Non-Darcy free convection induced by a vertical wavy surface in a thermally stratified porous medium

Abstract

The partial differential equations governing the natural convection heat transfer from a vertical wavy surface in a thermally stratified fluid saturated porous medium are analysed under Forchheimer based non-Darcian assumptions. Based on non-similarity transformation deduced by scale analysis the governing equations are reduced to boundary layer equations. These simplified partial differential equations are solved numerically by a finite difference scheme following the Keller Box approach. Extensive numerical simulations are carried out for various values of wavelength-to-amplitude ratio of wavy vertical surface at different thermal stratification levels of porous medium both under Darcian and non-Darcian assumptions. Results from the current study are compared with those available in literature. In Darcian case local heat fluxes along the wavy vertical surface are periodic with an oscillatory pattern of period, which is exactly half of the period of vertical wavy surface. In the non-Darcian case local heat fluxes continue to be periodic but with a complex oscillatory pattern of period exactly same as that of the vertical wavy surface. Increasing S or Gr ∗ or a leads to a fall in local Nusselt number.