Isothermal Heat Source Research Articles

Thermo-magnetic convection of MHD Casson fluid in a wavy triangular porous cavity with embedded a cold inverted triangle obstacle

The design of enclosures is crucial in thermal engineering applications and technologies, encompassing areas such as electronics, heat transfer devices, power reactors, heating systems, solar panels, and nuclear power plants. Thermal efficiency in microchannels is optimized and improved by using triangular enclosures with varying aspect ratios. Specifically, the purpose of these triangular enclosures with cool cylinders is to reduce energy loss in nanoscale thermal sinks and thermal exchange devices. The current study aims to explore the thermal radiation effects on magnetohydrodynamic MHD Casson fluid flow within a wavy triangular cavity that includes an embedded cold inverted triangle. The inner inverted triangle is kept at a lower temperature, while the wavy bottom wall of the outer triangular cavity acts as an isothermal heat source at a higher temperature. The numerical solution for this mathematical model is obtained using the open-source finite element software COMSOL. In this study, the wavy triangular enclosure is analyzed for key parameters such as Casson parameter β , Hartmann number Ha , Rayleigh number Ra , numbers of undulation N , radiation Rd and inclination γ . The study presents the local distribution of streamlines, velocity profiles, isothermals, and entropy production, along with the Nu avg . The results reveal the rate of heat transport and total entropy production raise with the increasing number of undulations N and the Casson parameter β , while they decrease with increasing Hartmann number Ha . The number Nu avg rises with the increasing radiation parameter Rd and Rayleigh number Ra . The maximum stream function is observed at an inclination angle of 60 ° .

Cold obstacle influence on nanofluid convection in porous cavity

Enclosure design has a substantial influence on thermal engineering procedures and technology, such as electronics, thermal exchangers, power engines, heating systems, solar panels, and nuclear power plants. Triangular enclosures with different aspect ratios are used for multiple-purpose optimization and enhanced thermal efficiency in microchannels. Triangle enclosures with cold cylinders are often used to reduce heat loss in thermal exchange devices and nanoscale thermal sinks. The objective of the current study is to explore the natural convection of a hybrid nanofluid within a wavy-bottom triangular porous cavity containing an embedded cold inverted triangle, all under the influence of an inclined magnetic field. The inner inverted triangle maintains a lower temperature, while the wavy bottom wall of the outer triangular cavity acts as an isothermal heat source at high temperatures. The space between the inner and outer triangles is filled with hybrid nanofluid (Ag–MgO– water). The numerical solution for the modeled mathematical framework is derived using the open-source finite element program COMSOL. A wavy triangle enclosure is used in this work to analyze key elements, such as the Hartmann number, Ha, the Rayleigh number, Ra, the volume fraction, ϕ, the Darcy number, Da, and the inclination, γ. The local distribution of streamlines, velocity profile, isotherms, and entropy production are demonstrated along with the average Nusselt number. The findings reveal that the heat transfer rate and the total entropy generation increase with increase in Da, while their values decrease with increase in Ha. The value of Nu is raised with increase in the volume fraction ϕ and Rayleigh number Ra. The velocity profile shows increase with increase in the volume fraction ϕ and Rayleigh number Ra.

Transient Thermal Spreading From a Circular Heat Source in Polygonal Flux Tubes

Abstract This study develops a numerical simulation to assess transient constriction resistance in various semi-infinite flux channel geometries, including circle on circle, triangle, square, pentagon, and hexagon, which are derived from various heat source arrangements in a large domain. Using both isothermal and isoflux circular heat sources in polygonal flux channels, and employing a finite volume method, the study evaluates transient constriction resistance. The research confirms that for different geometries, similar nondimensionalized constriction resistance results are obtained, particularly when using the square root of the source area as the characteristic length and the square root of the constriction area ratio. The study reveals that flux tube shape has a minimal impact on thermal spreading resistance, with the circle-on-triangle configuration displaying the largest deviation from a simple circle-on-circle model. These insights advance our understanding of thermal spreading resistance in polygonal flux channels and their applications in thermal engineering, especially in contact heat transfer problems.

