Author(s)

Gérard Degan^1,2, Julien Yovogan^1,2, Latif Fagbémi¹, Zineddine Allou³

¹Laboratoire d’Energétique et de Mécanique Appliquées (LEMA), Ecole Polytechnique d’Abomey-Calavi, Cotonou, Bénin.
²Université Nationale des Sciences Technologies, Ingénierie et Mathématiques (UNSTIM), Abomey, Bénin.
³Mechanical Engineering Department, Ecole Polytechnique, University of Montréal, Montréal, Canada.

The onset of thermal convection, due to heating from below in a system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity, is investigated analytically. The porous medium is both anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector and in thermal conductivity with principal directions coincident with the coordinate axes. The Beavers-Joseph condition is applied at the interface between the two layers. Based on parallel flow approximation theory, a linear stability analysis is conducted to study the geothermal river beds system and documented the effects of the physical parameters describing the problem. The critical Rayleigh numbers for both the fluid and porous layers corresponding, to the onset of convection arising from sudden heating and cooling at the boundaries are also predicted. The results obtained are in agreement with those found in the past for particular isotropic and anisotropic cases and for limiting cases concerning pure porous media and for pure fluid layer. It has demonstrated that the effects of anisotropic parameters are highly significant.

River Beds, Critical Rayleigh Numbers, Isotropic, Anisotropic

Degan, G. , Yovogan, J. , Fagbémi, L. and Allou, Z. (2019) Stability of Geothermal Convection in Anisotropic River Beds. Engineering, 11, 343-365. doi: 10.4236/eng.2019.117026.