Non-Similar Computational Solutions for Free Convection Boundary-Layer Flow of a Nanofluid from an Isothermal Sphere in a Non-Darcy Porous Medium

Buoyancy-driven laminar thermal convection flow from an isothermal sphere in a Nano fluid-saturated non-Darcy porous medium has been investigated numerically using an implicit finite difference scheme. This is the first paper presenting non-similar solutions for such a regime. The model used for the Nano fluid incorporates the effects of Brownian motion, buoyancy ratio and thermophoresis. A non-similarity solution is presented which depends on the Prandtl number (Pr), Sherwood number (Sc), Brownian motion number (Nb), buoyancy ratio (Nr), thermophoresis number (Nt), Darcy number (Da) and Forchheimer parameter (Lambda). The variation of the reduced Nusselt and reduced Sherwood numbers with Nb and Nt for various values of Pr and non-Darcy parameter Lambda are also tabulated and provided in graphical form. It is found that the reduced Nusselt number is a decreasing function of each dimensionless number, while the reduced Sherwood number is an increasing function of higher Pr and a decreasing function of lower Pr number. Velocity is reduced with increasing Forchheimer parameter whereas temperature and nano-particle concentration are both enhanced. The model finds applications in energy systems and thermal enhancement of industrial flow processes.