Maximum density effects on natural convection in a vertical annulus filled with a non-Darcy porous medium

Summary This article numerically studies the problem of natural convection in a porous medium saturated with cold water, under density inversion, within a vertical annulus. In modeling the flow in the porous medium the non-Darcy effects, which include the Forchheimer inertia and Brinkman viscous effects are taken into account. The governing equations are solved numerically by the finite difference method using the modified strongly implicit procedure. The effects of the inversion parameter_m, radius ratioR^*, aspect ratioAR, Forchheimer inertia parameter Fc/Pr, and Darcy number parameter Da on the heat transfer and fluid flow characteristics are discussed in detail. Results show that both the inversion parameter and radius ratio have a significant influence on the flow structure and heat transfer rate in the annulus. It is also found that the mean Nusselt number decreases as the Forchheimer inertia parameter or the Darcy number increases. Moreover, the results obtained here are also compared and favorably agree with numerical results and with experimental data.Nomenclature AR aspect ratio,H/L - d particle diameter - Da Darcy number,K/(L²) - Fc Forchheimer number,K/L - g gravitational acceleration - H annulus height - K permeability - K transport property defined in Eq. (5) - L gap width,r_o–r_i - Nu_i, Nu_o local Nusselt number of the inner and outer cylinders, respectively - mean Nusselt number of the inner and outer cylinders, respectively - p pressure - Pr Prandtl number, / - q constant in Eq. (9) - r radial coordinate - R dimensionless radial coordinate,(r–r_i)/L - r_i radius of inner cylinder - r_o radius of outer cylinder - R^* radius ratio,(r_o–r_i)/r_i - Ra Rayleigh number,K_mgL(T_h–T_c)^q/ - T dimensional temperature - T_c dimensional temperature of inner cylinder - T_h dimensional temperature of outer cylinder - T_m temperature corresponding to the density maximum, 4.029325°C - u, v Darcian velocity components inr andz directions, respectively