Variable Heat Source and Wall Radiation Effects on Boundary Layer Convection From an Inclined Plate in Non-Darcian Porous Medium

Abstract

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.

CFD Analysis of Free Convection in Non-Darcian Porous Medium and Comparison With Similarity Approach

“…The similarity method results found by Flilihi et al (2017Flilihi et al ( , 2019b are validated with those published in the literature and they showed a very good agreement.…”

“…The numerical results obtained by these authors are validated with experimental results. Afterward, Flilihi et al (2017) investigated the variable heat source and wall radiation effects on boundary layer convection from an inclined plate in non-Darcian porous medium. In this research, the problem is resolved numerically by a computational program based on the fifth order Runge-Kutta scheme coupled with shooting iteration technique.…”

Numerical Solution on Non-Uniform Mesh of Darcy-Brinkman-Forchheimer Model for Transient Convective Heat Transfer Over Flat Plate in Saturated Porous Medium

“…The obtained results show that the temperature profile increases for the increasing of thermal conductivity parameter, Eckert number and heat generation parameter. Also, Flilihi et al (2017) investigated the variable heat source and wall radiation effects on boundary layer convection from an inclined plate in non-Darcian porous medium.…”

“…The present paper is an extension of the works of Flilihi et al (2017Flilihi et al ( , 2019 to an unsteady convective boundary layer flow past an inclined plate in a non darcian porous medium in the presence of the viscous dissipation effects using the Darcy-Brinkman-Forchheimer model, which includes the effects of boundary and inertia forces taking into account the convective term. This study finds applications in the fields of petroleum engineering, geothermal energy, etc...…”