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The thermal instability of a viscoelastic (Kuvshiniski-type) fluid in a porous medium is considered. Following linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the medium permeability is found to have a destabilizing effect and a Kuvshiniski viscoelastic fluid behaves like a Newtonian fluid. The principle of exchange of stabilities is found to be satisfied. The thermal instability of a rotating Kuvshiniski viscoelastic fluid in a porous medium is also studied. For stationary convection, it is found that rotation has a stabilizing effect, whereas the medium permeability has both stabilizing and destabilizing effects. The uniform rotation introduces oscillatory modes in the system that were non-existent in its absence.

On a Viscoelastic Fluid Heated from Below in a Porous Medium