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Sets out to discuss laminar free convection characteristics of air confined to a square cavity and a horizontal rectangular cavity (aspect ratio A=2) along with the viable isosceles triangular cavities and right‐angle triangular cavities that may be inscribed inside the two original cavities.

The three distinct cavities shared the base wall as the heated wall, while the remaining sides and upper walls are cold. The finite volume method is used to perform the numerical computation of the transient conservation equations of mass, momentum and energy. The methodology takes into account the second‐order‐accurate quick scheme for the discretization of the convective term, whereas the pressure‐velocity coupling is handled with the simple scheme. The working fluid is air, which is not assumed as a Boussinesqian gas, so that all influencing thermophysical properties of air are taken as temperature‐dependent. The cavity problem is examined over a variety of height‐based Grashof numbers ranging from 10³ to 10⁶.

Numerical results are reported for the velocity fields, the temperature field as well as the local and mean wall heat fluxes along the heated base wall. It was found that the airflow remains symmetric for the isosceles triangular cavity with aspect ratio A=1 even at high Grashof numbers. In contrast, for an isosceles triangular cavity with an aspect ratio A=2, a pitchfork bifurcation begins to form at a critical Grashof number of 2 × 10⁵, breaking the airflow symmetry. The computed local and mean heat fluxes along the hot base wall are compared for the three configurations under study and the corresponding maximum heat transfer levels are clearly identified for the two aspect ratios A=1 and 2.

As a continuity of this work, there are two avenues that future research could explore and indeed are presently being explored by the authors within these geometries. The first deals with heat transfer enhancement using mixture of gases. The second is to re‐examine the problem under turbulent conditions.

The present study seeks to maximize the convection heat transport in cavities and minimize their sizes. The peculiarity of the derived cavities is their cross‐section area being half of the cross‐section area of the basic cavities.

A detailed review of the archival literature on: fluid dynamics, heat transfer and shape optimization reveals that the optimal shape of natural convective cavities has not been investigated so far, and of course, its physical features are not understood. A prominent application of cavities cooled by natural convection arises in the miniaturization of electronic packaging where some type of temperature constraint must be applied at the directly heated wall. This contemporary issue has been addressed in the present work in an elegant manner by linking a code on computational fluid dynamics with a shape optimization code. Once the velocity and temperature fields were accurately computed for an initial cavity with a certain heat load, a two‐step optimization procedure was implemented in a methodical fashion. A first optimization sub‐problem transformed a square cavity into a rectangular cavity, while the second optimization sub‐problem sculpted the shape of the upper horizontal insulated wall in order to bring down the maximum wall temperature of the directly heated vertical wall, i.e. the so‐called “hot spot”. A bird's eye inspection of the numerical results revealed that the first optimization sub‐problem produced a significant reduction in area (volume), while raising the maximum wall temperature of the heated vertical wall by a small amount. The second optimization sub‐problem supplied a remarkable decrease in the maximum wall temperature of the heated vertical wall, carrying with it a moderate increase in area (volume). At the end, the optimal shape of the cavity turns out to be a disfigured vertical rectangular cavity in which the upper insulated wall forming a parabolic‐skewed cap.

This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface.

It is assumed that the top moving wall is adiabatic and the bottom wall is heated in two modes, and the rest of the walls are maintained at uniform cold temperature. The coupled governing non-linear partial differential equations are solved numerically with MAC algorithm for conducting a parametric study with uniform and non-uniform temperature bottom wall.

The numerical results are depicted in the form of streamlines, temperature contours and variation of local Nusselt number. The local Nusselt number at the bottom wall of the cavity increases in presence of non-linear temperature parameter as compared with linear temperature parameter and heat transfer reduces with increasing of Ha for uniform and non-uniform heating of bottom wall.

The numerical investigation is conducted for unsteady, two-dimensional natural convective flow in a square cavity. An extension of the present study with the effect of inclination of cavity, wavy walls and triangular cavity will be the interest of future work.

This work studies the effect of magnetic field in the presence of linear convection and non-linear convection. This study might be useful to cooling of electronic components, alloy casting, crystal growth and fusion reactors, etc.

The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks.

The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works.

The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks.

No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.

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.

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

The authors believe that the presented results are original and have not been published elsewhere.

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.

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K.

The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density.

Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution.

The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.

The purpose of this paper is to conduct a numerical analysis of transient turbulent natural convection combined with surface thermal radiation in a square cavity with a local heater.

The domain of interest includes the air-filled cavity with cold vertical walls, adiabatic horizontal walls and isothermal heater located on the bottom cavity wall. It is assumed in the analysis that the thermophysical properties of the fluid are independent of temperature and the flow is turbulent. Surface thermal radiation is considered for more accurate analysis of the complex heat transfer inside the cavity. The governing equations have been discretized using the finite difference method with the non-uniform grid on the basis of the special algebraic transformation. Turbulence was modeled using the k–ε model. Simulations have been carried out for different values of the Rayleigh number, surface emissivity and location of the heater.

It has been found that the presence of surface radiation leads to both an increase in the average total Nusselt number and intensive cooling of such type of system. A significant intensification of convective flow was also observed owing to an increase in the Rayleigh number. It should be noted that a displacement of the heater from central part of the bottom wall leads to significant modification of the thermal plume and flow pattern inside the cavity.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady turbulent natural convection combined with surface thermal radiation in a square air-filled cavity in the presence of a local isothermal heater. The results would benefit scientists and engineers to become familiar with the analysis of turbulent convective–radiative heat transfer in enclosures with local heaters, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

The purpose of this study is to examine the radiation effect on the natural convective heat transfer of an alumina–water nanofluid in a square cavity in the presence of centered nonuniformly heated plate.

The square cavity filled with alumina–water nanofluid has a nonuniformly heated plate placed horizontally or vertically at its center. The plate is heated isothermally with linearly varying temperature. The vertical walls are cooled isothermally with a constant temperature, while the horizontal walls are insulated. The governing equations have been discretized using finite volume method on a uniformly staggered grid system. Simulations were carried out for different values of the heated plate nonuniformity parameter (λ = –1, 0 and 1), the nanoparticles solid volume fraction (Φ = 0.01 − 0.04) and the radiation parameter (R_d = 0 – 2) at the Rayleigh number of Ra = 1e+07.

It is found that the total heat transfer rate is enhanced with an increase in the radiation parameter for both the horizontal and vertical plates. The role of nanoparticles addition to the base fluid can have dual effects on the heat transfer rate by augmenting and dampening for the absence of radiation while it dampens the heat transfer rate for the presence of radiation.

The originality of this work is to analyze steady natural convection in a square cavity filled with a water-based nanofluid in the presence of centered nonuniformly heated plate. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids, and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.