Natural convection flowin a square cavity filled with porous medium for sinusoidal heated topwall

A numerical investigation of sinusoidal heated top wall on natural convection flows in a square cavity filled with a porous medium is presented when the bottom and side walls are insulated. Darcy-Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. The nondimensional governing equation is solved under appropriate boundary conditions using the penalty finite element method with biquadratic rectangular elements. The effects of Darcy number Da (10^-5 ≤ Da ≤ 10 ^-3), and Rayleigh number (Ra = 10⁶ - 10⁷) on flow and temperature is presented for Prandtl number Pr (0.026 ≤ Pr ≤ 100) in terms of stream functions and isotherm contours. It was found that the strength of circulation is increased and the eye of the vortex moves toward the top wall with increasing Darcy number and Rayleigh number. As a result, isotherm contours are confined near the top wall. Heat transfer rates at the top wall are presented in terms of local Nusselt number and average Nusselt number.