Melting and Heat Transfer Characteristics of Phase Change Material: A Comparative Study on Wire Mesh Finned Structure and Other Fin Configurations

Abstract In the present paper, a two-dimensional transient numerical study has been performed to investigate the influence of different fin designs on the melting and heat transfer characteristics of a phase change material (PCM), i.e., Paraffin wax, filled in square enclosures equipped with fin structures. Five distinct fin designs were examined: single rectangular, double rectangular, double triangular, double angled, and wire mesh. It is worth noting that all these fin designs have the equal heat transfer area. An isothermal heat source of temperature 350 K is provided at the left wall of the square enclosure and the remaining walls are assumed to be adiabatic. Six parameters were evaluated to determine the best fin configurations: melting time, enhancement ratio (ER), time savings, energy stored, mean power, and Nusselt number. The results show that all the fin designs outperformed as compared to model 1 (no fin configuration). Among the finned configurations, model 2 had the poorest performance, taking 1314 s to complete the melting, while model 6 had the most efficient fin design, with a melting time reduced by 67.53% compared to model 1. Model 6 also had the highest ER and mean power, i.e., 70.43% and 199.51%, respectively and as the melting process continued, the Nusselt number decreased. In addition to the above, we optimized the element size of the wire-mesh fin design using RSM methodology. This optimized design decreases the melting period by 70.04%. Overall, present study provides a comprehensive analysis of different finned configurations for improving the melting performance of the PCM in square enclosures and found wire-mesh fin design most appropriate and promising.

THERMAL SOURCE EFFECT ON THE NATURAL CONVECTION OF A NANOFLUID WITHIN A TRIANGULAR CAVITY

Natural convection is numerically studied in a triangular cavity whose inclined walls that is isothermal at temperature TC, while its base is thermally insulated. The cavity contains a hot isothermal cylindrical heat source TH of diameter D. In this study, we used the nanofluid (water + TiO2). The nanoparticle volume fraction is varied within the range 0.01 ≤ ϕ ≤ 0.05, and the Rayleigh number is set between 103 and 106. The main objective of this study is to explore the impact of nanoparticle concentration, Rayleigh number (Ra), and heat source position (h) on the enhancement of convective thermal transfer. The simulation results show that thermal exchange improves with increasing Ra, heat source diameter, and nanoparticle volume fraction (ϕ).

Thermal spreading resistance from an isothermal source into a finite-thickness body

Thermal spreading resistance is encountered during two-dimensional thermal conduction from a hot surface into a body. Thermal spreading and the opposite problem of thermal constriction resistance are of much technological relevance in the design of heat sinks and thermal spreaders for thermal management of microelectronics and other heat-generating devices. Much of the past work in the theoretical analysis of thermal spreading is based on a source with given heat flux. In contrast, the isothermal source problem presents difficulties due to the resulting mixed nature of the boundary condition, due to which, only approximate solutions are available. This work derives the steady-state thermal spreading resistance from an isothermal source into a finite-thickness slab or cylinder. The mixed boundary condition is handled by posing it in the form of a spatially varying convective boundary condition, with a sufficiently large Biot number over the source to represent its isothermal nature. A series solution for the problem is derived, along a sufficient set of linear algebraic equations to determine the series coefficients. Results are shown to agree well with finite-element simulations. Results are compared with previously-reported approximate solutions within the parametric range of validity of the approximate solutions. The impact of key non-dimensional parameters on thermal spreading resistance is quantified. It is shown that thermal spreading resistance increases with decreasing size of the isothermal heat source, as expected. A third-order polynomial correlation with very good accuracy is proposed. This work advances the theoretical understanding of a problem for which only approximate solutions have been reported in the past. Results presented here offer a practical tool for thermal design and optimization of a variety of practical thermal management problems involving spreading or constriction.

