Research Papers: Conduction

J. Heat Transfer. 2018;140(7):071301-071301-8. doi:10.1115/1.4038855.

A desirable feature of any parameter estimation method is to obtain as much information as possible with one experiment. However, achieving multiple objectives with one experiment is often not possible. In the field of thermal parameter estimation, a determination of thermal conductivity, volumetric heat capacity, heat addition rate, surface emissivity, and convection coefficient may be desired from a set of temperature measurements in an experiment where a radiant heat source is used. It would not be possible to determine all of these parameters from such an experiment; more information would be needed. The work presented in the present research shows how thermal parameters can be determined from temperature measurements using complementary experiments where the same material is tested more than once using a different geometry or heating configuration in each experiment. The method of ordinary least squares is used in order to fit a mathematical model to a temperature history in each case. Several examples are provided using one-dimensional conduction experiments, with some having a planar geometry and some having a cylindrical geometry. The parameters of interest in these examples are thermal conductivity and volumetric heat capacity. Sometimes, both of these parameters cannot be determined simultaneously from one experiment but utilizing two complementary experiments may allow each of the parameters to be determined. An examination of confidence regions is an important topic in parameter estimation and this aspect of the procedure is addressed in the present work. A method is presented as part of the current research by which confidence regions can be found for results from a single analysis of multiple experiments.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):071302-071302-10. doi:10.1115/1.4038712.

In the microelectronics industry, the multilayered structures are found extensively where the microelectronic device/system is manufactured as a compound system of different materials. Recently, a variety of new materials have emerged in the microelectronics industry with properties superior to Silicon, enabling new devices with extreme performance. Such materials include β-Gallium-oxide (β-Ga2O3), and black phosphorus (BP), which are acknowledged to have anisotropic thermal conductivity tensors. In many of these devices, thermal issues due to self-heating are a problem that affects the performance, efficiency, and reliability of the devices. Analytical solutions to the heat conduction equation in such devices with anisotropic thermal conductivity tensor offer significant computational savings over numerical methods. In this paper, general analytical solutions for the temperature distribution and the thermal resistance of a multilayered orthotropic system are obtained. The system is considered as a multilayered three-dimensional (3D) flux channel consisting of N-layers with different thermal conductivities in the three spatial directions in each layer. A single eccentric heat source is considered in the source plane while a uniform heat transfer coefficient is considered along the sink plane. The solutions account for the effect of interfacial conductance between the layers and for considering multiple eccentric heat sources in the source plane. For validation purposes, the analytical results are compared with numerical solution results obtained by solving the problem with the finite element method (FEM) using the ANSYS commercial software package.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2018;140(7):071501-071501-7. doi:10.1115/1.4038854.

Previous research in dropwise condensation (DWC) on rough microtextured superhydrophobic surfaces has demonstrated evidence of high heat transfer enhancement compared to smooth hydrophobic surfaces. In this study, we experimentally investigate the use of microporous sintered copper powder on copper substrates coated with a thiol-based self-assembled monolayer to attain enhanced DWC for steam in a custom condensation chamber. Although microtextured superhydrophobic surfaces have shown advantageous droplet growth dynamics, precise heat transfer measurements are underdeveloped at high heat flux. Sintered copper powder diameters from 4 μm to 119 μm were used to investigate particle size effects on heat transfer. As powder diameter decreased, competing physical factors led to improved thermal performance. At consistent operating conditions, we experimentally demonstrated a 23% improvement in the local condensation heat transfer coefficient for a superhydrophobic 4 μm diameter microporous copper powder surface compared to a smooth hydrophobic copper surface. For the smallest powders observed, this improvement is primarily attributed to the reduction in contact angle hysteresis as evidenced by the decrease in departing droplet size. Interestingly, the contact angle hysteresis of sessile water droplets measured in air is in contradiction with the departing droplet size observations made during condensation of saturated steam. It is evident that the specific design of textured superhydrophobic surfaces has profound implications for enhanced condensation in high heat flux applications.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):071502-071502-8. doi:10.1115/1.4039014.

