Effects of Prandtl Number on Natural Convection in a Cavity Filled with Silver/Water Nanofluid-Saturated Porous Medium and Non-Newtonian Fluid Layers Separated by Sinusoidal Vertical Interface

Abstract

This study investigates the effect of Prandtl number on the natural heat convection inside a square cavity filled with two layers of Ag/water nanofluid-saturated porous medium and non-Newtonian fluid separated by a sinusoidal vertical interface. The left wall, which is adjacent to the nanofluid porous layer, has a relatively hot temperature, while the right wall is cold. Other walls of the cavity are thermally insulated. All cavity walls are impermeable except for the sinusoidal vertical interface located between the two layers. Galerkin finite element method was used to numerically solve the governing differential equations. The study examined the effects of power-law index (0.6 < n < 1.4), Darcy number (10−5 < Da < 10−1), volume fraction (0 < ∅ < 0.2), and undulation number (1 < N < 4) on the thermal performance of the cavity for Prandtl numbers (Pr) ranging from 0.015 to 13.4 and Rayleigh number (Ra) equal to 105. Results showed that increasing Prandtl and Darcy numbers raised the average Nusselt number. However, increasing the power-law index reduced the average Nusselt number. When the non-Newtonian fluid behaves as a shear-thinning fluid (n = 0.7) and Pr = 13.4, the effect of the undulations number of the sinusoidal vertical interface on average Nu is not evident for a given range of volume fraction.