Numerical Solution of Mixed Convection Flow about a Sphere in a Porous Medium Saturated by a Nanofluid: Brinkman Model

Abstract

In the present study, the steady mixed convection boundary layer flow about a solid sphere with a constant surface temperature and embedded in a porous medium saturated by a nanofluid has been investigated via the Brinkman model for both the assisting and opposing flow cases. The resulting system of nonlinear boundary layer equations in the form of partial differential equations is solved numerically using an implicit finite-difference scheme known as the Keller-box method. Numerical results are obtained and discussed for the skin friction coefficient, local Nusselt number, local Sherwood number, velocity profiles, temperature profiles and nanoparticle volume fraction profiles. These results are presented for different values of the governing parameters, namely the mixed convection parameter and the Darcy- Brinkman parameter. It is found that the boundary layer separates from the sphere for some negative values of the mixed convection parameter (opposing flow). Increasing the mixed convection parameter delays the boundary layer separation and the separation can be completely suppressed for sufficiently large values of the mixed convection parameter.