A linear and weakly nonlinear stability analyses is performed to study the onset of Darcy–Brinkman double diffusive convection in a binary viscoelastic fluid‐saturated porous layer in the presence of the Soret effect. The modified Darcy–Brinkman–Oldroyd model including the time derivative term is employed for the momentum equation. The expressions for stationary, oscillatory, and finite amplitude Rayleigh number are obtained as a function of the governing parameters. There is a competition between the processes of the Soret coefficient, viscoelasticity, thermal diffusion, and solute diffusion that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effects of the Soret parameter, Darcy number, relaxation and retardation parameters, and Darcy–Prandtl number on the stationary, oscillatory, and finite amplitude convection is shown graphically. The weakly nonlinear theory is based on truncated representation of the Fourier series method and is used to find the Nusselt and Sherwood numbers. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta method. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 297–320, 2014; Published online 3 October 2013 in Wiley Online Library (http://wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21076
The linear and nonlinear stability analysis of double diffusive reaction-convection in a sparsely packed anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically. The linear analysis is based on the usual normal mode method and the nonlinear theory on the truncated representation of Fourier series method. The Darcy-Brinkman model is employed for the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Darcy number, Damkohler number, anisotropy parameters, Lewis number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effect of Darcy number and mechanical anisotropy parameter have destabilizing effect, while the thermal anisotropy parameter has stabilizing effect on the stationary, oscillatory and finite amplitude convection. The Damkohler number has destabilizing effect in the case of stationary mode, with stabilizing effect in the case of oscillatory and finite amplitude modes. Further, the transient behavior of the Nusselt and Sherwood numbers are investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge-Kutta method.
Recently, interest in a viscoelastic flows through porous media has grown considerably,
The effect of internal heat source on the onset of double diffusive reaction-convection in an anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically using linear stability analyses. The linear analysis is based on the usual normal mode method. The Darcy model is employed for the momentum equation. The effect of internal Rayleigh number, Damkohler number, mechanical anisotropy parameter and thermal anisotropy parameter on the stationary and oscillatory convection is shown graphically. It is found that the effect of internal Rayleigh number and mechanical anisotropy parameter have destabilizing effect, while the thermal anisotropy parameter has stabilizing effect on the stationary and oscillatory convection. The Damkohler number has destabilizing effect in the case of stationary mode, with stabilizing effect in the case of oscillatory mode.
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