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Research Papers: Conduction

J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339.

A thermal rectifier transmits heat asymmetrically, transmitting heat in one direction and acting as an insulator in the opposite direction. For conduction at steady-state, thermal rectification can occur naturally in systems where the thermal conductivity of the material(s) varies in space and with temperature. However, in practical applications, rectification may often need to be controlled or understood under transient conditions. Using a bulk composite, specifically a two-slab composite, as a model system, we analyze transient rectifying behavior. We find that under some conditions transient rectification can be several times larger than steady-state rectification. Further, both the thermal diffusivity of the system and the temperature-dependent thermal conductivity or thermal capacitance play an important role in affecting the transient rectifying behavior of the system, with the nonlinearity of the system leading to unusual behavior where rectification is maximized.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):091302-091302-11. doi:10.1115/1.4036526.

In this paper, a numerical model employing an approximately realistic three-dimensional (3D) foam structure represented by Weaire–Phelan foam cell is developed to study the steady-state heat conduction of high porosity open-cell metal foam/paraffin composite at the pore-scale level. The conduction problem is considered in a cubic representative computation unit of the composite material with a constant temperature difference between one opposite sides of the cubic unit (the other outer surfaces of the cubic unit are thermally insulated). The effective thermal conductivities (ETCs) of metal foam/paraffin composites are calculated with the developed pore-scale model considering small-scale details of heat conduction, which avoids using adjustable free parameters that are usually adopted in the previous analytical models. Then, the reason why the foam pore size has no evident effect on ETC as reported in the previous macroscopic experimental studies is explored at pore scale. Finally, the effect of air cavities existing within solid paraffin in foam pore region on conduction capacity of metal foam/paraffin composite is investigated. It is found that our ETC data agree well with the reported experimental results, and thus by direct numerical simulation (DNS), the ETC data of different metal foam/paraffin composites are provided for engineering applications. The essential reason why pore size has no evident effect on ETC is due to the negligible interstitial heat transfer between metal foam and paraffin under the present thermal boundary conditions usually used to determine the ETC. It also shows that overlarge volume fraction of air cavity significantly weakens the conduction capacity of paraffin, which however can be overcome by the adoption of high conductive metal foam due to enhancement of conduction.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2017;139(9):091501-091501-15. doi:10.1115/1.4036572.

Component-scale computational fluid dynamics (CFD) modeling of boiling via heat flux partitioning relies upon empirical and semimechanistic representations of the modes of heat transfer believed to be important. One such mode, “quenching,” refers to the bringing of cool water to the vicinity of the heated wall to refill the volume occupied by a departing vapor bubble. This is modeled in classical heat flux partitioning approaches using a semimechanistic treatment based on idealized transient heat conduction into liquid from a perfectly conducting substrate. In this paper, we apply a modern interface tracking CFD approach to simulate steam bubble growth and departure, in an attempt to assess mechanistically (within the limitations of the CFD model) the single-phase heat transfer associated with bubble departure. This is in the spirit of one of the main motivations for such mechanistic modeling, the development of insight, and the provision of quantification, to improve the necessarily more empirical component scale modeling. The computations indicate that the long-standing “quench” model used in essentially all heat flux partitioning treatments embodies a significant overestimate of this part of the heat transfer, by a factor of perhaps ∼30. It is of course the case that the collection of individual models in heat flux partitioning treatments has been refined and tuned in aggregate, and it is not particularly surprising that an individual submodel is not numerically correct. In practice, there is much cancelation between inaccuracies in the various submodels, which in aggregate perform surprisingly well. We suggest ways in which this more soundly based quantification of “quenching heat transfer” might be taken into account in component scale modeling.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2017;139(9):091701-091701-10. doi:10.1115/1.4036332.

This article emphasizes the significance of entropy generation analysis and nonlinear temperature density relation on thermally stratified viscous fluid flow over a vertical plate embedded in a porous medium with a thermal dispersion effect. In addition, the convective surface boundary condition is taken into an account. By using the suitable transformations, the governing flow equations in dimensional form are converted into set of nondimensional partial differential equations. Then the local similarity and nonsimilarity procedures are applied to transform the set of nondimensional partial differential equations into set of ordinary differential equations and then the resulting system of equations are solved by Chebyshev spectral collocation method along with the successive linearization. The effect of pertinent parameters, namely, Biot number, mixed convection parameter, and thermal dispersion on velocity, temperature, entropy generation rate, and heat transfer rate are displayed graphically and the salient features are explored in detail.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):091702-091702-12. doi:10.1115/1.4036281.

