Natural convection flow of a power-law non-Newtonian nanofluid in inclined open shallow cavities filled with porous media

Abstract

A numerical study of the laminar natural convection flow of non-Newtonian nanofluids in an inclined open shallow cavity filled with a porous medium is presented. The two-phase Buongiorno's model is used to simulate the nanofluid case and the Darcy model is applied to the porous medium. The apparent viscosity and stresses are given using the non-Newtonian power-law forms. The partial differential equations governing the flow are solved using the finite volume method with approximating the boundary conditions at the opening. Streamlines and isotherms are produced and local and average Nusselt number, Bejan and total entropy generation, horizontal and velocity components are calculated for the inclination angle α from 0 to π, the power-law index n from 0.4 to 1, the Rayleigh number Ra from 105 to 109 the Darcy number from 10 − 2 to 10 − 4, the cavity aspect ratio from 0.125 to 1 and the variations of the thermophoresis parameter Nt and the Brownian motion parameter Nb from 0.1 to 1. The results indicate that the increase in the power-index n reduces the rate of heat transfer and vertical velocity while the average Bejan number is enhanced. Also, the local and average Nusselt numbers are decreasing functions of the cavity aspect ratio.