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### Research Papers: Combustion and Reactive Flows

J. Heat Transfer. 2011;133(7):071201-071201-8. doi:10.1115/1.4003531.

The combination of a hot fluid (e.g., molten metals) and a cold vaporizing fluid (e.g., water) can undergo spontaneous or externally assisted explosive interactions. Such explosions are a well-established contributor to the risk for nuclear reactors exemplified by the infamous Chernobyl accident. Once fundamentals are understood, it may be possible to not only prevent but also, more importantly, control the intensity for useful applications in the areas covering variable thrust propulsion with tailored pressure profiles, for enhancing rapid heat transfer, and also for powder metallurgy (i.e., supercooled powder production, wherein materials turn superplastic with enhanced ductility). This paper discusses results of experiments conducted with various molten metals, specifically, tin, gallium, galinstan, and aluminum interacting with water (with and without salt), and with and without noncondensable gases such as hydrogen or air. It is found that under the appropriate conditions, spontaneous and energetic phase changes can be initiated within milliseconds if the hot metal is tin or galinstan, including the timed feedback of shocks leading to chain-type reactions. Using 3–10 g of tin or galinstan, shock pressures up to 25 bars (350 psig) and mechanical power over $∼2-4 kW$ were monitored about 4 cm from the explosion zone. The interaction could be intensified more than ten folds by dropping the melt through an argon atmosphere. A slow metal quenching interaction occurring over tens of seconds could be turned explosive to transpire within milliseconds if the thermal states are within the so-called thermal interaction zone. Such explosive interactions did not transpire with gallium or aluminum due to tough oxide coatings. However, by adding $∼10 w/o$ of salt in water, molten Gallium readily exploded. It was also conclusively revealed that, for an otherwise spontaneously explosive interaction of tin-water or galinstan-water, the inclusion of trace (0.3 w/o) quantities of aluminum has a radical influence on stabilizing the system and ensuring conclusive prevention of explosion triggering. This paper compares and presents the results obtained in this study and draws analogies with industrial scale aluminum casthouse safety involving thousands of kilograms of melt. Insights are provided for enabling physics-based prevention, or, alternately, the intentional initiation of explosions.

Commentary by Dr. Valentin Fuster

### Research Papers: Conduction

J. Heat Transfer. 2011;133(7):071301-071301-6. doi:10.1115/1.4003544.

A solution to the problem of transient one-dimensional heat conduction in a finite domain is developed through the use of parametric fractional derivatives. The heat diffusion equation is rewritten as anomalous diffusion, and both analytical and numerical solutions for the evolution of the dimensionless temperature profile are obtained. For large slab thicknesses, the results using fractional order derivatives match the semi-infinite domain solution for Fourier numbers, $Fo∊[0,1/16]$. For thinner slabs, the fractional order solution matches the results obtained using the integral transform method and Green’s function solution for finite domains. A correlation is obtained to display the variation of the fractional order $p$ as a function of dimensionless time $(Fo)$ and slab thickness $(ζ)$ at the boundary $ζ=0$.

Commentary by Dr. Valentin Fuster

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

J. Heat Transfer. 2011;133(7):071501-071501-8. doi:10.1115/1.4003572.

In this article, water based carbon nanotube (CNT) nanofluids have been used as quenchants to study their effects on the heat transfer rate during immersion quenching. For this purpose, water based CNT nanofluids were prepared by dispersing CNTs with and without the use of surfactant. Quench probes with a diameter of 20 mm and a length of 50 mm were prepared from 304L stainless steel. Thermocouples were fixed at the selected location inside the quench probes and the probes were quenched in distilled water and CNT nanofluids. During quenching, time-temperature data were recorded using a data acquisition system. The heat flux and temperature at the quenched surface were estimated through the inverse heat conduction method. The computation results showed that the peak heat flux was higher by 37.5% during quenching in CNT nanofluid prepared without surfactant than that in water. However, surfactant assisted CNT nanofluid promoted a prolonged vapor phase during quenching and hindered the heat transfer rates significantly. The peak heat flux was dropped by 24.9% during quenching in CNT nanofluid prepared with surfactant as compared with its base fluid of water.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2011;133(7):071701-071701-10. doi:10.1115/1.4003570.