We present a mathematical model for dropwise condensation (DWC) heat transfer on a surface with wettability gradient. We adapt well-established population balance model for DWC on inclined surfaces to model DWC on a surface with wettability gradient. In particular, our model takes into account the effect of wettability gradient and energy released during drop coalescence to determine the drop departure size. We validate our model with published experimental data of DWC heat flux and drop size distribution. Based on various experimental studies on drop motion, we also propose a mechanism that explains how the energy released during drop coalescence on a surface with wettability gradient and in a condensation environment aids drop motion. The mechanism correctly explains the shift of center of mass of two coalescing drops on a surface with wettability gradient toward the drop on high wetting region. Using the model, we analyze the effect of wettability gradient on the DWC heat flux. Our model predictions show that the optimal choice of wettability gradient is governed by differential variations in population density and heat transfer through a drop with change in wettability of the surface. We also demonstrate that contact angle at which there is maximum heat transfer through a drop varies with thickness of coating layer leading to change in optimal wettability gradient.

Commentary by Dr. Valentin Fuster

Research Papers: Experimental Techniques

J. Heat Transfer. 2018;140(7):071601-071601-7. doi:10.1115/1.4038874.

A high-speed (2 kHz) near-infrared (1.0–1.65 μm) multispectral pyrometer was used for noninvasive measurements of the subpixel temperature distribution near the sharp leading edge of a wing exposed to a supersonic plasma jet. The multispectral pyrometer operating in the field measurement mode was able to measure the spatial temperature distribution. Multiple spectra were used to determine the temperature distributions in the measurement region. The spatial resolution of the multispectral pyrometer was not restricted to one “pixel” but was extended to subpixel accuracy (the temperature distribution inside one pixel in the image space corresponding to the point region in the object space). Thus, this system gives high-speed, multichannel, and long working time spatial temperature measurements with a small data stream from high-speed multispectral pyrometers. The temperature distribution of the leading edge of a ceramic wing was investigated with the leading edge exposed to extreme convective heating from a high-enthalpy plasma flow. Simultaneous measurements with a multispectral pyrometer and an imaging pyrometer verify the measurement accuracy of the subpixel temperature distribution. Thus, this multispectral pyrometry can provide in situ noninvasive temperature diagnostics in supersonic plasma jet environments.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2018;140(7):071701-071701-9. doi:10.1115/1.4039352.

Hydrodynamically and thermally fully developed flow of a Sisko fluid through a cylindrical tube has been investigated considering the effect of viscous dissipation. The effect of the convective term in the energy equation has been taken into account, which was neglected in the earlier studies for Sisko fluid flow. This convective term can significantly affect the temperature distribution if the radius of the tube is relatively large. The equations governing the flow and heat transfer are solved by the least square method (LSM) for both heating and cooling of the fluid. The results of the LSM solution are compared with that of the closed form analytical solution of the Newtonian fluid flow case and are found to match exactly. The results indicate that Nusselt number decreases with the increase in Brinkman number and increases with the increase in the Sisko fluid parameter for the heating of the fluid. In case of cooling, Nusselt number increases with the increase in the Brinkman number asymptotically to a very large value, changes its sign, and then decreases with the increase in Brinkman number. With the increase in the non-Newtonian index, Nusselt number is observed to increase.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):071702-071702-9. doi:10.1115/1.4039419.

