Numerical Solution of Conjugate Free Convection From a Vertical Fin Embedded in a Non-Darcy Porous Medium

The problem of conjugate free convection from a vertical fin embedded in a fluid-saturated porous medium is investigated. The governing nonlinear equations are solved iteratively by a highly implicit finite difference scheme. In this paper, the results based on four models, viz the Darcy model, the Brinkman model, the non-Darcian model with nonlinear inertia and viscous terms, and also the non-Darcian model with viscous, nonlinear inertia and velocity square terms, are compared. It is seen that fin cooling is more effective at higher Grashof or Darcy numbers due to stronger convection effects. The local Nusselt number is observed to increase with the Grashof or Darcy numbers and decrease slightly with the conduction–convection parameter. The limitation of the Darcy’s law is observed at higher values of permeability when the non-Darcian models are more relevant.