Effect of modulation on the onset of thermal convection in a viscoelastic fluid-saturated sparsely packed porous layer

Abstract

The stability of a Boussinesq viscoelastic fluid-saturated horizontal porous layer, when the boundaries of the layer are subjected to periodic temperature modulation, is analyzed. The Darcy-Forchheimer-Brinkman-Oldroyd model is employed and only infinitesimal disturbances are considered. Three cases of the oscillating temperature field were examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of-phase modulation, and (c) only the bottom wall is modulated. Perturbation solution in powers of the amplitude of the applied field is obtained. The effect of the frequency of modulation on the stability is clearly shown. Possibilities of the occurrence of subcritical instabilities are also discussed. It is shown that an increase in the elastic parameters A₁ and A₂ has a stabilizing influence. An increase in the Prandtl number destabilizes the system for small values of the frequency but stabilizes the systems for large values of the frequency. It is shown that the system is most stable when the boundary temperatures are modulated out of phase. The maximum range of e when subcritical instabilities exist is also determined.