The detailed flow field and heat transfer were experimentally investigated in a channel with a circular cross section and equipped with a helical rib of low blockage ratio. Stereoscopic particle image velocimetry (S-PIV) was applied in order to measure the three components of the mean and turbulent velocities in the symmetry plane of the channel. Additionally, steady-state liquid crystal thermography (LCT) and infrared thermography were employed in order to study the convective heat transfer coefficient on the wall. Measurements were carried out more than six pitches downstream of the rib origin, presenting periodic velocity and heat transfer fields from this location on. The resulting velocity and heat transfer fields show similarities with those present in channels of plane walls, such as low momentum and heat transfer areas upstream and downstream of the obstacle, and high kinetic energy and heat transfer a few rib heights downstream of the obstacle. On the other hand, the shape of the rib induces a swirling motion with the same sense as the rib. The azimuthal mean velocity is negligible in the core of the pipe, but it increases considerably close to the wall.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):071703-071703-11. doi:10.1115/1.4039182.

The heat fluxes across the turbine tip gap are characterized by large unsteady pressure gradients and shear from the viscous effects. The classical Newton heat convection equation, based on the turbine inlet total temperature, is inadequate. Previous research from our team relied on the use of the adiabatic wall temperature. In this paper, we propose an alternative approach to predict the convective heat transfer problem across the turbine rotor tip using discrete Green's functions (DGF). The linearity of the energy equation in the solid domain with constant thermal properties can be applied with a superposition technique to measure the data extracted from flow simulations to determine the Green's function distribution. The DGF is a matrix of coefficients that relate the temperature spatial (GF) distribution with the heat flux. This methodology is first applied to a backward facing step, validated using experimental data. The final aim of this paper is to demonstrate the method in the rotor turbine tip. A turbine stage at engine-like conditions was assessed using cfd software. The heat flux pulses were applied at different locations in the rotor tip geometry, and the increment of temperature in this zone was evaluated for different clearances, with a consequent variation of the DGF coefficients. Ultimately, a detailed uncertainty analysis of the methodology was included based on the magnitude of the heat flux pulses used in the DGF coefficients calculation and the uncertainty in the experimental measurements of the wall temperature.

Commentary by Dr. Valentin Fuster

Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2018;140(7):072001-072001-10. doi:10.1115/1.4038829.

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

Commentary by Dr. Valentin Fuster

Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2018;140(7):072201-072201-10. doi:10.1115/1.4039015.

A comparative experimental and numerical study has been done on multiple-jet impingement heat transfer in narrow channels with different pin fin configurations on the target surfaces. Three different target plates including a flat plate, a plate with full-height pin fins, and another plate with miniature pin fins are investigated in the jet impingement cooling systems comparatively. The experiments were done under maximum cross flow scheme for the jet Reynolds numbers from 15,000 to 30,000. Narrow jet impingement spacing is kept the same as 1.5 times jet diameter for all the target plates. In the experiments, detailed jet impingement heat transfer characteristics on the flat plate and the full-height pin-fin plate were obtained by using the transient liquid crystal thermography technique, and additionally steady experiments were done to obtain the overall heat transfer performance of the jet impingement systems with all the three different target plates, which accounts for the heat transfer contribution from the pin fins' surface. Significant overall jet impingement heat transfer enhancement can be obtained with full-height pin-fin roughened surfaces with appreciable pressure loss; however, with miniature pin fins on the target plate, the jet impingement overall heat transfer performance can be remarkably improved with negligible pressure loss penalty. Furthermore, three-dimensional (3D) computational fluid dynamics (CFD) analysis was done to analyze the detailed flow structure and heat transfer characteristics in the jet impingement systems with different pin fin configurations.

Commentary by Dr. Valentin Fuster

Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2018;140(7):072401-072401-10. doi:10.1115/1.4038830.

The problem of flow maldistribution is very critical in microchannel heat sinks (MCHS). It induces temperature nonuniformity, which may ultimately lead to the breakdown of associated system. In the present communication, a novel approach for the mitigation of flow maldistribution problem in parallel MCHS has been proposed using variable width microchannels. Numerical simulation of copper made parallel MCHS consisting of 25 channels has been carried out for the conventional design (CD) and the proposed design (PD). It is observed that the PD reduces flow maldistribution by 93.7%, which facilitated in effective uniform cooling across the entire projected area of MCHS. Temperature fluctuation at fluid–solid interface is reduced by 4.3 °C, whereas maximum and average temperatures of microchannels projected area are reduced by 2.3 °C and 1.1 °C, respectively. PD is suitable in alleviating flow maldistribution problem for the extended range of off design conditions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):072402-072402-17. doi:10.1115/1.4039013.

