Abstract
AbstractA model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effect of variable permeability and thermal diffusivity has been studied using the Brinkman model. Moreover, we analyse the effect of slip boundary conditions on the stability of the model. Due to numerous applications in micro-electro-mechanical-systems (MEMS) and other microfluidic devices, such a study is essential to have. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.
Highlights
Double di usive convection in porous media has been a focus for researchers, since it has applications in a number of areas, including geophysics, the enhanced recovery of petroleum reservoirs, the underground di usion of chemical wastes, seabed hydrodynamics, and crystal growth, for more details see [1], [2] and the references therein
Harfash [8] studied this problem with variable gravity with respect to the vertical direction and tested the validity of both the linear instability and global nonlinear energy stability thresholds for this problem using a three-dimensional simulation
The object of this paper is to investigate a double di usive convection problem in an inhomogeneous Brinkman porous media
Summary
Double di usive convection in porous media has been a focus for researchers, since it has applications in a number of areas, including geophysics, the enhanced recovery of petroleum reservoirs, the underground di usion of chemical wastes, seabed hydrodynamics, and crystal growth, for more details see [1], [2] and the references therein. The critical Rayleigh number of the natural convection in anisotropic porous layers was analyzed by [3]. Capone et al [7] analyzed the onset of convection in a horizontal uid-saturated porous layer uniformly heated from below in which the permeability and thermal diffusivity vary linearly or exponentially in the vertical direction. They studied this problem with constant gravity. At nanoscales there is increasing evidence that boundary conditions of slip type are needed rather than those of no-slip, cf. Cercignani [10], Duan [11], Duan & Muzychka [12], Lauga et
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