Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer-Brinkman extended Darcy model

The present study addresses the transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel partially filled with porous medium. Forchheimer-Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Two regions are coupled by equating the velocity and shear stress in the case of momentum equation while matching of the temperature and heat flux is taken for thermal energy equation. Approximate solutions are obtained using perturbation technique. Variations in velocity field with Darcy number, Grashof number, kinematic viscosity ratio, distance of interface and variations in temperature distribution with thermal conductivity ratio, distance of interface are obtained and depicted graphically. The skin-friction and rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are tabulated.