Heat transfer analysis for a water droplet on micropost arrays is carried out while mimicking the environmental conditions. Since the micropost arrays spacing size alters the state of the hydrophilicity of the surface, the size of the micropost arrays spacing is varied and the resulting heat transfer characteristics are analyzed. Spreading rate of water droplet on the micropost arrays is considered and the adhesion force for the pinning of the water droplet on the micropost arrays is presented. Temperature and flow fields are predicted and the predictions of flow velocity inside the water droplet are validated through the particle image velocimetry (PIV). The Nusselt number variation for various sizes of the micropost arrays is obtained for two droplet volumes. It is found that reducing the solid fraction of micropost array beyond ϕs = 0.25, the Cassie and Baxter state of the surface changes to the Wenzel state; in which case, hydrophobic characteristics changes to hydrophilic characteristics for the water droplet. Heat transfer from the droplet bottom gives rise to development of the buoyancy and the Marangoni currents, which in turn generate two counter rotating circulation cells. The center of circulation cells moves further in the droplet upper part for the hydrophobic droplet case. The Nusselt number attains high values for the hydrophobic droplet at micropost array spacing size b = 10 μm and hydrophobic droplet at spacing size b = 50 μm due to fin effects of the micropost arrays.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):072403-072403-5. doi:10.1115/1.4038558.

Phase-change materials (PCM) with low supercooling degree (SD) are important in cold thermal energy storage (CTES) applications. The SD of nanosuspension PCM usually decreases with increasing nanoparticle concentration. However, the performance variation of nanosuspension PCM at high concentrations has been rarely studied, though it is important because nanoparticles tend to aggregate. In this paper, the SD and dispersion stability of nanosuspensions of TiO2, zirconium phosphate (ZrP), and TiO2 coupled with zirconium phosphate (TiO2-ZrP) were investigated at nanoparticle concentrations up to 5.0 wt %. Results show that the SD of TiO2 suspension did not remarkably varied with mass concentrations above 2.0 wt %. In contrast, the SD of TiO2-ZrP and ZrP were low and continuously decreased with increasing mass concentration of nanoparticles. The dispersion stability of TiO2-ZrP suspension improved compared with that of TiO2 suspension. Hence, TiO2-ZrP suspension provided more nucleation sites than TiO2 suspension to induce heterogeneous in water.

Commentary by Dr. Valentin Fuster

Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2018;140(7):072501-072501-9. doi:10.1115/1.4039490.

Mixed convection heat transfer of Al2O3 nanofluid in a lid-driven square cavity with differentially heated vertical walls is studied numerically with lattice Boltzmann method (LBM). In order to understand the reasons for the conflicting results on heat transfer enhancement in cavity problems, formulation of nondimensional properties and modeling thermophysical properties, in accordance with the relative effects of natural and forced convection flows, are examined. In addition to gain more insight into the physics, one of the goals of the study is to identify the reasons of existing contradictory findings; therefore, a single-phase formulation is adopted as has been the case in the majority of related literature to date. To isolate the effects of thermophysical properties on the results and to maintain the same natural and forced convection effects, all nondimensional parameters are defined using the corresponding thermophysical properties of the fluid under examination. Two different effective thermal conductivity and viscosity models are tested for a range of Reynolds and Rayleigh numbers to investigate their effects on the nanofluid behavior. Depending on the effective viscosity model, an increase or decrease is obtained in the average Nusselt number. It is also illustrated that the relative magnitudes of effective thermal conductivity values for different models do not translate into the heat transfer enhancement due to convective effects. Moreover, it is shown that thermal behavior of nanofluid approaches to the one of base fluid's as the buoyancy driven flow gets stronger, which is independent of the employed effective property models.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):072502-072502-13. doi:10.1115/1.4039213.

