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The purpose of this study is to obtain a general solution to the field equations of thermoelastic solid with voids and micro-temperatures under the gravitational field in the context of the three theories, namely, coupled theory (CT), Lord and Shulman theory and Green and Lindsay theory.

The normal mode analysis is used to obtain the exact expressions for the considered variables. Comparisons are made with the results obtained in the three theories with and without gravity. Some particular cases are also deduced from the present investigation.

The effect of the gravity on the displacement, the micro-temperature vector, the temperature distribution, the normal stress, the changes in the volume fraction field and the heat flux moments have been depicted graphically.

Some particular cases are also deduced from the present investigation.

The results of the physical quantities have been illustrated graphically by a comparison between three different theories in the presence and absence of gravity.

The purpose of this paper is to introduce the coupled theory, Lord-Shulman theory with one relaxation time and Green-Lindsay theory with two relaxation times to study the influence of rotation on generalized micropolar thermoelasticity subject to thermal loading due to laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam with pulse duration of 8 ps.

The problem has been solved numerically by using the normal mode analysis.

The thermal shock problem is studied to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and micro-rotation. The distributions of the considered variables are illustrated graphically. Comparisons are made with the results predicted by three theories in the presence and absence of laser pulse and for different values of time.

Generalized micropolar thermoelastic solid.

The purpose of this paper is to deal with unsteady double diffusive natural convection in a square enclosure filled with a porous medium with various boundary condition effects in the presence of heat source or sink.

Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, amplitude wave length ratio, dimensionless time parameter, Darcy number, buoyancy parameter and heat generation/absorption parameter on the streamlines, temperature and concentration contours, as well as Nusselt number and Sherwood number, were considered.

The sinusoidal variations of the temperature and concentration remove the singularities which appear in the case of fixed temperature and concentration.

The paper's results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.

The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects.

In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled.

Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase.

The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.

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.

The purpose of this paper is to study natural convective flow and heat transfer in a sinusoidally heated wavy porous cavity in the presence of internal heat generation or absorption.

Sinusoidal heating is applied on the vertical left wall of the cavity, whereas the wavy right wall is cooled at a constant temperature. The top and bottom walls are taken to be adiabatic. The Darcy model is adopted for fluid flow through the porous medium in the cavity. The governing equations and boundary conditions are solved using the finite difference method over a range of amplitudes and number of undulations of the wavy wall, Darcy–Rayleigh numbers and internal heat generation/absorption parameters.

The results are presented in the form of streamlines, isotherms and Nusselt numbers for different values of right wall waviness, Darcy–Rayleigh number and internal heat generation parameter. The flow field and temperature distribution in the cavity are affected by the waviness of the right wall. The wavy nature of the cavity also enhances the heat transfer into the system. The heat transfer rate in the cavity decreases with an increase in the internal heat generation/absorption parameter.

The present investigation is conducted for steady, two-dimensional natural convective flow in a wavy cavity filled with Darcy porous medium. The waviness of the right wall is described by the amplitude and number of undulations with a well-defined mathematical function. An extension of the present study with the effects of cavity inclination and aspect ratio will be the interest for future work.

The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

This work examines the effects of sinusoidal heating on convective heat transfer in a wavy porous cavity in the presence of internal heat generation or absorption. The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Pr_m) and Darcy numbers (Da_m) at Rayleigh number, Ra_m = 10⁶, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation.

Smooth end-to-end heatlines are seen at the low Da_m involving all the cases. At the high Da_m, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number ( Nur¯) at the low Da_m for all Pr_m. At the high Da_m, Nur¯ for the Case 1 (concave) is the largest involving the low Pr_m, whereas Nur¯ is the largest for Case 1 (convex) involving the high Pr_m.

Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications

The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.

The purpose of this paper is to analyze the effects of complex boundary conditions on natural convection of a yield stress fluid in a square enclosure heated from below (uniformly and non-uniformly) and symmetrically cooled from the sides.

The governing equations are solved numerically subject to continuous and discontinuous Dirichlet boundary conditions by Galerkin’s weighted residuals scheme of finite element method and using a non-uniform unstructured triangular grid.

Results show that the overall heat transfer from the heated wall decreases in the case of non-uniform heating for both Newtonian and yield stress fluids. It is found that the effect of yield stress on heat transfer is almost similar in both uniform and non-uniform heating cases. The yield stress has a stabilizing effect, reducing the convection intensity in both cases. Above a certain value of yield number Y, heat transfer is only due to conduction. It is found that a transition of different modes of stability may occur as Rayleigh number changes; this fact gives rise to a discontinuity in the variation of critical yield number.

Besides the new numerical method based on the finite element and using a non-uniform unstructured grid for analyzing natural convection of viscoplastic materials with complex boundary conditions, the originality of the present work concerns the treatment of the yield stress fluids under the influence of complex boundary conditions.

The purpose of the paper is to numerically simulate steady‐state thermo‐solutal convection in rectangular cavities with different aspect ratios, subject to horizontal temperature and concentration gradients, and validate the results against numerical and experimental data available from literature.

The fully explicit Artificial Compressibility (AC) version of the Characteristic Based Split (CBS) scheme is adopted to solve double diffusion (DD) problems. A stabilization analysis is carried out to efficiently solve the problems considered in the present work. The thermal and solutal buoyancy forces acting on the fluid have been taken into account in case of aiding and opposing flow conditions.

The stability limits derived by the authors for the thermo‐solutal convection assume a fundamental role to efficiently solve the DD problems considered. In the cases characterized by higher Rayleigh number the convergent solution is obtained only by employing the new stability conditions. The efficient matrix free procedure employed is a powerful tool to study complex DD problems.

In this paper, the authors extend the stabilization analysis for the AC‐CBS scheme to the solution of DD, fundamental to efficiently solve the present problems, and apply the present fully explicit matrix free scheme, based on finite elements, to the solution of DD natural convection in cavities.