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Research Papers

J. Thermal Sci. Eng. Appl. 2019;11(6):061001-061001-12. doi:10.1115/1.4042988.

The intense thermal fluxes and aero-thermomechanical loads generated at sharp leading edges of atmospheric hypersonic vehicles traveling above Mach 5 have motivated an interest in novel thermal management strategies. Here, we use a low-temperature stainless steel-water system to experimentally investigate the feasibility of metallic leading edge heat pipe concepts for thermal management in an efficient load supporting structure. The concept is based upon a two-phase, high thermal conductance “heat pipe” which redistributes the localized thermal flux created at the leading edge stagnation point over a larger surface for effective removal. Structural efficiency is achieved by configuring the system as a wedge-shaped sandwich panel with an I-cell core that simultaneously permits axial vapor and returns liquid flow. The measured axial temperature profiles resulting from a localized thermal flux applied to the tip are consistent with effective thermal spreading that lowered the peak leading edge temperature and reduced the temperature gradients when compared with an equivalent structure containing no working fluid. A simple finite element model that treated the vapor as an equivalent, high thermal conductivity material was in good agreement with these experiments. The model is then used to design a niobium alloy-lithium system that is shown to be suitable for enthalpy conditions representative of Mach 7 scramjet-powered flight. The study indicates that the surface temperature reductions of heat pipe-based leading edges may be sufficient to permit the use of nonablative, refractory metal leading edges with oxidation protection in hypersonic environments.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061002-061002-11. doi:10.1115/1.4043004.

With a substantial increase in thermal power density, the operating temperature of high-power light-emitting diodes (LEDs) rises rapidly, exerting a notable effect on chipsets’ performance. A water-cooled microchannel radiator and an air-cooled radiator are proposed to solve this problem. The effects of key factors of both radiators on heat dissipation in a high-power LED chipsets, and general comparisons between each method, are analyzed via Fluent. The simulation results indicate that heat dissipation from the water-cooled microchannel radiator is readily affected by the microchannel’s flow rate and aspect ratio. A larger flow rate and larger aspect ratio favor improved heat dissipation in the water-cooled microchannel radiator. Heat dissipation in the air-cooled radiator is related to volumetric flow rate, rib number, rib height, rib thickness, and substrate thickness. A larger volumetric flow rate, rib number, and rib height favor heat dissipation in the air-cooled radiator. However, there is a critical thickness value: if the thickness is less than the critical value, heat dissipation is greatly affected by rib thickness and substrate thickness, if the thickness is larger than the critical value, the influence is insignificant. The high-power LED chipsets’ temperature is also related to the insulating substrate’ input power and thermal conductivity. A large input power leads to a substantial increase in temperature, and larger thermal conductivity of the insulating substrate minimizes temperature increase in the high-power LED chipsets. When comparing the two radiators, results show an air-cooled radiator should be used in low-power LED chipsets. When an air-cooled radiator cannot satisfy the chipset’s needs, a water-cooled microchannel radiator should be utilized.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061003-061003-12. doi:10.1115/1.4043007.

In order to cool a heated surface surrounded by fluid flow, vortex generator plays a significant role. The presence of a vortex generator in the flow creates both latitudinal and longitudinal vortices. The vortices energize the boundary layer over the heated surface and excel convective mode of heat transfer. Therefore, the strength of these vortices is directly proportional to the heat transferal rate. The present study considers a vortex generator attached to a heated base plate. The system is studied numerically and experimentally. The existing rectangular vortex generator is modified computationally with a goal to escalate the overall heat transferal rate. The role of secondary surfaces fixed over the primary surface of the rectangular vortex generator is discussed. Water flows over the surface of the base plate at a Reynolds number of 350. And the plate has a constant heat flux of 1 kW/m2. The results show that the secondary surfaces fixed parallel to the heated plate over the vortex generator significantly augment the heat transfer rate to about 13.4%. However, it enhances the drag by 5.7%. A linear regression analysis predicts the suitable placement of the secondary surface with an enhancement of heat transfer rate of about 7.6%, with a decrease in the drag by about 0.7%. In order to validate the obtained results, the best configuration is fabricated and tested experimentally. The experimental outcomes are found to complement the numerical results. In this experiment, the modification yields 25% enhancement in heat transfer rate.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061004-061004-5. doi:10.1115/1.4043005.

Direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) are used to study the steady-state Rayleigh–Bénard convection (RB) in a two-dimensional unit aspect ratio box. The steady-state RB convection is characterized by analyzing the time-averaged temperature-field, and flow field for a wide range of Rayleigh number (2.1 × 105 ⩽ Ra ⩽ 2.1 × 108). It is seen that the time-averaged and space-averaged Nusselt number (Nuh¯) at the hot-wall monotonically increases with the increase in Rayleigh number (Ra) and the results show a power law scaling Nuh¯Ra0.2593. The current Nusselt number results are compared with the results available in the literature. The complex flow is analyzed by studying the frequency power spectra of the steady-state signal of the vertical velocity at the midpoint of the box for different Ra and probability density function of dimensionless temperature at various locations along the midline of the box.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061005-061005-9. doi:10.1115/1.4043093.

The evaporation of sessile drop has a wide range of application that includes printing, washing, cooling, and coating. Due to the complex nature of drop evaporation process, this phenomenon is reliant on several parameters such as ambiance and physiochemical properties of liquid and surface. In the present study, a mathematical model of water droplet evaporation on an engineered aluminum surface is developed. Experimental study is carried out for the validation of code. The data obtained from the simulation is validated against the data obtained from an experimental study as well as the data available in the literature and good agreement was found among them. Post-validation, the effect of surface wettability and environment conditions on a droplet evaporation rate is estimated. It is inferred from the outcomes that the temperature at the apex of the drop varies linearly with the increasing relative humidity. Droplet volume has a significant impact on the evaporation rate and comparatively higher evaporative flux for a smaller volume of the drop with large contact angles. This unveils the possibility of achieving the required evaporation rate by controlling surface wettability and relative humidity conditions near the drop.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061006-061006-7. doi:10.1115/1.4043090.

This paper presents an investigation of a three-phase oscillating heat pipe (3P OHP). The working fluid in the OHP consists of phase change material (PCM) and water. During the operation, the PCM changes the phase between solid and liquid, and water changes phase between liquid and vapor. The OHP investigated herein contains three phases: solid, liquid, and vapor. Erythritol was selected as the PCM with an instant cooling effect when dissolved in water due to the high fusion heat of 340 J/g. When the working fluid flows into the evaporator section, the PCM solid phase of the working fluid can become liquid phase in the evaporator, and the PCM liquid phase of the working fluid become solid phase in the condenser. The effects of heat input ranging from 100 to 420 W, and the erythritol concentration ranging from 1 to 50 wt % on the slug oscillations, and the OHP thermal performance was investigated. Experimental results show that while the erythritol can help to increase the heat transfer performance of an OHP, the heat transfer performance depends on the erythritol concentration. With a range of 1–5 wt % concentration of erythritol/water mixtures, a maximum 10% increase in the thermal performance was observed. When the erythritol concentration of erythritol/water mixtures was increased to a range of 10–50 wt %, the thermal performance of OHPs was lower than pure water-filled OHP, and the thermal performance decreased as the erythritol concentration was further increased. In addition, visualization results showed that slug oscillation amplitudes and velocities were reduced in the OHPs with erythritol solution compared with water-filled OHP.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061007-061007-11. doi:10.1115/1.4043185.

This study compares two numerical strategies for modeling flow and heat transfer through mini- and microchannel heatsinks, the unit cell approximation, and the full 3D model, with the objective of validating the former approach. Conjugate heat transfer and laminar flow through a 2 × 2 cm2 copper–water heatsink are modeled using the finite element package COMSOL Multiphysics 5.0. Parametric studies showed that as the heatsink channels’ widths were reduced, and the total number of channels increased, temperature and pressure predictions from both models converged to similar values. Relative differences as low as 5.4% and 1.6% were attained at a channel width of 0.25 mm for maximum wall temperature and channel pressure drop, respectively. Due to its computational efficiency and tendency to conservatively overpredict temperatures relative to the full 3D method, the unit cell approximation is recommended for parametric design of heatsinks with channels’ widths smaller than 0.5 mm, although this condition only holds for the given heatsink design. The unit cell method is then used to design an optimal heatsink for server liquid cooling applications. The heatsink has been fabricated and tested experimentally, and its thermal performance is compared with numerical predictions. The unit cell method underestimated the maximum wall temperature relative to experimental results by 3.0–14.5% as the flowrate rose from 0.3 to 1.5 gal/min (1.1–5.7 l/min).