This study investigates the convective heat transfer of a hybrid nanofluid filled in a triangular cavity subjected to a constant magnetic field and heated by a constant heat flux element from below. The inclined side of the cavity is cooled isothermally while the remaining sides are thermally insulated. The finite difference method with the stream function-vorticity formulation of the governing equations has been utilized in the numerical solution. The problem is governed by several pertinent parameters namely, the size and position of the heater element, B = 0.2–0.8 and D = 0.3–0.7, respectively, the Rayleigh number, Ra = 102–106, the Hartmann number, Ha = 0–100, the volume fraction of the suspended nanoparticles, ϕ = 0–0.2, and the heat generation parameter Q = 0–6. The results show significant effect of increasing the volume fraction of the hybrid nanofluid when the natural convection is very small. Moreover, the hybrid nanofluid composed of equal quantities of Cu and Al2O3 nanoparticles dispersed in water base fluid has no significant enhancement on the mean Nusselt number compared with the regular nanofluid.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):072503-072503-15. doi:10.1115/1.4039081.

Laminar natural convection in differentially heated square cavity with right cold wavy wall and horizontal conducting fin attached to its left hot wall has been investigated numerically. The vertical walls are maintained at different isothermal temperatures, while the horizontal walls are insulated. The fluid that filled the cavity is air with Prandtl number of 0.71. The investigation has been performed for Rayleigh number in the range of 103–106, the thermal conductivity ratio was varied from 10 to 105, three fin lengths and positions have been examined (0.25, 0.5, and 0.75), and three numbers of undulation were tested (one, two, and three undulations). The wave amplitude and the fin thickness were kept constant at 0.05 and 0.04, respectively. The results obtained show that increasing the fin thermal conductivity or the Rayleigh number increases the average Nusselt number especially when the fin length increases. It was also found that the fin position enhances the heat transfer when the fin is placed opposite to the crest of the wavy wall. The trend of the local Nusselt number is wavy. The effect of undulations number appears when the fin length is greater than 0.5. The average Nusselt number enhanced when a conducting fin is added to the cavity with wavy wall and without fin by 51.23% and 56.85% for one and three undulations, respectively, when the Rayleigh number is 105 and the fin length is 0.75.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(7):072504-072504-10. doi:10.1115/1.4038858.

In the present study, turbulent forced and mixed convection heat transfer to a liquid metal flowing upwards in a concentric annulus is numerically investigated by means of large eddy simulation (LES). The inner-to-outer radius ratio is 0.5. The Reynolds number based on bulk velocity and hydraulic diameter is 8900, while the Prandtl number is set to a value of 0.026. A uniform and equal heat flux is applied on both walls. LES has been chosen to provide sufficiently accurate results for validating Reynolds-averaged turbulence models. Moreover, with the thermal sublayer thickness of liquid metals being much larger than the viscous hydrodynamic one, liquid metals present a separation between the turbulent thermal and hydrodynamic scales. Thus, with the same grid resolution, it is possible to perform a LES for the flow field and a “thermal” direct numerical simulation (DNS) for the temperature field. Comparison of the forced convection results with available DNS simulations shows satisfying agreement. Results for mixed convection are analyzed and the differences with respect to forced convection at the same Reynolds number are thoroughly discussed. Moreover, where possible, a comparison with air is made.

Commentary by Dr. Valentin Fuster

Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2018;140(7):072701-072701-7. doi:10.1115/1.4039221.

Hyperbolic metamaterial (HMM) alternately stacked by graphene and silicon carbide (SiC) is proposed to theoretically study near-field radiative heat transfer. Heat transfer coefficients (HTCs) are calculated using the effective medium theory (EMT). We observe that HMMs can exhibit better heat transfer characteristic than graphene-covered SiC bulks when appropriate SiC thickness and chemical potentials of graphene are selected. Transfer matrix method (TMM) is also employed to calculate HTC between HMMs with thicker SiC, given the invalidity of EMT in this case. We deduce that with increasing SiC thickness, HTC first increases rapidly and then decreases slowly when it reaches maximum value. HTC is high for graphene with small chemical potential. Results may benefit applications of thermophotovoltaic devices.

