Instability of mixed convection in a differentially heated channel filled with porous medium: A finite amplitude analysis

Abstract

This paper reports the instability mechanism of parallel mixed convection flow in a differentially heated vertical channel filled with a highly permeable porous medium. Linear and weakly nonlinear stability analysis involving the finite-amplitude expansion method is considered to investigate the instability mechanism of the flow. Darcy–Brinkman's model is considered. The results are presented for both water-saturated and oil-saturated porous medium flows. The linear stability results show that the stability of the flow decreases on increasing the Reynolds number as well as the Darcy number, and the contribution of viscous dissipation in the kinetic energy balance is not negligible for highly permeable porous medium flows. The results from the weakly nonlinear analysis show only supercritical bifurcation in the vicinity of the critical or bifurcation point for both the fluids; however, for water, the parallel flow may experience subcritical bifurcation away from the critical point, which depends on the value of the Darcy number. The variation of neutral stability curves of the parallel flow of water reveals that a bifurcation that is supercritical for some wavenumber may be subcritical at other nearby wavenumbers. The nonlinear interaction of different harmonics enhances the heat transfer rate as well as the friction coefficient in the linearly unstable regime. A comparison with the results using a model based on volume averaged Navier–Stokes equation reveals the possibility of subcritical bifurcation even in the vicinity of the critical point.