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### Research Papers: Conduction

J. Heat Transfer. 2019;141(3):031301-031301-8. doi:10.1115/1.4042462.

For the steady-state heat transfer process, a fuzzy adaptive regularization method (FARM) is proposed to estimate the distributed thermal boundary condition in heat transfer system. First, the relationship model between temperatures at measurement points and parameters to be estimated is established based on sensitivity matrix. The regularization term is introduced into the least-squares objective function, and then the distributed thermal boundary condition is estimated by optimizing the new objective function. A fuzzy inference mechanism is developed to ensure the adaptive ability of FARM in which the regularization parameter is updated based on the residual norm between calculated and measured temperatures at measurement points and the norm of inversion parameters. Taking the plate heat conduction system and fluid–solid conjugate heat transfer system as research objects, the effects of the parameter distribution, the number of measurement points, and measurement errors on the inversion results are discussed by numerical experiments, and comparison with the classical regularization method is also conducted. Results indicate that FARM exhibits a good adaptive ability.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2019;141(3):031302-031302-12. doi:10.1115/1.4042491.

The Laplace transform (LT) is a widely used methodology for analytical solutions of dual phase lag (DPL) heat conduction problems with consistent DPL boundary conditions (BCs). However, the inversion of LT requires a series summation with large number of terms for reasonably converged solution, thereby, increasing computational cost. In this work, an alternative approach is proposed for this inversion which is valid only for time-periodic BCs. In this approach, an approximate convolution integral is used to get an analytical closed-form solution for sinusoidal BCs (which is obviously free of numerical inversion or series summation). The ease of implementation and simplicity of the proposed alternative LT approach is demonstrated through illustrative examples for different kind of sinusoidal BCs. It is noted that the solution has very small error only during the very short initial transient and is (almost) exact for longer time. Moreover, it is seen from the illustrative examples that for high frequency periodic BCs the Fourier and DPL model give quite different results; however, for low frequency BCs the results are almost identical. For nonsinusoidal periodic function as BCs, Fourier series expansion of the function in time can be obtained and then present approach can be used for each term of the series. An illustrative example with a triangular periodic wave as one of the BC is solved and the error with different number of terms in the expansion is shown. It is observed that quite accurate solutions can be obtained with a fewer number of terms.

Commentary by Dr. Valentin Fuster

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

J. Heat Transfer. 2019;141(3):031501-031501-10. doi:10.1115/1.4042492.

Inspired by the thermoregulation of mammals via perspiration, cooling strategies utilizing continuously fed evaporating droplets have long been investigated in the field, yet a comprehensive modeling capturing the detailed physics of the internal liquid flow is absent. In this study, an innovative computational model is reported, which solves the governing equations with temperature-dependent thermophysical properties in an iterative manner to handle mass and heat transfer coupling at the surface of a constant shape evaporating droplet. Using the model, evaporation from a spherical sessile droplet is simulated with and without thermocapillarity. An uncommon, nonmonotonic temperature variation on the droplet surface is captured in the absence of thermocapillarity. Although similar findings were reported in previous experiments, the temperature dip was attributed to a possible Marangoni flow. This study reveals that buoyancy-driven flow is solely responsible for the nonmonotonic temperature distribution at the surface of an evaporating steadily fed spherical water droplet.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2019;141(3):031701-031701-14. doi:10.1115/1.4042299.

Air turbine power generation system is considered as a feasible power generation system for hypersonic aircraft with Mach 6. However, the incoming air with high temperature cannot be used as coolant while turbine has to be cooled. Since hydrocarbon fuel is the only cooling source onboard, the scheme of fuel cooling air turbine is put forward. In this paper, square cooling channel, including inlet part, outlet part and U-duct, is established based on the typical air turbine. The hydraulic diameter of the channel is 2 mm and four types of U-ducts are used to compare the performance with simulation using k-Epsilon turbulence model. The density and specific heat capacity of fuel are considered as constant as the temperature difference in this study is small. The Reynolds number varies from 2760 to 16,559 and rotating number ranges from 0 to 6.9. The results show that the pressure distribution in radial direction is proportional to the square of radial distance and the square of rotating speed. The regulations of velocity and normalized Nusselt number distributions depend on rotating number. Furthermore, the heat transfer is enhanced with fin while the pressure loss is also increased. The position of fins cannot significantly influence pressure loss but can influence heat transfer obviously. The normalized Nusselt number of inlet-fin U-duct is higher than the outlet-fin U-duct both on leading side surface and trailing side (TS) surface, while the pressure losses for the two types of ducts are almost same.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2019;141(3):031702-031702-10. doi:10.1115/1.4042331.