A two-dimensional numerical model is developed to study the effect of the turbulent Prandtl number $Prt$ on momentum and energy transport in a highly variable property flow of supercritical fluids in a vertical round tube. Both regimes of enhanced and deteriorated heat transfer have been investigated. The equations of the $Prt$ leading to the best agreement with the experiments in either regime of heat transfer were specified. The results of this study show that the increase in the $Prt$ causes the heat transfer coefficients to decrease. When the buoyancy force increases, a better agreement with the experimental data is reached if values lower than 0.9 are used for the $Prt$. A decrease in the $Prt$ values results in an increase in turbulent activities. From the effect that the $Prt$ has on heat transfer coefficients, it may be deduced that the buoyancy effects in the upward flow of a supercritical fluid lead to the decrease in the $Prt$ value and hence to the increase in the heat transfer coefficients. Furthermore, the value of the $Prt$ in the laminar viscous sublayer as expected does not have a significant effect on heat transfer rate. The effect of the turbulence model on the extent to which the $Prt$ influences the rate of heat transfer is also examined. The results obtained are shown to be valid regardless of the turbulence model used.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):071702-071702-7. doi:10.1115/1.4002596.

Stodola’s area-Mach number relation is one of the most widely used expressions in compressible flow analysis. From academe to aeropropulsion, it has found utility in the design and performance characterization of numerous propulsion systems; these include rockets, gas turbines, microcombustors, and microthrusters. In this study, we derive a closed-form approximation for the inverted and more commonly used solution relating performance directly to the nozzle area ratio. The inverted expression provides a computationally efficient alternative to solutions based on traditional lookup tables or root finding. Here, both subsonic and supersonic Mach numbers are obtained explicitly as a function of the area ratio and the ratio of specific heats. The corresponding recursive formulations enable us to specify the desired solution to any level of precision. In closing, a dual verification is achieved using a computational fluid dynamics simulation of a typical nozzle and through Bosley’s formal approach. The latter is intended to confirm the truncation error entailed in our approximations. In this process, both asymptotic and numerical solutions are compared for the Mach number and temperature distributions throughout the nozzle.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):071703-071703-7. doi:10.1115/1.4003530.

Heat transfer to objects immersed in a fluidized bed has been studied extensively across a relatively large range of geometries, though most work has looked at cylinders, a geometry important in power generation fluidized bed applications. As the power generation industry has been the primary stimulant to fluidized bed heat transfer research, very little information is available regarding geometries significant in heat treating applications. In this work, heat transfer to thin flat strips immersed in a fluidized bed is examined. This geometry is important in the steel strap manufacturing industry where many manufacturers use environmentally damaging molten lead baths to heat-treat their product. In order to determine the feasibility of a fluidized bed heat treating system as an alternative to the more hazardous lead-based process, an experimental investigation has been conducted in which Nusselt number data for flat strips with widths in the range of 6.35–25.4 mm are obtained using a laboratory-scale fluidized bed (310 mm diameter). Aluminum oxide sand particles in the range of $dp=145–330 μm$ (50–90 grit) are used as the fluidized media within the fluidized operating range from $0.15Gmf$ to approximately $10Gmf$. The strip orientation angle $θo$ was also varied to establish the position from which maximum heat transfer is obtained. It was found that a decrease in particle diameter, an increase in fluidizing rate, and an increase in sample diameter resulted in an increase in Nusselt number. It was also observed that for the smaller samples tested, a maximum Nusselt number plateau was reached, at approximately $G/Gmf=2.5$. Finally, it was shown that an increase in $θo$ (from 0 deg to 90 deg) resulted in an increase in Nusselt number. A correlation for the maximum Nusselt number was developed, providing excellent agreement within ±15%.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):071704-071704-13. doi:10.1115/1.4003604.

The effect of suction and blowing in the study of flow and heat transfer of a viscous incompressible fluid between two vertically eccentric rotating spheres is presented when the spheres are maintained at different temperatures and rotating about a common axis while the angular velocities of the spheres are arbitrary functions of time. The resulting flow pattern, temperature distribution, and heat transfer characteristics are presented for the various cases including exponential and sinusoidal angular velocities. These presentations are for various values of the flow parameters including rotational Reynolds number Re, and the blowing/suction Reynolds number $Rew$. The effects of transpiration and eccentricity on viscous torques at the inner and outer spheres are studied, too. As the eccentricity increases and the gap between the spheres decreases the viscous torque remains nearly unchanged. Results for special case of concentric spheres are obtained by letting eccentricity tend to zero.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):071705-071705-10. doi:10.1115/1.4003573.

A theoretical analysis is presented to explore the transport characteristics of electro-osmotic flow and associated heat transfer of non-Newtonian power-law fluids in a parallel plate microchannel. The formulation shows that the key parameters governing the current problem include the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), and the Joule heating parameter (ratio of Joule heating to surface heat flux). Analytical expressions are presented for velocity and temperature profiles, the friction coefficient, and the fully developed Nusselt number. In particular, closed-form solutions are obtained for several special values of the flow behavior index. The results reveal that reducing the length scale ratio tends to increase the friction coefficient, and the friction coefficient approaches infinite for slug flow. The increase in the friction coefficient due to increasing the flow behavior index is more noticeable for a smaller length scale ratio. For surface heating, increasing the flow behavior index amplifies the temperature difference between the wall and the fluid, and thus the temperature distribution broadens; while the opposite trend is observed for surface cooling with sufficiently large Joule heating parameter with negative sign. Depending on the value of Joule heating parameter, the fully developed Nusselt number can be either increased or decreased by increasing the flow behavior index and/or the length scale ratio. The effect of flow behavior index on the Nusselt number vanishes as the length scale ratio approaches zero (the limiting case for slug flow).

