the overall apparent thermal conductivity of large diameter opaque fibrous materials was developed by considering the radiation heat transfer, solid conduction and air conduction components separately. The model utilized the physical parameters of emissivity, the density of the solid fiber material, the percentage composition and range of fiber diameter, and the mean fiber diameter to develop specific equations for piecewise contribution from radiation, solid fiber conduction, and air conduction toward the overall effective thermal conductivity. It can be used to predict the overall apparent thermal conductivity for any opaque fibrous specimen of density (ρ), known thickness (t), mean temperature (T), and temperature gradient (ΔΤ). Thermal conductivity measurements were conducted in accordance with ASTM C518 specifications on 52 mm thick, 254 mm square test specimens for coconut and sugarcane fibers. The test apparatus provided results with an accuracy of 1%, repeatability of 0.2%, and reproducibility of 0.5%. The model was applied to and compared with experimental data for coconut and sugarcane fiber specimens and predicted the apparent thermal conductivity within 7% of experimental data over the density range tested. The model also predicted the optimum density range for both coconut and sugarcane fibers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):072602-072602-11. doi:10.1115/1.4006104.

A porous media approach based on the volume-averaging theory has been proposed to investigate solute diffusion and ultrafiltration processes associated with hemodialysis using a hollow fiber membrane dialyzer. A general set of macroscopic governing equations has been derived for the three individual phases, namely, the blood phase, the dialysate phase, and the membrane phase. Thus, conservations of mass, momentum, and species are considered for blood compartments, dialysate compartments, and membranes within a dialyzer to establish a three concentration equation model. These macroscopic equations can be simultaneously solved for the various cases of inlet velocities of blood and dialysate. An analytic expression for the solute clearance was obtained for the one-dimensional case, in which important dimensionless parameters controlling the dialyzer system are identified for the first time.

Commentary by Dr. Valentin Fuster

J. Heat Transfer. 2012;134(7):072701-072701-9. doi:10.1115/1.4006088.

There have been growing interests in selective control of thermal emission by using micro/nanostructures. The present study describes direct measurements of infrared thermal emission at elevated temperatures of an asymmetric Fabry–Perot resonator at variable angles for each polarization. The multilayered structure mainly contains a SiO2 optical cavity sandwiched between a thick (opaque) Au film and a thin Au film. Metallic adhesive and diffusion-barrier layers were deposited on a Si substrate before depositing the thick Au film. A dielectric protection layer was deposited atop the thin Au film to prevent oxidation at high temperatures. A SiC wafer was used as the reference to test the emittance measurement facility, which includes a heated sample holder, a blackbody source, mirror assembly, a polarizer, and a Fourier-transform infrared spectrometer with different detectors. The measured emittance spectra of the Fabry–Perot structure exhibit peak broadening and shifting as temperature increases; the mechanisms are elucidated by comparison with theoretical modeling.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Heat Transfer. 2012;134(7):074501-074501-4. doi:10.1115/1.4006034.

For understanding and accurately modeling combustion, the important questions are what species are present in the flame, and the spatial distribution and temperature of these species. Traditional optical methods used only the electromagnetic waves in the wavelength region from the ultraviolet region up to the infrared. Terahertz time-domain spectroscopy technique can be used for the combustion research as a novel tool. However, for some sooty combustion environments, the strong absorption, spectral interference from soot scattering, and fluorescence from large molecules must be considered. The optical properties of soot in the terahertz domain are the main basic data for terahertz application. In this paper, the terahertz time-domain spectroscopy technique was used to study the optical properties of flame soot within 0.2–1.6 THz. The complex refractive indices of the soot were deduced by the fixed-point iteration method. In order to validate the results, the complex refractive indices of the soot from the four different fuel flames were deduced. It was found that the complex refractive indices in the terahertz domain of the soot from the different fuel flames are very close to each other. The comparisons of complex refractive indices between the visible–IR domain and the terahertz domain indicate that the value of absorption index in terahertz domain is smaller than in IR domain, which implies that the terahertz wave will penetrate the sooty flame with smaller absorption than the IR rays. The results can provide the basic optical data of flame soot for the application of terahertz time-domain spectroscopy technique in the optical combustion diagnostics and extend the optical combustion diagnostics application area.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):074502-074502-4. doi:10.1115/1.4006111.

An experimental investigation of an oscillating heat pipe (OHP) with a superhydrophobic inner surface coated with a superhydrophobic self-assembled monolayer (SAM) of n-octadecyl mercaptan was conducted. The experimental results show that the oscillating motion in an OHP with a superhydrophobic surface can be generated and the OHP can function well. This is very different from the conventional wicked heat pipe, which cannot function if the inner surface is hydrophobic. The functionality of a superhydrophobic OHP is not sensitive to the wetting condition of the inner surface of the OHP. The investigation results in a better understating of heat transfer mechanism occurring in an OHP.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2012;134(7):074503-074503-4. doi:10.1115/1.4006160.

In this paper, we study the steady state heat transfer process within a spatial domain of the transporting medium whose length is of the same order as the distance traveled by thermal waves. In this study, the thermal conductivity is defined as a function of a spatial variable. This is achieved by analyzing an effective thermal diffusivity that is used to match the transient temperature behavior in the case of heat wave propagation by the result obtained from the Fourier theory. Then, combining the defined size-dependent thermal conductivity with Fourier’s law allows us to study the behavior of the heat flux at nanoscale and predict that a decrease of the size of the transporting medium leads to an increase of the heat transfer coefficient which reaches its finite maximal value, contrary to the infinite value predicted by the classical theory. The upper limit value of the heat transfer coefficient is proportional to the ratio of the bulk value of the thermal conductivity to the characteristic length of thermal waves in the transporting medium.

Commentary by Dr. Valentin Fuster

### Errata

J. Heat Transfer. 2012;134(7):077001-077001-1. doi:10.1115/1.4005738.
FREE TO VIEW

In the paper of Duan [1], there is an error in the range of the Prandtl number (Pr) for Eqs. (14) and (15). The correlations of Notter and Sleicher [2], Eqs. (14) and (15), are valid for 0.004 < Pr < 0.1 not 0.04 < Pr < 0.1.

Commentary by Dr. Valentin Fuster