Natural Convection Flow in an Inclined Wavy Porous Medium in the Presence of an Inclined Periodic Magnetic Field

In this study, unsteady natural convection flow in an inclined porous wavy cavity under the effect of an inclined periodic magnetic field (MF) is investigated. Mathematical model for the porous medium is chosen as Brinkman-extended Darcy model. Galerkin weighted residual finite element method is implemented to simulate the governing unsteady dimensionless equations. For discretization of time derivatives, Crank-Nicolson method is utilized. The obtained discrete nonlinear algebraic systems are iteratively solved by using the adaptive Newton’s method. The behavior of fluid flow and heat transfer is examined in distinct parameters as inclination angle of the cavity ( \(\theta _c=0^\circ -90^\circ \) ), amplitude ( \(A=0.025-0.2\) ) of wavy wall, the number of undulations ( \(N=1-4\) ), Hartmann number ( \(Ha=0-100\) ), angle ( \(\theta _b=0^\circ -90^\circ \) ) and period ( \(\lambda \) =0.1-1) of the periodic MF. The rise in Hartmann number has a dampening effect on both heat transfer and fluid flow. Period \(\lambda =1\) and amplitude \(A=0.2\) has the most reducing influence on both fluid velocity and convective heat transfer. Oblique angle of periodic MF is efficient on fluid flow and heat transfer at \(\theta _b=45^\circ \) . Average Nusselt number is the largest at \(\theta _c=45^\circ \) when the periodic MF affects the system at \(\theta _b=0^\circ \) .