Convection in a rectangular enclosure with internally heated porous medium: impact of boundary conditions

Abstract

The present work is focussed on analyzing the stability of fluid within the porous structure, accounting for constant internal heat generation by employing both linear (normal mode technique) and nonlinear stability (energy) techniques. The impact of diverse sets of boundary constraints, encompassing impermeable, conducting, porous, and insulating on the stability is also explored. The governing equations are transformed into an eigenvalue problem derived from stability analysis, which is transformed into a fourth-order problem on separating Fourier component and then numerically solved using the Chebyshev pseudospectral method for finding the critical Rayleigh numbers. It is found that the presence internal heat generation gives rise to the potential of subcritical instability. Five models are considered based on bounding surfaces and the impact of internal heating is analysed which suggest that the stability can be enhanced or convection can be accelerated by taking appropriate combination of these models and values of heat generation parameter. It is also noted that in the absence of internal heating the subcritical region of instability does not exist.