Natural convection inside a heat source embedded wavy porous cavity containing an insulated obstacle

Abstract

In this finite element analysis of natural convection, cooling of a heat source embedded with a wavy porous cavity containing an insulated obstacle is investigated. A heat source is submitted to the left vertical wall, and the wavy right vertical wall is kept at fixed low temperature keeping top and bottom walls as insulated. The insulated obstacle which is placed inside the cavity is either square or circular in shape. The non-dimensional governing equations are solved by Galerkin finite element method and the results are presented in terms of streamlines and isotherms. The parameters considered for the investigation are Rayleigh-Darcy number ( $Ra=10,{10}^2,{10}^3$ ), amplitude of the wavy wall $(a=0.05,0.15,0.25)$ , undulation of wavy wall per unit length (N = 3) and shape of the obstacle. From the obtained results, mathematical correlations to calculate the maximum temperature of the heater and average Nusselt number with governing parameters are presented, and it is observed that the presence of a square insulated body reduces the convection process over a circular body; also, for a fixed Ra, the effect of obstacle at a particular portion of the cavity falls off with increment in a.