Instability of Thermosolutal Convection of Kelvin-Voigt Fluid in a Porous Medium Using Darcy-Brinkman Model

Abstract

In this article, we investigate the problem of thermosolutal convection of a class of viscoelastic fluids in a porous medium of Darcy-Brinkman type. This phenomenon takes place when a layer is heated from beneath while also being exposed to salt either from the upper or lower side. Both linear instability and conditional nonlinear stability analyses are applied in this study. The eigenvalue system have been solved using the Chebyshev collocation technique and the QZ algorithm. The computation of instability boundaries is undertaken for the occurrence of thermosolutal convection in a fluid containing dissolved salt, where the fluid is of a complex viscoelastic nature resembling the Navier-Stokes-Voigt type. Notably, the Kelvin-Voigt parameter emerges as a critical factor in maintaining stability, particularly for oscillatory convection. In instances where the layer is heated from below and salted from above, the thresholds of stability align with those of instability, substantiating the appropriateness of the linear theory in predicting the thresholds for convection initiation. Conversely, when the layer is subjected to salting from the bottom while being heated, the thresholds of stability remain constant even with variations in the salt Rayleigh number. This leads to a significant disparity between the thresholds of linear instability and those of nonlinear stability.