Slip and non-slip flows of MHD nanofluid through microchannel to cool discrete heat sources in presence and absence of viscous dissipation

This paper investigates heat transfer (HTR) and fluid flows of a magnetohydrodynamic (MHD) nanofluid (NFD) in a two-parallel-plate microchannel with three isothermal heat sources and under temperature jump and slip (0 < B* < 0.1) and non-slip regimes. The flow is subjected to a magnetic field (0 < Ha < 60) in three zones in the presence and absence of viscous dissipation (VDS) (0 < Br < 0.1). Using SIMPLE algorithm, it is found that a rise in the Re (0 < Re < 100) increases HTR under both slip and non-slip conditions. VDS decreases HTR from the isothermal heat source to the NFD flow. An increase in the slip coefficient raises the Nu, particularly at higher Ha. A rise in the Ha leads to greater HTR under the slip boundary condition. An increase in the slip coefficient raises the Nu by 52.52% in the presence of VDS and by 1.16% in the absence of VDS.

Computational analysis of natural convection with water based nanofluid in a square cavity with partially active side walls: Applications to thermal storage

Heat transport induced by buoyancy caused natural convection inside a segmented or selectively heated enclosure has grown in importance over the decades due to its significance in many fields in industrial implementations such as heat source cooling, food sterilizers, crystal growth, geothermal power systems, solar thermal collectors, melting and recrystallization procedures, microelectronic and nuclear industries, biomedical, and so forth. The novelty of current modern analysis is to scrutinize the natural convection of Titanium Oxide-water nanofluid in the cavity with partially active walls simulated by the finite element (FEM) method. The fluid flow and the thermal transportation within the enclosure are scrutinized. Two cases are carried out in this novel study, heat sink with constant temperature Tc consists in case 1 from the left and right partially active cavity walls and isothermal heat source having temperature Th correspondingly, whereTh>Tc. While upper and lower walls with inactive portions of the left and right walls are kept insulated. In case 2 the left and right walls of the cavity are heated while a partially active bottom wall is cold with other inactive parts insulated by the cavity walls. The finite element method is applied to tackle the governing equations. The Significance of Rayleigh number (100⩽Re⩽1e6) and volume fractions of nanopowders (0.01⩽ϕ⩽0.06) against fluid flow and heat transfer is demonstrated through streamlines and isotherms. From the results it is concluded that velocity amount is increased with escalating the values of Rayleigh number. The thermal results are enhanced with Rayleigh number. Furthermore the heat transfer is rised with volume fraction of nanoparticles. Additionally, from the analysis reveals that local Nusselt number is enhanced with Rayleigh number and nanoparticle volume fraction.

Analysis of internal cooling system in a vented cavity using P, PI, PID controllers

The investigation of the problem of internal cooling system inside a vented cavity utilizing P, PI, and PID controllers are carried out in this paper. The cavity consists of an outlet, an airflow inlet, a temperature sensor, and an isothermal heat source. The remaining walls are kept at ambient temperature. A temperature probe at a central location is used to measure the internal cooling condition and hence, to control the inlet air velocity via three different types of controller arrangements. The governing Navier-Stokes and energy equations along with appropriate boundary conditions are solved using Galerkin finite element technique. Parametric simulation is conducted by considering different values of proportional (0.01, 0.05, 0.1 ms−1K−1), integral (0.1, 0.2, 0.5 ms−2K−1), and derivative (0.001, 0.0001, 0.00001 mK−1) gains for three different types of controllers. The velocity and temperature contours are used to visualize the thermo-fluid behaviors of airflow inside the cavity. Besides, non-dimensional fluid temperature of the cavity at the set point is monitored closely to determine and compare the performance of the controllers.

