Natural-Convection Flow of Nanofluids Over Vertical Cone Embedded in Non-Darcy Porous Media

Abstract

In this paper, non-Darcy flow and natural convection over a vertical cone embedded in a porous medium saturated with a nanofluid is studied using the Forchheimer-extended Darcy law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. An analytical technique, similarity solution method, is used to convert the governing equations into a set of ordinary differential equations, and then numerically solved using the finite difference method. The effect of non-Darcy parameter and nanofluid parameters on the velocity, temperature, and nanoparticles volume fraction profiles, as well as on the two important parameters of heat and mass transfer, i.e., reduced Nusselt and Sherwood numbers, are discussed. The results show that an increase in the non-Darcy parameter decreases the velocity profiles, whereas it would increase the temperature and concentration profiles. Simulation results also show that an increase in the non-Darcy parameter would decrease the reduced Nusselt and Sherwood numbers, whereas an increase of Lewis number would increase the reduced Nusselt and Sherwood numbers.