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The purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices.

The domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed.

The results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

This paper aims to study numerically the simulation of convective–radiative heat transfer under an effect of variable thermally generating source in a rotating square chamber. The performed analysis deals with a development of passive cooling system for the electronic devices.

The domain of interest of size H rotating at a fixed angular velocity has heat-conducting solid walls with a constant cooling temperature for the outer boundaries of the vertical walls and with thermal insulation for the outer borders of the horizontal walls. The chamber has a heater on the bottom wall with a time-dependent volumetric heat generation. The internal surfaces of the walls and the energy element are both grey diffusive emitters and reflectors. The fluid is transparent to radiation. Computational model has been written using non-dimensional parameters and worked out by the finite difference technique. The effect of the angular velocity, volumetric heat generation frequency and surface emissivity has been studied and described in detail.

The results show that growth of the surface emissivity leads to a diminution of the mean heater temperature, while a weak rotation can improve the energy transport for low volumetric thermal generation frequency.

An efficient computational approach has been used to work out this problem. The originality of this work is to analyze complex (conductive–convective–radiative) energy transport in a rotating system with a local element of time-dependent volumetric heat generation. To the best of the authors’ knowledge, an interaction of major heat transfer mechanisms in a rotating system with a heat-generating element is scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of complex heat transfer in rotating enclosures with internal heat-generating units, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Nowadays, the most important challenge in mechanical engineering, power engineering and electronics is a development of effective cooling systems for heat-generating units. Taking into account this challenge, this study aims to deal with computational investigation of thermogravitational energy transport of pseudoplastic nanoliquid in an electronic chamber with a periodic thermally producing unit placed on the bottom heat-conducting wall of finite thickness under an influence of isothermal cooling from vertical side walls.

The control equations formulated using the Boussinesq approach, Ostwald–de Waele power law and single-phase nanofluid model with experimentally based correlations of Guo et al. for nanofluid dynamic viscosity and Jang and Choi for nanofluid thermal conductivity have been worked out by the in-house computational procedure using the finite difference technique. The impact of the Rayleigh number, nanoadditives concentration, frequency of the periodic heat generation from the local element and thickness of the bottom solid substrate on nanoliquid circulation and energy transport has been studied.

It has been found that a raise of the nanoadditives concentration intensifies the cooling of the heat-generating element, while a growth of the heat-generation frequency allows reducing the amplitude of the heater temperature.

Mathematical modeling of a pseudoplastic nanomaterial thermogravitational energy transport in an electronic cabinet with a periodic thermally generating unit, a heat-conducting substrate and isothermal cooling vertical surfaces to identify the possibility of intensifying heat removal from a heated surface.

This paper aims to examine the thermal transmission and entropy generation of hybrid nanofluid filled containers with solid body inside. The solid body is seen as being both isothermal and capable of producing heat. A time-dependent non-linear partial differential equation is used to represent the transfer of heat through a solid body. The current study’s objective is to investigate the key properties of nanoparticles, external forces and particular attention paid to the impact of hybrid nanoparticles on entropy formation. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates. Hybrid nanofluid has been proven to have useful qualities, making it an attractive coolant for an electrical device. The findings would help scientists and engineers better understand how to analyse convective heat transmission and how to forecast better heat transfer rates in cutting-edge technological systems used in industries such as heat transportation, power generation, chemical production and passive cooling systems for electronic devices.

Thermal transmission and entropy generation of hybrid nanofluid are analysed within the enclosure. The domain of interest is a square chamber of size L, including a square solid block. The solid body is considered to be isothermal and generating heat. The flow driven by temperature gradient in the cavity is two-dimensional. The governing equations, formulated in dimensionless primitive variables with corresponding initial and boundary conditions, are worked out by using the finite volume technique with the SIMPLE algorithm on a uniformly staggered mesh. QUICK and central difference schemes were used to handle convective and diffusive elements. In-house code is developed using FORTRAN programming to visualize the isotherms, streamlines, heatlines and entropy contours, which are handled by Tecplot software. The influence of nanoparticles volume fraction, heat generation factor, external magnetic forces and an irreversibility ratio on energy transport and flow patterns is examined.

