Mixed Convection in Porous Media With Heat Source/Sink. With Boundary condition of Third Kind

      Аннотация: A numerical study of mixed convection in a vertical channel filled with a porous medium,including the effects of inertia forces, is studied by taking into account the effects of viscous and Darcy dissipations with heat source or sink. The flowis modeled using the Brinkman Forchheimer–extended Darcy equations.The plate exchanges heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. The governing equations are solved using Runge–Kutta fourth-order method with shooting technique for extended Darcy model and analytically using the perturbation series method for the Darcy model. The velocity and temperature fields are obtained for various porous parameters, inertia effect, and perturbation parameters for equal and unequal Biot numbers and are shown graphically. It is also found that both analytical and numerical solutions agree to a great extent with the small values of the perturbation parameter in the absence of inertial forces.

Ключевые слова: Runge-Kutta method, Mixed Convection, boundary condition of third kind, Perturbation Method