We consider convective heat transfer for laminar flow of liquid between parallel plates that are textured with isothermal ridges oriented parallel to the flow. Three different flow configurations are analyzed: one plate textured and the other one smooth; both plates textured and the ridges aligned; and both plates textured, but the ridges staggered by half a pitch. The liquid is assumed to be in the Cassie state on the textured surface(s), to which a mixed boundary condition of no-slip on the ridges and no-shear along flat menisci applies. Heat is exchanged with the liquid either through the ridges of one plate with the other plate adiabatic, or through the ridges of both plates. The thermal energy equation is subjected to a mixed isothermal-ridge and adiabatic-meniscus boundary condition on the textured surface(s). Axial conduction is neglected and the inlet temperature profile is arbitrary. We solve for the three-dimensional developing temperature profile assuming a hydrodynamically developed flow, i.e., we consider the Graetz–Nusselt problem. Using the method of separation of variables, the thermal problem is essentially reduced to a two-dimensional eigenvalue problem in the transverse coordinates, which is solved numerically. Expressions for the local Nusselt number and those averaged over the period of the ridges in the developing and fully developed regions are provided. Nusselt numbers averaged over the period and length of the domain are also provided. Our approach enables the aforementioned quantities to be computed in a small fraction of the time required by a general computational fluid dynamics (CFD) solver.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):091703-091703-13. doi:10.1115/1.4036523.

The diffusion hole constructed on a slot-type cross section has the potential to obtain high film cooling performance. However, the end shape of the cross section can greatly affect film cooling characteristics. This study examined eight cases of diffusion slot holes with various cross-sectional end shapes. The comparison of the eight diffusion slot holes and a typical fan-shaped hole was performed with a flat plate model using a three-dimensional (3D) steady computational fluid dynamics (CFD) method. The rectangular cross section had an aspect ratio of about 3.4. The end shape variation can be described based on sidewall contraction location, size, and form. The simulations were performed under an engine-representative condition of mainstream inlet Mach number 0.3 and turbulence intensity 5.2%. The simulated results showed that a strip separation bubble caused by inlet “jetting effect” occurs near the downstream wall of the diffusion slot hole and interacts with the diffusion flow. The different end shape of the rectangular cross section leads to different sidewall static pressure and exit velocity profiles, thereby produces three cooling effectiveness patterns, single-peak, bipeak, and tripeak patterns. The tripeak pattern produces higher cooling effectiveness and relatively uniform film coverage. The structure with moderate contraction and smooth transition on two sides of the downstream wall favors creation of a tripeak pattern. Compared with the fan-shaped hole, the discharge coefficient of diffusion slot hole is slightly small in low pressure ratio range, the pressure loss ratio has little difference.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):091704-091704-12. doi:10.1115/1.4036524.

This work focuses on an experimental investigation of convection heat transfer to a gas in a vertical tube under strongly heated conditions at high temperatures and pressures up to 943 K and 65 bar. A unique test facility for convection heat transfer experiments has been constructed, and used to obtain experimental data useful for better understanding and validation of numerical simulation models. This test facility consists of a single flow channel in a 2.7 m long, 0.11 m diameter graphite column with four 2.3 kW heaters placed symmetrically around the 16.8 mm diameter flow channel. Upward flow convection experiments with air and nitrogen were conducted for inlet Reynolds numbers from 1300 to 60,000, thus covering laminar, transition, and fully turbulent flow regimes. Experiments were performed at different flow rates (3.8 × 10−4 to 1.5 × 10−2 kg/s) and heater power up to 6 kW. Importantly, the data analysis considered the thermophysical properties of the gas and graphite changing with temperature and pressure. Nusselt number results are further compared to existing correlations. The effect of pressure and heater power on degraded heat transfer is examined. The analyses of the experimental data showed significant reductions in Reynolds number of up to 50% and Nusselt numbers of up to 90% between the gas inlet and outlet.

Commentary by Dr. Valentin Fuster

Research Papers: Heat Exchangers

J. Heat Transfer. 2017;139(9):091801-091801-6. doi:10.1115/1.4036597.

Pressure oscillations in supercritical jet-A fuel flowing through four parallel heated tubes connected to common manifolds have been observed in this study. Tests were performed with fuel inlet temperatures ranging from 70 °F to 700 °F, and fuel pressures ranging from 360 to 700 psi. Total fuel flow rate ranged from 5 to 55 lb/h. Tubes were heated by blowing 800–950 °F nitrogen over them. Acoustic-mode oscillations, typically ranging from 100 to 500 Hz, occurred only when a large temperature gradient was created inside the heated fuel tubes. Pressure oscillation amplitudes ranged from 0.1 to 1.0 psi. Oscillations at the inlet and outlet manifolds that were caused by a mode with the characteristic length of a single fuel tube were separated by a phase lag that was a function of the manifold cross-passage diameter. A lower frequency mode was also observed, which had a characteristic length based on the summed lengths of a single fuel tube and a single manifold passage. An acoustic simulation using the comsol acoustics module was performed to predict frequencies based on geometry and flow conditions of the experiment.

