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Double-diffusive convection in a porous medium with a concentration based internal heat source. (English) Zbl 1145.76441
Summary: Linear and nonlinear stability analyses of double-diffusive convection in a fluid-saturated porous layer with a concentration based internal heat source are studied. Darcy’s law and the Boussinesq approximation are employed, with the equation of state taken to be linear with respect to temperature and concentration. Both the numerical and analytical analysis for the linear theory strongly suggest the presence of a critical value \(\gamma_c\), where \(\gamma\) is essentially a measure of the internal heat source, for which no oscillatory convection occurs when \(\gamma_c \leq \gamma\). This, in the present literature, appears to be an unobserved phenomenon.
A nonlinear energy stability analysis demonstrates more comparable linear and nonlinear thresholds when the linear theory predicts the onset of fully stationary convection. However, irrespective of the \(\gamma\) value, the agreement of the thresholds does deteriorate as the solute Rayleigh number \(R_c\) increases.

MSC:
76S05 Flows in porous media; filtration; seepage
76E06 Convection in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
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