Thermo-magnetic convection of nanofluid in a triangular cavity with a heated inverted triangular object

The present study aims to explore the buoyancy-driven convective phenomena of nanofluid flow in a cavity of an isosceles triangle with an inverted triangular heat source under the effect of a sloped magnetic field. The cases of different heating loads are analyzed considering various sizes of the heating triangle. The outer triangular cavity is kept at a lower temperature; whereas the inner inverted triangular is maintained as the isothermal heat source. Space in-between the inner and other triangle is filled with nanofluid (Al2O3-water). Finite element methodology is adapted to compute the coupled transport equations numerically. The convective phenomena and associated heat transfer characteristics are examined systematically for a range of control parameters like Rayleigh numbers (103–106), Hartmann number (0–70), and magnetic field inclination angle (0−180°), and the size of the inner inverted triangular heat source. The illustrations of local distribution of streamlines, isotherms, entropy generation are presented along with the average Nusselt number, Nu. It shows that the size of the inner triangular heat source controls the overall thermal behavior. The maximum convective heat transfer is obtained with the least flow obstruction (i.e. smaller size of the inner triangle). The study of magnetic field inclination shows that maximum heat transfer is obtained at an inclination of 90° and minimum flow obstruction.

Numerical Investigation of Rayleigh–Benard Natural Convection and Entropy Generation in a Cubic Cavity With Discrete Heat Sources

Abstract Three-dimensional (3D) natural convection with isothermal discrete heat sources in a cubical cavity has been carefully studied using the 3D vector potential–vorticity formulation. Based on the finite volume method, the governing equations are solved with a homemade computational code (written in Fortran). Assuming that all cavity vertical walls are adiabatic, the upper wall of the cavity is kept at a cold temperature. However, in the bottom face, heat sources are placed under different configurations. The size of the discrete sources, their positions, and their numbers are varied for different Rayleigh numbers. The Prandtl number is fixed at 0.71. Three-dimensional distribution of the temperature iso-surfaces, the heat transfer rate, and entropy generation is evaluated. It is found that heat transfer and entropy generation are strongly affected by the arrangement of the discrete heated sources. In conclusion, the heat transfer rate is maximized, and the entropy generation is minimized for the inline arrangement of more than two heaters compared to the diagonal one.

Thermal spreading resistance of hollow hemi-sphere with internal convective cooling

The 2-D steady-state heat transfer in a hollow hemi-sphere subjected to an arbitrary general heat flux on its pole, and convective cooling at the inner surface, is studied analytically. Closed-form mathematical expressions for temperature distribution and non-dimensional thermal resistance as a function of radii ratio, contact angle, and the Biot number, are derived and presented for two cases that simulate the flux distribution from isoflux and isothermal heat sources. The analytical solution is verified by using a finite-element numerical solution, developed in a commercially-available software, and comparing the results. Moreover, it is demonstrated that the present fundamental analysis provides a general solution for other problems found in the literature, including spreading resistance in hollow spheres with insulated walls, as well as the heat source on a half-space and infinite disk with an isothermal end.

Device modeling and performance optimization of thermoelectric generators under isothermal and isoflux heat source condition

Thermoelectric generator (TEG) is considered as promising way of clean energy generation by recycling waste heat, but its poor performance due to several kinds of energy losses impedes wide scale commercialization. Since, most of the waste heat sources have constant heat flux (isoflux) conditions it is necessary to evaluate the performance of TEG under such conditions. Here, various kinds of parasitic heat losses such as conduction, and radiation along with energy losses through contacts are numerically simulated in order to predict the performance of TEG for both isothermal and isoflux heat source conditions. Further, optimizations of controlling parameters of TEG such as leg geometry, leg length, cross sectional area, and external load resistance are done to maximize the efficiency and power output of TEG. To overcome the cumbersome optimization process by experimental trials, Taguchi and ANOVA methods are employed to optimize all the device parameters for both types of operating conditions i.e. isothermal and isoflux. Under optimized conditions, maximum power of ~48 W (an increase of 52%) is predicted under isothermal condition for cylindrical legged TEG and 10.6 W (an increase of 100%) is obtained under constant heat flux of 63 kW/m2 for pyramid legged TEG.