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2019;141(3):032001-032001-10. doi:10.1115/1.4042333.

Particle-based heat transfer fluids for concentrated solar power (CSP) tower applications offer a unique advantage over traditional fluids, as they have the potential to reach very high operating temperatures. Gravity-driven dense granular flows through cylindrical tubes demonstrate potential for CSP applications and are the focus of the present study. The heat transfer capabilities of such a flow system were experimentally studied using a bench-scale apparatus. The effect of the flow rate and other system parameters on the heat transfer to the flow was studied at low operating temperatures (<200 °C), using the convective heat transfer coefficient and Nusselt number to quantify the behavior. For flows ranging from 0.015 to 0.09 m/s, the flow rate appeared to have negligible effect on the heat transfer. The effect of temperature on the flow's heat transfer capabilities was also studied, examining the flows at temperatures up to 1000 °C. As expected, the heat transfer coefficient increased with the increasing temperature due to enhanced thermal properties. Radiation did not appear to be a key contributor for the small particle diameters tested (approximately 300 μm in diameter) but may play a bigger role for larger particle diameters. The experimental results from all trials corroborate the observations of other researchers; namely, that particulate flows demonstrate inferior heat transfer as compared with a continuum flow due to an increased thermal resistance adjacent to the tube wall resulting from the discrete nature of the flow.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2019;141(3):032002-032002-12. doi:10.1115/1.4042441.

Due to the microscopic roughness of contacting materials, an additional thermal resistance arises from the constriction and spreading of heat near contact spots. Predictive models for contact resistance typically consider abutting semi-infinite cylinders subjected to an adiabatic boundary condition along their outer radius. At the nominal plane of contact, an isothermal and circular contact spot is surrounded by an adiabatic annulus and the far-field boundary condition is one of constant heat flux. However, cylinders with flat bases do not mimic the geometry of contacts. To remedy this, we perturb the geometry of the problem such that, in cross section, the circular contact is surrounded by an adiabatic arc. When the curvature of this arc is small, we employ a series solution for the leading-order (flat base) problem. Then, Green's second identity is used to compute the increase in spreading resistance in a single cylinder, and thus the contact resistance for abutting ones, without fully resolving the temperature field. Complementary numerical results for contact resistance span the full range of contact fraction and protrusion angle of the arc. The results suggest as much as a 10–15% increase in contact resistance for realistic contact fraction and asperity slopes. When the protrusion angle is negative, the decrease in spreading resistance for a single cylinder is also provided.

Commentary by Dr. Valentin Fuster

### Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2019;141(3):032201-032201-15. doi:10.1115/1.4042159.

Impinging heat transferred by a pulsed jet induced by a six-chevron nozzle on a semicylindrical concave surface is investigated by varying jet Reynolds numbers (5000 ≤ Re ≤ 20,000), operational frequencies (0 Hz ≤ f ≤ 25 Hz), and dimensionless nozzle-to-surface distances (1 ≤ H/d ≤ 8) while fixing the duty cycle as DC = 0.5. The semicylindrical concave surface has a cylinder diameter-to-nozzle diameter ratio (D/d) of 10. The results show that the nozzle-to-surface distance has a significant impact on the impingement heat transfer of the pulsed chevron jet. An optimal nozzle-to-surface distance for achieving the maximum stagnation Nusselt number appears at H/d  =  6. In the wall jet zone, the averaged Nusselt number is the largest at H/d = 2 and the smallest at H/d = 8. In comparison with the chevron steady jet impingement, the effect of nozzle-to-surface distance on the convective heat transfer becomes less notable for the pulsed chevron jet impingement. The stagnation Nusselt number under the pulsed chevron jet impingement is mostly less than that under the chevron steady jet impingement. However, at H/d = 8, the pulsed chevron jet is more effective than the steady jet. This study confirmed that the pulsed chevron jet produced higher azimuthally averaged Nusselt numbers than the steady chevron jet in the wall jet flow zone at large nozzle-to-surface distances. The stagnation Nusselt numbers by the pulsed chevron jet impingement have a maximum reduction of 21.0% (f = 20 Hz, H/d = 4, and Re = 2000) compared with that of the steady chevron jet impingement. Also, the pulsed chevron jet impingement heat transfer on a concave surface is less effective compared to a flat surface. The stagnation Nusselt numbers on the semicylindrical concave surface have a maximum reduction of about 37.7% (f = 20 Hz, H/d = 8, and Re = 5000) compared with that on the flat surface.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2019;141(3):032401-032401-10. doi:10.1115/1.4042329.

