Abstract
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.
Highlights
Natural convection in composite fluid and porous layers heated from below can be encountered in many engineering and environmental problems
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 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
Summary
Natural convection in composite fluid and porous layers heated from below can be encountered in many engineering and environmental problems. The onset of surface-tension driven convection has been investigated by Shivakumara et al [6] in a two layer-system Both BeaversJoseph and the Jones conditions [7] were applied at the contact surface between the fluid saturated porous medium and the adjacent bulk fluid. A study of buoyancy-driven flow in a confined fluid overlying a porous layer has been investigated by Valenca-Lopez and Ochoa-Tapia [8], using two different models. The influence of the interfacial jump boundary condition on the onset of the convection in superposed fluid and porous layers has been studied by Hirata et al [10] [11]. More recently a linear stability analysis of the onset of thermosolutal convection in horizontal superposed fluid and porous layers was performed by Hirata et al [12] using the one-domain approach. For negative thermal Rayleigh numbers the onset of motion is characterized by a multi-cellular flow in the fluid
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