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061008-061008-12. doi:10.1115/1.4043260.

The lean combustion chamber of low NOx emission engines has a short distance between combustion outlet and nozzle guide vanes (NGVs), with strong swirlers located upstream of the turbine inlet to from steady circulation in the combustion region. Although the lean combustion design benefits emission control, it complicates the turbine’s aerodynamics and heat transfer. The strong swirling flow will influence the near-wall flow field where film cooling acts. This research investigates the influence of inlet swirl on the film cooling of cascades. The test cascades are a 1.95 scale model based on the GE-E3 profile, with an inlet Mach number of 0.1 and Reynolds number of 1.48 × 105. Film cooling effectiveness is measured with pressure-sensitive paint (PSP) technology, with nitrogen simulating coolant at a density ratio of near to 1.0. Two neighboring passages are investigated simultaneously, so that pressure and suction side the film cooling effectiveness can be compared. The inlet swirl is produced by a swirler placed upstream, near the inlet, with five positions along the pitchwise direction. These are as follows: blade 1 aligned, passage 1–2 aligned, blade 2 aligned, passage 2–3 aligned and blade 3 aligned. According to the experimental results, the near-hub region is strongly influenced by inlet swirl, where the averaged film cooling effectiveness can differ by up to 12% between the neighboring blades. At the spanwise location Z/Span = 0.7, when the inlet swirl is moved from blade 1 aligned (position 5) to blade 2 aligned (position 3), the film cooling effectiveness in a small area near the endwall can change by up to 100%.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061009-061009-15. doi:10.1115/1.4043262.

The heat transfer in a pin finned duct is augmented by the protrusion in this study. The realizable k–ε turbulence model coupled with the enhanced wall function is used to obtain the flow structure and heat transfer characteristics. Six different rotational numbers (Ro = 0, 0.2, 0.4, 0.6, 0.8, and 1.0) and three different protrusion locations have been introduced. The pin fins and protrusions are placed on a simplified three-dimensional rectangular duct. Numerical results reveal that the Nusselt number in the pin finned channel has remarkable increase after adoption of the protrusions. In addition, the protrusion location and the rotational number have significant influence on the heat transfer distribution. The high rotational number is in favor of heat transfer enhancement on the endwall surface. Furthermore, the highest Nusselt number is occurred where protrusion is near the pin fin windward side.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061010-061010-10. doi:10.1115/1.4043467.

Refrigerated vehicle plays an essential role in the cold-chain applications. It directly affects the quality and shelf life of specialized perishable goods. However, the cold energy dissipation caused by natural convection through an open door during partial unloading breaks the isothermal cold environment and notably elevates the air temperature inside the refrigerated container. This temperature rise is harmful to the remaining food. In this study, an air curtain was introduced near the container doorway to attempt to reduce the cold energy dissipation caused by partial unloading. A numerical model was established to explore the effects of the key parameters of the air curtain such as the airflow rate, nozzle width, and jet angle on the air flow and temperature evolution inside the refrigerated container after the door is opened. The numerical results show that the key parameters need to be tailored to form a stable and effective air curtain for preventing the internal cold energy loss or external hot air invasion. An effective and stable air curtain was formed to make the inner air temperature increase only by about 3 °C from the initial temperature of 5 °C after the door was opened, when the jet velocity was set to 2 m/s, the nozzle width was set as 7.5 cm, and the jet angle was set between 0 deg and 15 deg. This work can offer significant guidance for the introduction of an effective air curtain in a refrigerated vehicle to avoid the failure of cold-chain transportation.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061011-061011-13. doi:10.1115/1.4043468.

