Flow instability in a large aspect ratio porous medium with an internal heat source

Abstract

The problem of convective heat transfer in a fluid saturated porous medium is of great importance in various applications ranging from geothermal engineering to underground nuclear waste disposal. Previous studies in this regard were mainly done for a low range of Rayleigh number and small aspect ratio. In this paper, natural convection in a horizontal as well as inclined porous channel with uniform internal heat generation is investigated for a large aspect ratio. Numerical solutions are obtained using the Arakawa-Dufort-Frankel scheme and are mainly governed by two parameters, namely, the aspect ratio of the duct, γ = b a and the Rayleigh number Ra = KβgaA′ Q g / ανk. For a duct with an aspect ratio of 10, a complicated solution structure, i.e. the presence of stable, periodic, quasi-periodic and chaotic behavior is observed upon increasing the Rayleigh number. The results show that when the angle of inclination of a porous channel increases, chaotic behavior appears for a smaller Ra. Results also show that the flow stability increases with increasing angle of inclination.