Free Convection in a Porous Enclosure by Virtue of Sinusoidal Heating and Cooling on Lateral Side: A Variable Periodicity Perspective

A numerical study has been made on free convection in the anisotropic porous enclosure. By nonuniform sinusoidal heating, flow is induced on the right side wall along with three adiabatic walls. The principal directions of the gravity vector have been taken obliquely to the permeability tensor. The performed study is conducted by using the Brinkman-extended non-Darcy model. The vorticity–streamfunction approach of the spectral element method is applied to solve the governing equations. The significance is specified on the impact of the periodicity parameter (N), local heat transfer rate (Nu\(_{y}\)) along with the flow mechanism in the enclosure with reference to orientation angle (\(\phi\)), permeability ratio (K\(^{*}\)) and anisotropic parameters. The outcome for odd N shows that a particular heat transfer at \(y=1.5\) is pointed extreme. Additionally, the increase in the permeability media while switching K\(^{*}\) from 1 to 0.2 increases the heat transfer rate. This increment occurs at the right corner, below the enclosure’s right. Moreover, considering every N, the profiles of Nu\(_{y}\) in both media (isotropic and anisotropic) are similar. However, it varies slightly for N\(=2\). Remarkably, this analysis shows that the flow pattern has been affected by distinct N via boundary conditions of temperatures. Consequently, the local heat transfer phenomena have also been affected.