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

Abstract

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 Theta(m), radius ratio R*, aspect ratio AR, 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

Numerical study of natural convection in a vertical porous annulus with discrete heating

“…Relative to a large volume of investigations in the porous annulus, we noticed that the preceding works on natural convection in a vertical porous annulus are limited to uniform heating of the inner wall by either isothermal or isoflux wall-heating conditions [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, in many practical applications, heating takes place over a portion of one of the vertical walls, where the size and location of the heating segment may significantly affect the heat transport process in the annular enclosure filled with a fluid-saturated porous media.…”

“…Using the Brinkman-extended Darcy-Forchheimer model, Marpu [19] numerically investigated the natural convection heat transfer in a vertical cylindrical porous annulus. Char and Lee [20] applied a finite difference method to examine the natural convection of cold water in a vertical porous annulus under density inversion. They found that both the Forchheimer inertia parameter and the Darcy number have the same influence on the heat transfer characteristics.…”

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

“…Among the finite porous enclosures, free convective heat transfer in a differentially heated vertical porous annulus has received considerable attention owing to its importance in high performance insulation for buildings and porous heat exchangers (Hickox and Gartling 1985;Char and Lee 1998;Al-Zahrani and Kiwan 2009;Shivakumara et al 2003;Prasad 1986). Natural convection in square and rectangular porous enclosures subject to discrete heating has drawn much attention in recent years.…”

Numerical investigation of double-diffusive mixed convection in horizontal annulus partially filled with a porous medium

“…The phenomenon has been studied considering different boundary conditions, such as imposed temperature (Prasad and Kulacki, 1985; Rong et al , 2010), as well as constant heat flux, at the wall (Prasad, 1986; Jha, 2005) for a wide range of Rayleigh numbers, aspect ratios and radius ratios. Char and Lee (1998) studied the effects of the radius ratio, aspect ratio, Forchheimer inertia parameter and Darcy number parameter to examine the natural convection of cold water in a vertical porous annulus using a finite difference method and the modified strongly implicit procedure and found that both the Forchheimer inertial parameter and the Darcy number have the same influence on the heat transfer characteristics; it is also found that the mean Nusselt number decreases as the Forchheimer inertia parameter or the Darcy number increases. From the analysis of the open literature, fully explicit solutions, based on the finite element method, do not seem to be available for the problem under investigation.…”