The results show that the hybrid nanoparticles concentration augments the thermal transmission and the entropy production increases also while the augmentation of temperature difference results in a diminution of entropy production. Finally, magnetic force has the significant impact on heat transfer, isotherms, streamlines and entropy. It has been observed that the external magnetic force plays a good role in thermal regulations.

Hybrid nanofluid is a desirable coolant for an electrical device. Various nanoparticles and their combinations can be analysed. Ferro-copper hybrid nanofluid considered with the help of prevailing literature review. The research would benefit scientists and engineers by improving their comprehension of how to analyses convective heat transmission and forecast more accurate heat transfer rates in various fields.

Due to its helpful characteristics, ferrous-copper hybrid nanofluid is a desirable coolant for an electrical device. The research would benefit scientists and engineers by improving their comprehension of how to analyse convective heat transmission and forecast more accurate heat transfer rates in cutting-edge technological systems used in sectors like thermal transportation, cooling systems for electronic devices, etc.

Entropy generation is used for an evaluation of the system’s performance, which is an indicator of optimal design. Hence, in recent times, it does a good engineering sense to draw attention to irreversibility under magnetic force, and it has an indispensable impact on investigation of electronic devices.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyse convective energy transport and entropy generation in a chamber with internal block, which is capable of maintaining heat and producing heat. Effects of irreversibility ratio are scrutinized for the first time. Analysis of convective heat transfer and entropy production in an enclosure with internal isothermal/heat generating blocks gives the way to predict enhanced heat transfer rate and avoid the failure of advanced technical systems in industrial sectors.

The purpose of this paper is to consider flow over heat generating bodies in an open‐ends cavity, which finds applications in electronics cooling and industrial processing. Heat transfer rates depend on the flow situation in the cavity, which is influenced by the cavity inlet and exit port locations, heat transferring body size and its orientation in the cavity, and the cavity size. Consequently, modeling of flow over heat transferring bodies in an open‐ends cavity and examination of the effect of the aspect ratio and orientation of the heat transferring bodies on the flow field and heat transfer rates becomes essential.

The flow over heat generating solid blocks situated in an open‐ends cavity is considered and the effects of blocks' orientations and aspect ratios on flow field as well as heat transfer rates are examined. A numerical scheme using a control volume approach is introduced to predict flow field in the cavity and heat transfer rates from the blocks.

It is found that complex flow structure is generated in the cavity due to the aspect ratios and orientations of the blocks. This, in turn, influences significantly heat transfer rates from the blocks in the cavity.

Surface areas of blocks are kept the same and aspect ratio is varied such that the surface area of each block remains the same in the simulations. In addition, Steady flow situation is considered for governing equations of flow and heat transfer in the cavity. However, for the future study transient heating and flow situations can be considered while varying the surface araes of the blocks. This will provide useful information on the circulations in the cavity and the enhancement of heat transfer due to the complex flow structure.

In practice, cooling effectiveness can be improved through changing the aspects ratio of the heat generating bodies in the cavity.

The findings are original and will be useful for the scientists and the design engineers working the specific area of heat transfer and fluid flow.

This paper aims to investigate thermal geometric optimisation of rectangular heat conductive cooling structures within solid heat‐generating media for the purpose of minimising peak temperatures and enabling optimum use of spatial volume within integrated power electronics.

A vortex‐centred finite volume numerical solver was developed, employing a fully implicit solution algorithm to obtain 3D temperature distributions. By comparing the peak temperatures obtained for a wide range of related cases, optimised cross‐sectional shapes for particular input conditions were obtained.

