A semi -analytical investigation is performed to analyze the thermal convection flow with a radiation flux and a variable internal heat generation along an inclined plate embedded in a saturated porous medium. The flow in the porous medium is modeled with the Darcy-Brinkman law taking into account the convective term, while the temperature field is obtained from the energy equation. These governing equations with the boundary conditions are first cast into a dimensionless form by using a unique similarity transformation and the resulting coupled differential equations are then solved numerically by a computational program based on the fifth order Runge-Kutta scheme with shooting iteration technique. The obtained results are presented in dimensional and dimensionless form. The effects of the main governing parameters, such as permeability, radiation, internal heat generation, inclination angle, Grashof number, Prandtl number, fluid suction on the isothermal lines distributions, the local Nusselt number and the local skin-friction profiles are examined and the physical aspect of the problem is discussed. The comparison with previously published work shows excellent agreement.
In this work, a numerical simulation of steady and laminar free convection flow over a heated vertical flat plate embedded in a saturated porous medium by a Newtonian fluid is presented and analyzed. The Brinkman-Forchheimer extension of Darcy's law has been adopted to describe the movement of fluid within the porous matrix. A numerical solution of the governing continuity, momentum and energy equations was made with the appropriate boundary conditions using ANSYS/FLUENT software based on finite volume method. The found results are graphically presented and physically discussed for main controling parameters. Subsequently, we compared our CFD calculation by the results obtained with the similarity method in terms of temperature profiles for selected values of the Rayleigh number. It is essentially found that the increase in the Rayleigh number promotes the flow and the transfer of heat by convection in the porous medium.
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