A simultaneously developing microchannel gas flow is analyzed numerically, using the vorticity–stream function form of the Navier–Stokes equation, together with the fluid energy equation and the solid wall heat conduction equation. Rarefaction, shear work, viscous dissipation, pressure work, axial conduction, and conjugate effects on heat transfer characteristics are investigated. The shear work contribution to the wall heat flux is evaluated in both the developing and the fully developed flow regions and compared with the conductive wall heat flux. The assumption of hydrodynamically fully developed, thermally developing flow—normally used in the analysis of channel heat transfer—is assessed and compared with the simultaneously developing flow case. Analytical expressions for the fluid flow and heat transfer parameters under fully developed conditions are also derived and compared with the numerical results for verification. The analysis presented shows that the shear work and the combined viscous dissipation and pressure work result in extending the thermal entrance length by far. Heat conduction in the wall also contributes to increase the thermal entry length. The results presented also demonstrate the shear work contribution to heat transfer in the slip flow regime, although minor in the very first portion of the thermal entrance length, and it becomes progressively more significant as the flow thermal development conditions are approached and turns out to be exactly equal in magnitude to the conductive wall heat flux in the thermally fully developed region, resulting in a zero Nusselt number, as verified by both the exact and numerical solutions.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061012-061012-13. doi:10.1115/1.4043261.

Both analytical and computational methods for solidification problems are introduced. First, the inward solidification process in a spherical vessel is studied. Expressions of the stress, displacement in the solid phase, and the liquid pressure are deduced based on the solidification interface position. A phase-change expansion orientation factor is introduced to characterize the nonisotropic expansion behavior at the freezing interface. Then, an efficient coupled thermomechanical finite-element method is proposed to evaluate the thermal stress, strain, displacement, and pressure in solidification problems with highly nonlinear constitutive relations. Two particular methods for treating the liquid phase with fixed-grid approaches are introduced. The thermal stress is computed at each integration point by integrating the elastoviscoplastic constitutive equations. Then, the boundary value problem described by the global finite-element equations is solved using the full Newton–Raphson method. This procedure is implemented into the finite-element package abaqus via a FORTRAN subroutine UMAT. Detailed implementation steps and the solution procedures are presented. The numerical model is validated first by the analytical solutions and then by a series of benchmark tests. Finally, an example of solidification in an open reservoir with a free liquid surface is introduced. Potential industrial applications of the numerical model are presented.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061013-061013-11. doi:10.1115/1.4043464.

The thermal behavior of a compact mini-loop thermosyphon is experimentally studied at different filling ratios (20%, 30%, 40%, 50%, and 70%) and tilt angles (0 deg, 30 deg, 45 deg, 60 deg, and 90 deg) for the heat loads of 20–300 W using distilled water as the heat pipe fluid. The presence of microfins at the evaporator results in an average decrease of 37.4% and 15.3% in thermal resistance and evaporator wall temperature, respectively, compared with the evaporator with a plain surface. Both filling ratio (FR) and tilt angle influence the heat transfer performance significantly, and the best performance of the mini-loop thermosyphon is obtained at their optimum values. The thermal resistance and thermal efficiency values lie in the ranges of 0.73–0.076 K/W and 65–88.3% for different filling ratios and tilt angles. Similarly, evaporator heat transfer coefficient and evaporator wall temperature show significant variation with changes in filling ratio and tilt angle. A combination of the optimum filling ratio and tilt angle shows a lowest thermal resistance of 0.076 K/W and a highest evaporator wall temperature of 68.6 °C, which are obtained at 300 W. The experimental results recommend the use of mini-loop thermosyphon at an optimum filling ratio for electronics cooling applications, which have a heat dissipation of 20–300 W.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061014-061014-9. doi:10.1115/1.4043465.

High-pressure stage gas turbine blades feature serpentine passages where rib turbulators are installed to enhance heat transfer between the relatively colder air bled off from the compressor and the hot internal walls. Most of the prior studies have been restricted to Reynolds number of 90,000 and several studies have been carried out to determine geometrically optimized parameters for achieving high levels of heat transfer in this range of Reynolds number. However, for land-based power generation gas turbines, the Reynolds numbers are significantly high and vary between 105 and 106. The present study is targeted toward these high Reynolds numbers where traditional rib turbulator shapes and prescribed optimum geometrical parameters have been investigated experimentally. A steady-state liquid crystal thermography technique is employed for measurement of detailed heat transfer coefficient. Five different rib configurations, viz., 45 deg, V-shaped, inverse V-shaped, W-shaped, and M-shaped have been investigated for Reynolds numbers ranging from 150,000 to 400,000. The ribs were installed on two opposite walls of a straight duct with an aspect ratio of unity. For very high Reynolds numbers, the heat transfer enhancement levels for different rib shapes varied between 1.4 and 1.7 and the thermal hydraulic performance was found to be less than unity.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061015-061015-12. doi:10.1115/1.4043471.

