Effect of thermal radiation on mixed convection flowof a nanofluid about a solid sphere in a saturated porous medium under convective boundary condition

This work focuses on the numerical modeling of a steady mixed convection boundary layer flow of a nanofluid about a solid sphere embedded in a porous medium with convective surface in the presence of the thermal radiation effect using the Brinkman-extended Darcy model. A model is developed to analyze the behavior of nanofluids, taking into account the nanoparticle volume fraction parameter, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. An appropriate transformation is employed, and the transformed equations are solved numerically using an efficient implicit iterative tri-diagonal finite difference method. Comparisons to previously published works are performed, and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the local skinfriction coefficient and local Nusselt number are illustrated graphically to show interesting features of the solutions. It is concluded that both the local skin-friction coefficient and local Nusselt number decreased due to increases in Darcy number, while they are increased as in either the mixed convection parameter, Biot number, or thermal radiation parameter increase. In addition, an increase in the values of the nanoparticle volume fraction produced enhances in the local skin friction and reductions in the local Nusselt number.