Multi Relaxation Time Lattice Boltzmann Method Simulation of Natural Convection Combined with Surface Radiation in a Square Open Cavity from Three Discrete Heat Sources

Heat transfer induced by combined surface radiation and laminar natural convection in an open square cavity heated by three identical isothermal heat sources is studied numerically by using the multirelaxation time scheme of the lattice Boltzmann method. The working fluid is air. The heat sources, separated by adiabatic segments, are mounted on a vertical wall facing the aperture of the cavity and the horizontal walls of the latter are insulated. The parameters governing the problem are the emissivity of the walls (varied from 0 to 1) and the Rayleigh number (varied from to ). The results obtained show that the convective heat transfer outclasses the radiative one even when the emissivity of the walls is high. The disproportionality observed in the cooling rates of the heat sources may be strongly attenuated by the inclusion of radiation in the heat transfer mechanism. Results obtained for the heat transfer from each of the three heat sources and the volumetric flow rate aspired into the cavity are grouped in useful correlations.

Numerical investigation of mixed convection heat transfer behavior of nanofluid in a cavity with different heat transfer areas

The main purpose of this research is the numerical modeling of laminar mixed convection heat transfer inside an open square cavity with different heat transfer areas. In the considered geometry, cold fluid enters the cavity. At the middle of the cavity, there is a hot isothermal circular heat source. For increasing the heat transfer, solid silver nanoparticles with volume fractions (φ) of 0, 2 and 4% are added to water. Studied Re numbers are 10, 50, 120 and 200. The location of the hot zone changes the temperature distribution in the fluid layers. If the heat transfer area is located in an appropriate location, temperature distribution becomes more uniform. Increasing Re leads to smaller temperature gradients in regions near the hot surface and higher temperature at fluid layers close to the surface. By increasing fluid velocity, backflows do not improve heat transfer but it is able to change the heat transfer mechanism. By decreasing the fluid velocity, the effects of velocity gradients and extension of the velocity boundary layer increase and friction coefficient attains the maximum value.

Entropy generation and natural convection in a wavy-wall cavity filled with a nanofluid and containing an inner solid cylinder

This work investigates the problem of entropy generation and natural convection in a wavy-wall cavity filled with a nanofluid and containing solid inner cylinder using the Galerkin finite-element method. An isothermal heat source fixed at the left vertical wall of the cavity and the horizontal walls have taken adiabatic, while the right wavy wall cooled isothermally. An Al2O3-water nanofluid fills the space between the wavy-wall cavity and the solid cylinder. To study this problem, the influence of three variables have taken into account. These variables are Rayleigh number (103 ≤ Ra ≤ 106), nanoparticle volume fraction (0 ≤ φ ≤ 0.04), and the number of undulations (1≤ N ≤ 4). The numerical results can be in the forms of streamlines, isotherms and local entropy generation as well as the average Nusselt number. The obtained results indicate that the effect of the nanoparticles addition on the heat transfer rate is essential for low Rayleigh number and number of undulations.

Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel

This paper investigates the mixed convection and entropy generation of an Ag-water nanofluid in an L-shaped channel fixed at an inclination angle of 30° to the horizontal axis. An isothermal heat source was positioned in the middle of the right inclined wall of the channel while the other walls were kept adiabatic. The finite volume method was used for solving the problem’s governing equations. The numerical results were obtained for a range of pertinent parameters: Reynolds number, Richardson number, aspect ratio, and the nanoparticles volume fraction. These results were Re = 50–200; Ri = 0.1, 1, 10; AR = 0.5–0.8; and φ = 0.0–0.06, respectively. The results showed that both the Reynolds and the Richardson numbers enhanced the mean Nusselt number and minimized the rate of entropy generation. It was also found that when AR. increased, the mean Nusselt number was enhanced, and the rate of entropy generation decreased. The nanoparticles volume fraction was predicted to contribute to increasing both the mean Nusselt number and the rate of entropy generation.