Commentary by Dr. Valentin Fuster

Research Papers: Thermal Systems

J. Heat Transfer. 2018;140(7):072801-072801-7. doi:10.1115/1.4039584.

In one of the launch vehicles of ISRO, there are two solid strap-ons attached to the core liquid engine. During the ascent phase, the external nozzle divergent of the strap-ons experiences heating due to radiation from the strap-ons as well as convective heating from the impingement of plumes from the core engine. Hence, the nozzle divergent of the strap-on beyond compliance ring is thermally protected by a coating of PC10 insulation applied over carbon/epoxy structural backup. Though the system worked satisfactorily, application of PC10 had increased the inert weight of each nozzle by 165 kg and took long time for realization. To reduce the inert weight as well as the time of application, precast phenolic based cork sheets (CkP) having lower density than PC10 were selected, as a replacement to PC10. As part of evaluating the thermal performance of the CkP material, specimen level tests with different configurations were carried out in 250 kW plasma jet facility of Vikram Sarabhai Space Centre (VSSC) wherein both the heat flux and the shear stress as expected in flight were simulated simultaneously. At the end of the test program, CkP was found to be superior to PC10 for external thermal protection system (TPS). This paper highlights details of the qualification tests carried out for clearing the cork phenolic system for use in the future launches.

Commentary by Dr. Valentin Fuster

Research Papers: Max Jakob Award Paper

J. Heat Transfer. 2018;140(7):073001-073001-8. doi:10.1115/1.4038844.

Experiments were performed to investigate the local development of roughness and its effect on mass transfer in an S-shaped bend at Reynolds number of 200,000. The tests were performed over four consecutive time periods using a 203-mm-diameter test section with a dissolving gypsum lining to water in a closed flow loop at a Schmidt number of 1200. The surface roughness and the mass transfer over the test periods were measured using X-ray computed tomography (CT) scans of the surface. Two regions of high mass transfer are found: along the intrados of the first and second bends. The surface roughness in these two regions, characterized by the height-to-spacing ratio, grows more rapidly than in the upstream pipe. There is an increase in the mass transfer with time, which corresponds well with the local increase in the height-to-spacing ratio of the roughness. The two regions of high mass transfer enhancement in the bend can be attributed to both a roughness effect and a flow effect due to the bend geometry. The geometry effect was determined by normalizing the local mass transfer with that in a straight pipe with equivalent surface roughness. The mass transfer enhancement due to the geometry effect was found to be relatively constant for the two high mass transfer regions, with a value of approximately 1.5.

Commentary by Dr. Valentin Fuster

Technical Brief: Technical Briefs

J. Heat Transfer. 2018;140(7):074501-074501-5. doi:10.1115/1.4038790.

If a steady thermal boundary layer is sufficiently thick, wall heat fluxes and associated convective heat transfer coefficients can be directly calculated from measured temperature distributions taken within it using a traversing thermocouple probe. The boundary layer can be laminar, turbulent, or transitional and on a surface of arbitrary surface temperature distribution and geometry. Herein, this technique is presented and validated in a steady, turbulent, two-dimensional boundary layer on a flat, uniform-heat-flux wall. Care is taken to properly account for radiation from the wall and conduction within the thermocouple wire. In the same setting, heat flux measurements are made for verification purposes using an energy balance on a segment of the test wall carefully designed to minimize and include radiation and conduction effects. Heat flux values measured by the boundary layer measurement technique and by the energy balance measurement agree to within 4.4% and the difference between the two lie completely within their respective measurement uncertainties of 5.74% and 0.6%.

Commentary by Dr. Valentin Fuster

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