A study of natural convection in a two dimensional rectangular channel filled with anisotropic porous media is considered, when the fluid and solid phases are not in local thermal equilibrium. Walls of the channel are non-uniformly heated to establish a linear temperature gradient and they are assumed to be impermeable and perfectly conducting. Darcy model with anisotropic permeability is used to describe the flow and a two field models are used for energy equation each representing fluid and solid phases separately. The critical Rayleigh number for the onset of convection using linear stability analysis is obtained numerically as a function of mechanical anisotropy parameters, interphase heat transfer coefficient and aspect ratio, and the same is plotted graphically, and discussed in detail.
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The convective stability of a horizontal layer of viscoelastic conducting liquid (Walters' liquid B') heated from below and rotating about a vertical axis in the presence of a magnetic field and thermal relaxation has been investigated. Linear stability theory and normal mode analysis are used to derive an eigenvalue system of eighth order, and an exact eigenvalue equation for a neutral instability is obtained. Critical Rayleigh numbers and wave numbers for the onset of instability are presented graphically as functions of Taylor number for various values of the Chandrasekhar number and the relaxation time at a Prandtl number Pr = l.
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