Commentary by Dr. Valentin Fuster

Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2017;139(9):092001-092001-7. doi:10.1115/1.4036039.

This work presents a simple method based on electrical and thermal properties of materials. It permits researchers, in the field of manufacturing and characterization of thin and thick films in solid state to take appropriate experimental conditions before the preparation process. The calculation of the thermal diffusion length, its comparison with thicknesses of the substrate, the thin layer deposited on the substrate, the use of photothermal deflection technique, and the Cahill's law permit to highlight the necessary conditions that allow researchers to manufacture samples with high thermoelectric power such as the required thickness, electric conductivity, and thermal conductivity.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):092002-092002-10. doi:10.1115/1.4036340.

Volume diffusion (or bi-velocity) continuum model offers an alternative modification to the standard Navier–Stokes for simulating rarefied gas flows. According to this continuum model, at higher Knudsen numbers the contribution of molecular spatial stochasticity increases. In this paper, we study a microcavity heat transfer problem as it provides an excellent test for new continuum flow equations. Simulations are carried out for Knudsen numbers within the slip and higher transition flow regimes where nonlocal-equilibrium and rarefaction effects dominate. We contrast the predictions by a Navier–Stokes model corrected by volume diffusion flux in its constitutive equations to that of the direct simulation Monte Carlo (DSMC) method and the standard Navier–Stokes model. The results show improvement in the Navier–Stokes prediction for the high Knudsen numbers. The new model exhibits proper Knudsen boundary layer in the temperature and velocity fields.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):092003-092003-11. doi:10.1115/1.4036460.

Closed-loop pulsating heat pipes (CLPHPs) are a new type of two-phase heat transfer devices that can transfer considerable heat in a small space via two-phase vapor and liquid pulsating flow and work with various types of two-phase instabilities so the operating mechanism of CLPHP is not well understood. In this work, two CLPHPs, made of Pyrex, were manufactured to observe and investigate the flow regime that occurs during the operation of CLPHP and thermal performance of the device under different laboratory conditions. In general, various working fluids were used in filling ratios of 40%, 50%, and 60% in horizontal and vertical modes to investigate the effect of thermo-physical parameters, filling ratio, nanoparticles, gravity, CLPHP structure, and input heat flux on the thermal performance of CLPHP. The results indicate that three types of flow regime may be observed given laboratory conditions. Each flow regime exerts a different effect on the thermal performance of the device. There is an optimal filling ratio for each working fluid. The increased number of turns in CLPHP generally improves the thermal performance of the system reducing the effect of the type of the working fluid on the aforementioned performance. The adoption of copper nanoparticles, which positively affect fluid motion, decreases the thermal resistance of the system as much as 6.06–42.76% depending on laboratory conditions. Moreover, gravity brings about positive changes in the flow regime decreasing thermal resistance as much as 32.13–52.58%.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):092004-092004-14. doi:10.1115/1.4036388.

The present study examines the flow field and heat transfer inside a sessile droplet on oil-impregnated surface when subjected to a small temperature difference at the droplet–oil interface. Temperature and flow fields inside the droplet are predicted and the flow velocities predicted are validated through the data obtained from a particle image velocimetry (PIV). Several images of droplets in varying sizes are analyzed and the droplet geometric features and experimental conditions are incorporated in the simulations. A polycarbonate wafer is used to texture the surface via incorporating a solvent-induced crystallization method. Silicon oil is used for impregnation of the textured surfaces. It is found that two counter-rotating circulation cells are formed in the droplet because of the combined effect of the Marangoni and buoyant currents on the flow field. A new dimensionless number (Merve number (MN)) is introduced to assess the behavior of the Nusselt and the Bond numbers with the droplet size. The Merve number represents the ratio of the gravitational force over the surface tension force associated with the sessile droplet and it differs from the Weber number. The Nusselt number demonstrates three distinct behaviors with the Merve number; in which case, the Nusselt number increases sharply for the range 0.8 ≤ MN ≤ 1. The Bond number increases with increasing the Merve number, provided that its values remain less than unity, which indicates the Marangoni current is dominant in the flow field.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(9):092005-092005-8. doi:10.1115/1.4036461.

