Validity of the boundary layer assumptions for natural convection around a cylinder in a porous medium

Abstract

In this research, it has been investigated that under what conditions it is correct to use the boundary layer equations for natural convection over an embedded horizontal cylinder in an infinitely porous medium, assuming Local Thermal Non-Equilibrium. For this purpose, the results obtained for the average Nusselt values using boundary layer assumptions have been compared with the results obtained from COMSOL software (complete two-dimensional equations). For the boundary layer results, the physical coordinate of the problem has been converted to a computational Cartesian system, and then the parabolic equations of the boundary layer have been solved numerically by coding in Fortran 90 using the implicit finite difference method of Keller box. Removing some terms in the boundary layer equations in order to make the equations parabolic causes errors in the results. The effect of Rayleigh number, ratio of solid-to-fluid conduction coefficient, Bio number, porosity, and diameter ratio parameter on the amount of this deviation has been shown. Difference between the consequences of the two methods increases by increasing the contribution of the solid matrix in heat transfer. In high porosity, high Bio number, low conductivity ratio, and the low ratio diameter of cylinder to particle, the results of the two solution methods approach each other. So, in this condition, the boundary layer equations for the free convection on the embedded horizontal cylinder in the porous medium can be used and other than these conditions, the assumption of the boundary layer equations has a significant error.