In this work, the equilibrium molecular dynamics (MD) simulation combined with the Green–Kubo method is employed to calculate the thermal conductivity and investigate the impact of the liquid layer around the solid nanoparticle (NP) in enhancing thermal conductivity of nanofluid (argon–copper), which contains the liquid argon as a base fluid surrounding the spherical or cylindrical NPs of copper. First, the thermal conductivity is calculated at temperatures 85, 85.5, 86, and 86.5 K and for different volume fractions ranging from 4.33% to 11.35%. Second, the number ΔN of argon atoms is counted in the liquid layer formed at the solid–liquid interface with the thickness of Δr = 0.3 nm around the NP. Finally, the number density n of argon atoms in this layer formed is calculated in all cases. Also, the results for spherical and cylindrical NPs are compared with one another. It is observed that the thermal conductivity of the nanofluid increased with the increasing volume fraction and the number ΔN. Likewise, the thermal conductivity of nanofluid containing spherical NPs is higher than that of nanofluid containing cylindrical NPs. Furthermore, the number density n of argon atoms near the surface of spherical NPs is higher than that of argon atoms attached in the curved surface of cylindrical NPs. As a result, the liquid layer around the solid NP has been considered one of the mechanisms responsible contributing to the thermal conductivity enhancement in nanofluids.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2019;141(3):032402-032402-9. doi:10.1115/1.4042298.

In magnetic nanoparticle hyperthermia, a required thermal dosage for tumor destruction greatly depends on nanoparticle distribution in tumors. The objective of this study is to conduct in vivo experiments to evaluate whether local heating using magnetic nanoparticle hyperthermia changes nanoparticle concentration distribution in prostatic cancer (PC3) tumors. In vivo animal experiments were performed on grafted PC3 tumors implanted in mice to investigate whether local heating via exposing the tumor to an alternating magnetic field (5 kA/m and 192 kHz) for 25 min resulted in nanoparticle spreading from the intratumoral injection site to tumor periphery. Nanoparticle redistribution due to local heating is evaluated via comparing microCT images of resected tumors after heating to those in the control group without heating. A previously determined calibration relationship between microCT Hounsfield unit (HU) values and local nanoparticle concentrations in the tumors was used to determine the distribution of volumetric heat generation rate ($q‴MNH$) when the nanoparticles were subject to the alternating magnetic field. sas,matlab, and excel were used to process the scanned data to determine the total heat generation rate and the nanoparticle distribution volumes in individual HU ranges. Compared to the tumors in the control group, nanoparticles in the tumors in the heating group occupied not only the vicinity of the injection site, but also tumor periphery. The nanoparticle distribution volume in the high $q‴MNH$ range (>1.8 × 106 W/m3) is 10% smaller in the heating group, while in the low $q‴MNH$ range of 0.6–1.8 × 106 W/m3, it is 95% larger in the heating group. Based on the calculated heat generation rate in individual HU ranges, the percentage in the HU range larger than 2000 decreases significantly from 46% in the control group to 32% in the heating group, while the percentages in the HU ranges of 500–1000 and 1000–1500 in the heating group are much higher than that in the control group. Heating PC3 tumors for 25 min resulted in significant nanoparticle migration from high concentration regions to low concentration regions in the tumors. The volumetric heat generation rate distribution based on nanoparticle distribution before or after local heating can be used in the future to guide simulation of nanoparticle redistribution and its induced temperature rise in PC3 tumors during magnetic nanoparticle hyperthermia, therefore, accurately predicting required thermal dosage for safe and effective thermal therapy.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2019;141(3):032501-032501-11. doi:10.1115/1.4042490.