Varying aspect ratio (AR) channels are found in modern gas turbine airfoils for internal cooling purposes. Corresponding experimental data are needed in understanding and assisting the design of advanced cooling systems. The present study features a two-pass rectangular channel with an AR = 4:1 in the first pass with the radial outward flow and an AR = 2:1 in the second pass with the radial inward flow after a 180 deg tip turn. Effects of rib coverage near the tip region are investigated using profiled 45 deg ribs (P/e = 10, e/Dh ≈ 0.11, parallel and in-line) with three different configurations: less coverage, medium coverage, and full coverage. The Reynolds number (Re) ranges from 10,000 to 70,000 in the first passage. The highest rotation number achieved was Ro = 0.39 in the first passage and 0.16 in the second passage. Heat transfer coefficients on the internal surfaces were obtained by the regionally averaged copper plate method. The results showed that the rotation effects on both heat transfer and pressure loss coefficient are reduced with an increased rib coverage in the tip turn region. Different rib coverage upstream of the tip turn significantly changes the heat transfer in the turn portion. Heat transfer reduction (up to −27%) on the tip wall was seen at lower Ro. Dependence on the Reynolds number can be seen for this particular design. The combined geometric, rib coverage, and rotation effects should be taken into consideration in the internal cooling design.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061016-061016-9. doi:10.1115/1.4043470.

High-porosity metal foams are known for providing high heat transfer rates, as they provide a significant increase in wetted surface area as well as highly tortuous flow paths resulting in enhanced mixing. Further, jet impingement offers high convective cooling, particularly at the jet footprint areas on the target surface due to flow stagnation. In this study, high-porosity thin metal foams were subjected to array jet impingement, for a special crossflow scheme. High porosity (92.65%), high pore density (40 pores per inch (ppi)), and thin foams (3 mm) have been used. In order to reduce the pumping power requirements imposed by full metal foam design, two striped metal foam configurations were also investigated. For that, the jets were arranged in 3 × 6 array (x/dj = 3.42, y/dj = 2), such that the crossflow is dominantly sideways. Steady-state heat transfer experiments have been conducted for varying jet-to-target plate distance z/dj = 0.75, 2, and 4 for Reynolds numbers ranging from 3000 to 12,000. The baseline case was jet impingement onto a smooth target surface. Enhancement in heat transfer due to impingement onto thin metal foams has been evaluated against the pumping power penalty. For the case of z/dj = 0.75 with the base surface fully covered with metal foam, an average heat transfer enhancement of 2.42 times was observed for a concomitant pressure drop penalty of 1.67 times over the flow range tested.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061017-061017-8. doi:10.1115/1.4043513.

Turbulent characteristics of Czochralski melt flow are presented using the unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modeling approach. Three-dimensional, transient computations were performed using the Launder and Sharma low-Re k-ε model and Menter shear stress transport (SST) k-ω model on an idealized Czochralski setup with counterrotating crystal and crucible. A comparative assessment is performed between these two Reynolds-averaged Navier–Stokes (RANS) models in capturing turbulent thermal and flow behaviors. It was observed that the SST k-ω model predicted a better resolution of the Czochralski melt flow capturing the near wall thermal gradients, resolving stronger convective flow at the melt free surface, deciphering more number of characteristics Czochralski recirculating cells along with predicting large number of coherent eddy structures and vortex cores distributed in the melt and hence a larger level of turbulent intensity in the Czochralski melt compared with that by Launder and Sharma low-Re k-ε model.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061018-061018-7. doi:10.1115/1.4043741.

