Transient non-Darcian forced convection flow in a pipe partially filled with a porous material

In this paper, a numerical simulation is presented for the transient forced convection in the developing region of a cylindrical channel partially filled with a porous substrate. The porous substrate is attached to the inner side of the cylinder wall, which is exposed to a sudden change in temperature. The flow within the porous domain is modeled by the Brinkman-Forchheimer-extended Darcy model. The effects of several parameters on the hydrodynamic and thermal characteristics of the present problem are studied. These parameters include the porous substrate thickness, Darcy number and Forchheimer coefficient. Results of the current model show that the existence of the porous substrate may improve the Nusselt number at the fully developed region by a factor of 8. However, there is an optimum thickness of the porous substrate beyond which no significant improvement in the Nusselt number is achieved. Also, in the present work, the macroscopic inertial term in the porous domain momentum equation is included due to its significant effect. It is found that the steady state time increases as the substrate thickness increases up to a certain limit and then the steady state time decreases upon further increase in the substrate;thickness. Also, increasing the Forchheimer coefficient and decreasing the Darcy number increase the steady state time. (C) 1997 Elsevier Science Ltd.