Unsteady Non-Darcian Forced Convection Analysis in an Annulus Partially Filled With a Porous Material

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Abstract
Numerical solutions are presented for the problem of transient, developing, forced-convection flow in concentric annuli partially filled with porous substrates. The porous substrate is attached either to the inner cylinder (case I), or to the outer cylinder (case O). In both cases, the boundary in contact with the porous substrate is exposed to a sudden change in its temperature while the other boundary is kept adiabatic. Including the macroscopic inertial term, the Brinkman-Forchheimer-extended Darcy model is used to model the flow inside the porous domain. The effects of different parameters regarding the geometry, the solid matrix, and the fluid on the hydrodynamic and thermal behavior are investigated. It is shown that porous substrates may improve Nusselt number by 1200 percent keeping other flow and geometrical parameters fixed. Also, it is found that there is an optimum thickness for the porous substrate beyond which there is no significant improvement in Nusselt number. In the present work, the dimensionless hydrodynamic entrance length Zen varies within the range 2–45 and it has significant effect on the fully developed Nusselt number at steady-state conditions. As a result, the macroscopic inertial term in the porous domain momentum equation should not be neglected.