Buoyancy driven turbulent plume induced by protruding heat source in vented enclosure

The buoyancy driven thermal plume behavior inside a partial square enclosure with protruding isothermal heat source block is numerically investigated. The turbulent flow is modeled by using unsteady Favre-averaged Navier-Stokes (UFANS) equation with buoyancy modified Lam Bremhorst low Reynolds number k−ϵ model. A Simplified Marker and Cell algorithm (SMAC) is used to solve the governing equations and the computations are performed using an in-house code based on Finite difference method. The heat transfer characteristics and the bidirectional exchange across the vent are analyzed for different Grashof number 108 ≤ Gr ≤ 1011. Further, the thermal plume patterns are investigated by mounting the heat source block at five different locations δ = 0.25 H, 0.35 H, 0.5 H, 0.65 H and 0.75 H. A significant enhancement in the net mass flow rate and average Nusselt number is observed by increasing the Grashof number. It is found that the heat source location has strong influence on the vent bidirectional exchange rate, thermal mixing and heat transfer characteristics inside the enclosure. The present model is validated with the experimental and numerical benchmark results available in literature.

Spreading and Contact Resistance Formulae Capturing Boundary Curvature and Contact Distribution Effects

There is a substantial and growing body of literature which solves Laplace's equation governing the velocity field for a linear-shear flow of liquid in the unwetted (Cassie) state over a superhydrophobic surface. Usually, no-slip and shear-free boundary conditions are applied at liquid–solid interfaces and liquid–gas ones (menisci), respectively. When the menisci are curved, the liquid is said to flow over a “bubble mattress.” We show that the dimensionless apparent hydrodynamic slip length available from studies of such surfaces is equivalent to (i) the dimensionless spreading resistance for a flat, isothermal heat source flanked by arc-shaped adiabatic boundaries and (ii) the dimensionless thermal contact resistance between symmetric mating surfaces with flat contacts flanked by arc-shaped adiabatic boundaries. This is important because real surfaces are rough rather than smooth. Furthermore, we demonstrate that this observation provides a significant source of new and explicit results on spreading and contact resistances. Significantly, the results presented accommodate arbitrary solid-to-solid contact fraction and arc geometry in the contact resistance problem for the first time. We also provide formulae for the case when each period window includes a finite number of no-slip (or isothermal) and shear free (or adiabatic) regions and extend them to the case when the latter are weakly curved. Finally, we discuss other areas of mathematical physics to which our results are directly relevant.

Effect of two isothermal obstacles on the natural convection of nanofluid in the presence of magnetic field inside an enclosure with sinusoidal wall temperature distribution

In this study, the effect of magnetic field on the natural convection of Al2O3-water nanofluid inside a square enclosure with isothermal obstacles and sinusoidal wall temperature distribution has been numerically studied. The sidewalls were subject to sinusoidal boundary conditions, while the top and bottom walls were insulated. Two isothermal heat sources were implemented within the enclosure at the same distance from the center. The governing equations were transformed into the algebraic form using finite volume method and were then simultaneously solved using the SIMPLE algorithm. The proposed model by Vajjha was used to calculate the coefficient of thermal conductivity by taking Brownian motion of particles into account. In this study, the effect of Rayleigh number, aspect ratio, Hartmann number, direction change of applied magnetic field, and the volumetric percentage of nanoparticles was investigated. The results indicated that by increasing the Hartmann number, the fluid velocity as well as the Nusselt number decreased at all volumetric fractions of nanoparticles. An increase in the volumetric fraction of nanoparticles increased the Nusselt number, so that at a nanoparticle concentration of 6%, the mean Nusselt number increased by 9.04% compared to that of the base fluid. Moreover, the Nusselt number increased by increasing the magnetic field angle and the Rayleigh number, while it decreased as the aspect ratio was increased.