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.

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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.

In this paper, we made a numerical simulation of convective heat transfer in a rectangular section pipe of a air flat plate solar collector using three forms of the absorber plate namely, simple shape, rectangular-shape, and half circle-shape. The flow is considered laminar and stationary, where the heat exchange between the absorber plate and the fluid takes place in useful area. The computer code in fluid dynamics, the fluent, is applied to integrate the governing equations on each control volume. A detailed description of the fluid flow and heat transfer in the rectangular channel was made. Several simulation were carried out in order to determine the influencing parameters allowing better performances of the collector and ensuring a good homogeneity of the temperature at the exit of the channel. The obtained results showed that the lows mass flow rates of the air increase the average outlet temperature. Also, the use of the second configuration of the absorber (rectangular shape) increases the velocity of the air at the downstream of the channel and promotes more the thermal homogeneity at the outlet of the channel.

A numerical investigation is performed to analyze the transient laminar free convection over an isothermal inclined plate embedded in a saturated porous medium with the viscous dissipation effects. The flow in the porous medium is modeled with the Darcy-Brinkman-Forchheimer model, taking into account the convective term. The dimensionless nonlinear partial differential equations are solved numerically using an explicit finite difference method. The effects of different parameters: (1 ≤ Re ≤ 10 ; 10 −2 ≤ Da ≤ 10 ; 0 ≤ Gr ≤ 50 ; 0 ≤ F r ≤ 3 ; 0 ≤ Ec ≤ 1 ; 0 ≤ φ ≤ 90 0 and P r = 0.71) that enter into the problem on the dimensionless streamlines of the velocity field, the isothermal lines distributions and the local Nusselt number are examined. Also, the physical aspects of the problem are discussed in details. It is found that the viscous dissipation and the inertial forces have a significant effect on the temperature field whereas the wall heat transfer rate is optimal for the vertical position of the plate.