The influence of the variable properties on the buoyancy-driven flows of liquid sodium established in a square enclosure including two inner heated plates is numerically investigated. Two-dimensional turbulent simulations are obtained, considering uniform wall temperature heating conditions. The low-Reynolds k–ω turbulence model is employed. The average Nusselt number and the dimensionless mass-flow rate evaluated between the inner plates are obtained for a wide range of the Rayleigh number, varying from 103 to 1012. Several practical correlations are presented. The results obtained for different heating intensities are analyzed and compared. The expected decay in the heat transfer coefficients is less relevant than that previously obtained for airflows. The thermal structure of the flow into the enclosure is also shown.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2019;141(3):032701-032701-9. doi:10.1115/1.4042365.

Despite the dominant role of the Monte Carlo ray-trace (MCRT) method in modern radiation heat transfer analysis, the contemporary literature remains surprisingly reticent on the uncertainty of results obtained using it. After first identifying the radiation distribution factor as a population proportion, standard statistical procedures are used to estimate its mean uncertainty, to a stated level of confidence, as a function of the number of surface elements making up the enclosure and the number of rays traced per surface element. This a priori statistical uncertainty is then shown to compare favorably with the observed variability in the distribution factors obtained in an actual MCRT-based analysis. Finally, a formal approach is demonstrated for estimating, to a prescribed level of confidence, the uncertainty in predicted heat transfer. This approach provides a basis for determining the minimum number of rays per surface element required to obtain the desired accuracy.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2019;141(3):032702-032702-10. doi:10.1115/1.4042442.

Origami tessellations have been proposed as a mechanism for control of radiative heat transfer through the use of the cavity effect. This work explores the impact of a changing projected surface area and varying apparent radiative properties on the net radiative heat transfer of an accordion fold comprised of V-grooves. The net radiative heat transfer of an accordion tessellation is obtained by a thermal energy balance at the cavity openings with radiative properties of the cavities given as a function of various cavity parameters. Results of the analytical model are experimentally confirmed. An accordion tessellation, constructed of stainless-steel shim stock, is positioned to achieve a specified fold angle and placed in a vacuum environment while heated by Joule heating. A thermal camera records the apparent temperature of the cavity openings for various fold angles. Results are compared to apparent temperatures predicted with the analytical model. Analytically and experimentally obtained temperatures agree within 5% and all measurements fall within experimental uncertainty. For diffusely irradiated surfaces, the decrease in projected surface area dominates, causing a continuous decrease in net radiative heat transfer for a collapsing accordion fold. Highly reflective specular surfaces exposed to diffuse irradiation experience large turn-down ratios (7.5× reduction in heat transfer) in the small angle ranges. Specular surfaces exposed to collimated irradiation achieve a turn down ratio of 3.35 between V-groove angles of 120 deg and 150 deg. The approach outlined here may be extended to modeling the net radiative heat transfer for other origami tessellations.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2019;141(3):034501-034501-5. doi:10.1115/1.4042330.

This study deals with the mixed convection flow through a shallow horizontal vent linking two compartments (one over the other). Depending on the temperature difference of gas as well as the ventilation flow rate between the two compartments, the flow through the vent can be bi- or uni-directional. A literature survey highlights that three correlations are used in safety engineering to calculate these upward and downward mixed convection flow rates. Unfortunately, for the same conditions, these correlations give very different results and, to date, there is no common agreement in the scientific community to identify quantitatively the most accurate model. This study proposes a new assessment of these correlations based on new experimental data obtained from the laboratory facility as well from the industrial apparatus. In addition, an improvement of the best model is proposed which better reproduced the experimental results.

Commentary by Dr. Valentin Fuster

### Errata

J. Heat Transfer. 2019;141(3):037001-037001-1. doi:10.1115/1.4042106.

Figures 2 and 6 in the publication are referred to our previous published paper “‘Heat Flow Choking in Carbon Nanotubes,’ 53(9–10), pp. 1796–1800 (2010)” [DOI: 10.1016/j.ijheatmasstransfer.2010.01.010]. These figures and data are reused with permissions from Elsevier. The statement of permission is missing in the published paper. Also our previous published paper should be added in the reference list, which is missing in the current published paper.

Commentary by Dr. Valentin Fuster