In this note, two aspects in the theory of heat conduction model with memory-dependent derivatives (MDDs) are studied. First, the discontinuity solutions of the memory-dependent generalized thermoelasticity model are analyzed. The fundamental equations of the problem are expressed in the form of a vector matrix differential equation. Applying modal decomposition technique, the vector matrix differential equation is solved by eigenvalue approach in Laplace transform domain. In order to obtain the solution in the physical domain, an approximate method by using asymptotic expansion is applied for short-time domain and analyzed the nature of the waves and discontinuity of the solutions. Second, a suitable Lyapunov function, which will be an important tool to study several qualitative properties, is proposed.

Commentary by Dr. Valentin Fuster

Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2017;139(9):092501-092501-12. doi:10.1115/1.4036595.

When certain fractal geometries are used in the design of fins or heat sinks, the surface area available for heat transfer can be increased while system mass can be simultaneously decreased. In order to assess the thermal performance of fractal fins for application in the thermal management of electronic devices, an experimental investigation was performed. The experimental investigation assessed the efficiency, effectiveness, and effectiveness per unit mass of straight rectangular fins inspired by the first four iterations of the Sierpinski carpet fractal pattern. The thermal performance of the fractal fins was investigated in a natural convection environment with thermal radiation accounted for. Fin performance was analyzed under power inputs of 2.5, 5, 10, and 20 W. While fin efficiency was found to decrease with fractal iteration, fin effectiveness per unit mass increased with fractal iteration. In addition, a fractal fin inspired by the fourth iteration of the Sierpinski carpet fractal pattern was found to be more effective than a traditional straight rectangular fin of equal width, height, and thickness. When compared to a traditional straight rectangular fin, or the zeroth fractal iteration, a fin inspired by the fourth fractal iteration of the Sierpinski carpet fractal pattern was found to be on average 3.63% more effective, 16.19% less efficient, and 65.99% more effective per unit mass. The amount of the total heat transfer attributed to thermal radiation was also dependent on fractal iteration. Thermal radiation accounted for, on average, 57.00% of the total heat transfer for the baseline case, or zeroth fractal iteration. Thermal radiation accounted for 53.67%, 50.33%, 48.84%, and 45.84% of the total heat transfer for the first, second, third, and fourth fractal iterations, respectively.

Commentary by Dr. Valentin Fuster

Research Papers: Porous Media

J. Heat Transfer. 2017;139(9):092601-092601-9. doi:10.1115/1.4036525.

Hydrodynamics and heat transfer in micro/nano channels filled with porous media for different porosities and Knudsen numbers, Kn, ranging from 0.1 to 10, are considered. The performance of standard lattice Boltzmann method (LBM) is confined to the microscale flows with a Knudsen number less than 0.1. Therefore, by considering the rarefaction effect on the viscosity and thermal conductivity, a modified thermal LBM is used, which is able to extend the ability of LBM to simulate wide range of Knudsen flow regimes. The present study reports the effects of the Knudsen number and porosity on the flow rate, permeability, and mean Nusselt number. The Knudsen's minimum effect for micro/nano channels filled with porous media was observed. In addition to the porosity and Knudsen number, the obstacle sizes have important role in the heat transfer, so that enhanced heat transfer is observed when the obstacle sizes decrease. For the same porosity and Knudsen number, the inline porous structure has the highest heat transfer performance.

Commentary by Dr. Valentin Fuster

Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2017;139(9):092701-092701-7. doi:10.1115/1.4036154.

In this paper, a new hybrid numerical algorithm is developed to solve coupled convection–radiation heat transfer in a two-dimensional cavity containing an absorbing, emitting, and scattering medium. The radiative information is obtained by solving the radiative transfer equation (RTE) using the control volume finite element method (CVFEM), and the density, velocity, and temperature fields are calculated using the two double population lattice Boltzmann equation (LBE). To the knowledge of the authors, this hybrid numerical method is applied at the first time to simulate combined transient convective radiative heat transfer in 2D participating media. In order to test the efficiency of the developed method, two configurations are examined: (i) free convection with radiation in a square cavity bounded by two horizontal insulating sides and two vertical isothermal walls and (ii) Rayleigh–Benard convection with and without radiative heat transfer. The obtained results are validated against available works in literature, and the proposed method is found to be efficient, accurate, and numerically stable.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Heat Transfer. 2017;139(9):094501-094501-4. doi:10.1115/1.4036328.

The present work is concerned with the heat transfer enhancement and efficiency in the moving longitudinal fins having trapezoidal cross sections. Finding analytical solutions is targeted so that efficiency of trapezoidal fins over the known fin sections can be comparatively searched. It is shown that certain type of trapezoidal fins may have advantageous fin design features. The formulas given in this paper may also be used as benchmark analysis.

Commentary by Dr. Valentin Fuster

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