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):071706-071706-8. doi:10.1115/1.4003605.

A concentric micro-annular passage is a basic and important microgeometry of microfluidic-systems from simple heat exchanger to the most complicated nuclear reactors. Therefore, heat transfer characteristics of gaseous flows in concentric micro-annular tubes with constant heat flux whose value was positive or negative were numerically investigated. The slip velocity, temperature jump, and shear stress work were considered on the slip boundary conditions. The numerical methodology was based on the arbitrary-Lagrangian–Eulerian method. The computations were performed for two thermal cases. That is, the heat flux that was constant at the inner wall and outer wall was adiabatic (case 1) and the heat flux that was constant at the outer wall and the inner wall was adiabatic (case 2). Each constant heat flux of $104 Wm−2$ for the positive value and $−104 Wm−2$ for the negative value was chosen. The outer tube radius ranged from $20 μm$ to $150 μm$ with the radius ratios of 0.02, 0.05, 0.1, 0.25, and 0.5 and the ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranges from 0.1 to 0.8. The outlet pressure was fixed at the atmospheric pressure. The heat transfer characteristics in concentric micro-annular tubes were obtained. The wall and bulk temperatures with positive heat flux are compared with those of negative heat flux cases and also compared with those of the simultaneously developing incompressible flow. The results show that the Nusselt number of compressible slip flow is different from that of incompressible flow. However, the temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the heat transfer characteristics of gas slip flow in concentric micro annular tubes is proposed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):071707-071707-9. doi:10.1115/1.4003606.

The experimental work presented in this paper relates to the local convective heat transfer on the rotor surface in the airgap of a discoidal rotor stator system. The stator used in these experiments is a multiperforated disk in which an air suction due to the rotation of the rotor comes through and enters the airgap. A thermal balance equation was used to identify the local convective heat transfer coefficient, with temperatures as boundary conditions, which have been measured by infrared thermography. The influence of the suctions is discussed for an interdisk dimensionless spacing interval $G$ ranging from 0.01 to 0.16 and for Re between 129,000 and 516,000. Results are compared with precedent studies in which we obtained Nusselt numbers with a closed rotor stator system in which stator is a full disk and a rotor stator system with one hole at the stator center. It is shown that multiperforated stator can or cannot improve the rotor cooling, depending on $G$ and Re.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Exchangers

J. Heat Transfer. 2011;133(7):071801-071801-10. doi:10.1115/1.4003556.

High performance heat exchangers represent nowadays the key of success to go on with the trend of miniaturizing electronic components as requested by the industry. This numerical study, based on Bejan’s Constructal theory, analyzes the thermal behavior of heat removing fin modules, comparing their performances when operating with different types of fluids. In particular, the simulations involve air and water (as representative of gases and liquids), to understand the actual benefits of employing a less heat conductive fluid involving smaller pressure losses or vice versa. The analysis parameters typical of a Constructal description (such as conductance or Overall Performance Coefficient) show that significantly improved performances may be achieved when using water, even if an unavoidable increase in pressure losses affects the liquid-refrigerated case. Considering the overall performance: if the parameter called Relevance tends to 0, air prevails; if it tends to 1, water prevails; if its value is about 0.5, water prevails in most of the case studies.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2011;133(7):072401-072401-14. doi:10.1115/1.4003577.

A recently developed Shastry’s formalism for energy transport is used to analyze the temporal and spatial behaviors of the electron energy and heat transport in metals under delta function excitation at the surface. Comparison with Cattaneo’s model is performed. Both models show the transition between nonthermal (ballistic) and thermal (ballistic-diffusive) regimes. Furthermore, because the new model considers the discrete character of the lattice, it highlights some new phenomena, such as damped oscillations, in the energy transport both in time and in space. The energy relaxation of the conduction band electrons in metals is considered to be governed by the electron-phonon scattering, and the scattering time is taken to be averaged over the Fermi surface. Using the new formalism, one can quantify the transfer from nonthermal modes to thermal ones as energy propagates in the material and it is transformed into heat. While the thermal contribution shows a wave-front and an almost exponentially decaying behavior with time, the nonthermal part shows a wave-front and a damped oscillating behavior. Two superimposed oscillations are identified, a fast oscillation that is attributed to the nonthermal nature of energy transport at very short time scales and a slow oscillation that describes the nature of the transition from the nonthermal regime to the thermal regime of energy transport.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2011;133(7):072501-072501-10. doi:10.1115/1.4003554.

