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A numerical investigation is implemented on the unsteady natural convection with a temperature-dependent viscosity inside a square porous cavity. The vertical walls of the cavity are kept at constant but different temperatures, while the horizontal walls are adiabatic. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Rayleigh number, Darcy number, viscosity variation parameter and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall as well as on the streamlines and isotherms are analyzed. The results show an intensification of convective flow and heat transfer with an increase in the viscosity variation parameter for the porous media, while in the case of pure fluid, the effect is opposite.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

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A numerical study of the natural convection combined with thermal radiation inside a square porous cavity filled with a fluid of temperature-dependent viscosity is carried out. The side horizontal walls are assumed to be adiabatic while both the left and right vertical walls are kept at constant but different temperatures. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing equations formulated in dimensionless stream function, vorticity, and temperature variables are solved using finite difference method. A parametric analysis illustrating the effects of the radiation parameter (0 ≤ Rd ≤ 10), Darcy number (10-5 ≤ Da ≤ 10-2), and viscosity variation parameter (0 ≤ C ≤ 6) on fluid flow and heat transfer is implemented. The results show an essential intensification of convective flow with an increase in the radiation parameter.

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