Forchheimer and Brinkman extended Darcy flow model of natural convection in a vertical cylindrical porous annulus
The paper treats numerically the Forchheimer and Brinkman extended Darcy flow model for studying the natural convection heat transfer in vertical cylindrical annuli filled with fluid saturated porous media. Numerical results are obtained employing the SAR scheme proposed by the author. In order to investigate the influence of Brinkman viscous terms on heat transfer, numerical results are given neglecting Forchheimer inertial terms. The average Nusselt number at the inner wall, \(\overline{\text{Nu}}_i\), based on the annulus gap, has been calculated for different values of involved parameters. The obtained results are compared with experimental results available in the literature. It is shown that for an annulus filled with water and glass spheres of diameter \(d=22.5\text{ mm}\) having an aspect ratio of unity and a radii ratio of \(4.338\), the \(\overline{\text{Nu}}_i\) is significantly lower that the theoretically obtained value of \(\overline{\text{Nu}}_i\) by employing the Darcy flow model. This is due to the fact that Darcy's law is applicable only to low permeability porous media. The difference between experimental and theoretical values can be reduced by considering, in general, the non-Darcy extensions, since the non-Darcy extension decreases the average Nusselt number. This work is certainly an improvement over earlier work concerning the natural convection in a vertical cylindrical porous annulus. The reviewer recommends this valuable paper to all workers in convective flow in porous media.
scientific article; zbMATH DE number 885169