Experimental results for the natural convection in a rocking enclosure are presented. A square closed cavity heated from below and cooled from above periodically turns around of its horizontal symmetry central line. The oscillation amplitude was from −15 deg to 15 deg, and four time periods were employed (30 min, 60 min, 90 min, and 120 min) for three established Rayleigh numbers ($3×104$, $6×104$, and $1×105$). High purity glycerin was used as the working fluid, and particle image velocimetry (PIV) was employed to obtain the velocity fields. The obtained flow patterns have a strong dependence on the Rayleigh number.

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2011;133(7):072601-072601-9. doi:10.1115/1.4003667.

An analytic solution is obtained for the problem of fully developed forced convection in a channel between parallel plane walls, partly occupied by a bidisperse porous medium (BDPM) and partly by a fluid clear of solid material, the distribution of material being symmetrical with the BDPM forming either the core or the sheath portion of the channel. The case of uniform flux boundaries is considered. For the porous medium, a two-velocity two-temperature model based on Darcy’s law is employed and the Beavers–Joseph interface condition is imposed. In each case, Nusselt number values are obtained in terms of various parameters.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):072602-072602-7. doi:10.1115/1.4003557.

The thermal entrance region in a plane-parallel channel filled by a fluid saturated porous medium is investigated with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The asymptotic temperature distributions are determined analytically. The governing equations in the thermal entrance region are solved numerically by a finite element method and by the method of lines.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2011;133(7):072701-072701-7. doi:10.1115/1.4003543.

The determination of emissivity of layered structures is critical in many applications, such as radiation thermometry, microelectronics, radiative cooling, and energy harvesting. Two different approaches, i.e., the “indirect” and “direct” methods, are commonly used for computing the emissivity of an object. For an opaque surface at a uniform temperature, the indirect method involves calculating the spectral directional-hemispherical reflectance to deduce the spectral directional emissivity based on Kirchhoff’s law. On the other hand, a few studies have used a combination of Maxwell’s equations with the fluctuation-dissipation theorem to directly calculate the emissivity. The present study aims at unifying the direct and indirect methods for calculating the far-field thermal emission from layered structures with a nonuniform temperature distribution. Formulations for both methods are given to illustrate the equivalence between the indirect and the direct methods. Thermal emission from an asymmetric Fabry–Pérot resonance cavity with a nonuniform temperature distribution is taken as an example to show how to predict the intensity, emissivity, and the brightness temperature. The local density of states, however, can only be calculated using the direct method.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):072702-072702-9. doi:10.1115/1.4003607.

This paper presents a numerical investigation for laminar forced convection flow of a radiating gas over an inclined backward facing step in a horizontal duct subjected to bleeding condition. The fluid is treated as a gray, absorbing, emitting, and scattering medium. The two-dimensional Cartesian coordinate system is used to simulate flow over inclined surface by considering the blocked-off region in regular grid. The governing differential equations consisting the momentum and energy are solved numerically by the computational fluid dynamics techniques to obtain the velocity and temperature fields. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. Since the gas is considered as a radiating medium, convection, conduction, and radiation heat transfer mechanisms take place simultaneously in the gas flow. For computation of the radiative term in the gas energy equation, the radiative transfer equation is solved numerically by the discrete ordinate method to find the radiative heat flux distribution inside the radiating medium. The effects of bleeding coefficient, inclination angle, optical thickness, albedo coefficient, and the radiation-conduction parameter on the flow and temperature distributions are carried out.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Heat Transfer. 2011;133(7):074501-074501-4. doi:10.1115/1.4003575.

We present a new model for predicting thermal boundary conductance in the classical limit. This model takes a different form than those of the traditionally used mismatch theories in the fact that the temperature dependence of thermal boundary conductance is driven by the phononic scattering mechanisms of the materials comprising the interface as opposed to the heat capacities of those materials. The model developed in this work assumes that a phonon on one side of an interface may not scatter at the interface itself but instead scatter with phonons in the adjacent material via the scattering processes intrinsic in the adjacent material. We find that this model is in good agreement with classical molecular dynamics simulations of phonon transport across a Si/Ge interface.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(7):074502-074502-4. doi:10.1115/1.4003551.

This study presents a generalized confined boiling correlation applicable for various working fluids and operating conditions. A dimensionless parameter, Bond number, has been incorporated into the correlation to include the effects of confinement in the ebullition process of boiling. The proposed correlation is compared with an existing correlation based on their capability in predicting confined boiling data from the literature. A phenomenon of heat transfer coefficient stagnation is found for boiling in narrow spaces despite an increase in heat flux. Results show that the proposed correlation entails an excellent agreement with experimental data, and the predictions have a reasonably low mean absolute error of 17.3% for the entire database.

Commentary by Dr. Valentin Fuster