Optimum shapes are dependent on seven identified parameters. In cases where a low percentage of volume is occupied by cooling structures, a high tendency exists for continuous thin cooling layers, as opposed to discrete rectangular cooling inserts, to present the best thermal behaviour. At higher volume percentages, the opposite is true.

The reduced dimensions of cooling inserts have caused manufacturability to be a concern. Research has shown that at small dimensional scale ranges the cross‐sectional shape of the cooling insert has little influence on its thermal performance. In such cases little or no thermal advantage or loss is incurred by making use of continuous cooling layers, which are easiest to manufacture.

The tendencies of optimum cooling structure shapes were obtained and described in terms of seven geometric and material property‐related parameters. Thermal performance of individual inserts is not linearly proportional to dimensional scaling and it was found that, at small‐scale ranges, optimisation from a manufacturing viewpoint would not significantly impact on thermal performance.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

The Galerkin finite element method (FEM) based on the characteristic-based split (CBS) scheme is applied to simulate the nanofluid flow and thermal fields inside an inclined geometry filled by a heat-generating hydrodynamically and thermally anisotropic non-Darcy porous medium using the local thermal non-equilibrium model (LTNEM). Property of the hydrodynamic anisotropy is taken in both the Forchheimer coefficient and permeability and these tools are considered as functions of inclination of the principal axes. Also, the thermal conductivity for the porous phase is assumed to be anisotropic.

The Galerkin FEM based on the CBS scheme is applied to solve the partial differential equations governing the flow and thermal fields.

It is noted that the net rate of the heat transfer between the nanofluid and solid phases are influenced by variations of the anisotropic properties. Also, the system is reached to the thermal equilibrium state at H > 100. Further, the maximum nanofluid temperature is reduced by 12.27% when the nanoparticles volume fraction is varied from 0% to 4%.

This paper aims to study the nanofluid flow and heat transfer characteristics inside an inclined enclosure filled with a heat-generating, hydrodynamically and thermally anisotropic porous medium using the CBS scheme. The LTNEM is considered between the nanofluid and porous phases while the local thermal equilibrium model (LTEM) between the base fluid (water) and the nanoparticles (alumina) is taken into account. The Galerkin FEM is introduced to discretize the governing system of equations. Also, examine influences of the anisotropic properties (permeability, Forchheimer terms and thermal conductivity of the porous medium), inclination angle and nanoparticles volume fraction on the net rate of the heat transfer between the nanofluid and porous phases and on the local thermal non-equilibrium state is one of the concerns of this paper.

This study/paper aims to deal with thermal convection and entropy production of a ferrofluid in an enclosure having an isothermally warmed solid body placed inside. It should be noted that this research deals with a development of passive cooling system for the electronic devices.

The domain of interest is a square chamber of size L including a rectangular solid block of sizes l₁ and l₂. Thermal convection of ferrofluid (water–Fe₃O₄ nanosuspension) is analyzed within this enclosure. The solid body is considered to be isothermal with temperature T_h and also its area is L²/9. The vertical borders are cold with temperature T_c and the horizontal boundaries are adiabatic. The flow driven by temperature gradient in the cavity is two-dimensional. The governing equations, formulated in dimensionless primitive variables with corresponding initial and boundary conditions, are worked out by using the finite volume technique with the semi-implicit method for pressure-linked equations algorithm on a uniformly staggered mesh. The influence of nanoparticles volume fraction, aspect ratio of the solid block and an irreversibility ratio on energy transport and flow patterns are examined for the Rayleigh number Ra = 10⁷.

The results show that the nanoparticles concentration augments the thermal transmission and the entropy production increases also, while the augmentation of temperature difference results in a diminution of entropy production. Finally, lower aspect ratio has the significant impact on heat transfer, isotherms, streamlines and entropy.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze convective energy transport and entropy generation in a chamber with internal block. To the best of the authors’ knowledge, the effects of irreversibility ratio are scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer and entropy production in enclosures with internal isothermal blocks, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.