An air-to-air heat pipe heat exchanger was built and tested for a domestic condenser tumble clothes dryer in this study, which can achieve better drying performance than a water-cooled type condenser tumble clothes dryer. The heat pipe heat exchanger was made asymmetrical, which can make full use of the irregular internal space without changing the original structure of the dryer. Under the same test conditions, the condenser tumble clothes dryer with the asymmetric heat pipe heat exchanger had lower final moisture content and a faster average drying rate than the water-cooled type condenser tumble clothes dryer. The average drying rate increased by 10.032% compared with the water-cooled type dryer. At the same time, it can achieve the objective of drying clothes without using water. This can save 2600–13,000 L of water for one year and reduce the cost of drying clothes. Besides, the energy consumption was investigated. More energy consumption and drying time can reach better dry results. With the increase in the hot fluid flow rate, the energy efficiency of the dryer has a decreasing trend. As the drying process progresses, the average drying rate decreases. These conclusions are helpful in optimizing domestic condenser tumble clothes dryers.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061019-061019-9. doi:10.1115/1.4043624.

Large eddy simulation (LES) of nonreacting turbulent flow in a multiswirler model combustor is carried out at elevated pressure and high temperature. Flow interaction between the main stage and the pilot stage is discussed based on the time-averaged and instantaneous flowfield. Flow dynamics in the multiswirling flow are analyzed using a phase-averaged method. Proper orthogonal decomposition (POD) is used to extract dominant flow features in the multiswirling flow. Numerical results show that the main stage and the pilot stage flows interact with each other generating a complex flowfield. Flow interaction can be divided into three regions: converging region, merging region, and combined region. A precessing vortex core (PVC) is successfully captured in the pilot stage. PVC rotates with a first dominant frequency of 2756 Hz inducing asymmetric azimuthal flow instabilities in the pilot stage. POD analyses for the velocity fields also show dominant high-frequency modes (mode 1 and mode 2) in the pilot stage. However, the dominant energetic flow is damped rapidly downstream of the pilot stage such that it has a little effect on the main stage flow.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061020-061020-4. doi:10.1115/1.4043809.

Effect of the size of a closed cavity and different nanoparticles on natural convection heat transfer is investigated using the finite volume method. In the current numerical study, free convection of nanofluid with Cu, multi-walled carbon nanotubes, and Al2O3 nanoparticles is considered at Rayleigh numbers (Ra) of 10–100,000 inside a two-dimensional rectangular cavity with different aspect ratios. Results of this study show that in the presence of cooling fluid with low temperature and hot zone in the cavity, due to the temperature difference between the fluid and hot zone, heat transfer occurs. Heat transfer in the cavity is influenced by fluid circulation caused by natural convection heat transfer and conductive heat transfer mechanism.

Commentary by Dr. Valentin Fuster
J. Thermal Sci. Eng. Appl. 2019;11(6):061021-061021-12. doi:10.1115/1.4043742.

In this paper, fluid flow pattern and heat transfer behavior are numerically studied in a trapezoidal enclosure inclined at different tilt angles. The enclosure has isothermally heated cylindrical inner wall and cooled cylindrical outer wall, whereas sidewalls have linearly varying temperature profile. The numerical analysis is performed at different Rayleigh numbers (103 ≤ Ra ≤106) and Prandtl numbers (0.71 ≤ Pr ≤ 40) assuming steady, incompressible, laminar, Newtonian, and two-dimensional flow. The angle between two nonparallel sidewalls is varied from 10 deg to 90 deg, while the tilt angle is varied from 5 deg to 175 deg. Governing equations along with the Poisson type equation for heatfunctions are solved to obtain fluid flow and direction of heat flow in the trapezoidal enclosure. At low Raleigh number, the isotherms are smooth, indicating the dominance of conduction heat transfer dominates. The streamlines, isotherms, and heatlines in high Prandtl number (Pr = 6.99 ad 40) fluids show a similar pattern as that in the air (Pr = 0.71) at Ra = 106; however, the strength of heatfunctions increases. With the increase in the aspect ratio of the enclosure, thermally stratified region is found to increase in size. Stronger convection is present in the enclosure with a higher angle between two nonparallel sidewalls.

Commentary by Dr. Valentin Fuster

Discussion

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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