Maxwell Cattaneo double diffusive convection (DDC) in a viscoelastic fluid layer

Abstract

The onset of Maxwell-Cattaneo DDC in a viscoelastic fluid layer is studied using linear stability analysis with the help of normal mode
technique. The parabolic advection diffusion equation, which presupposes classical fickian diffusion for both heat and salt, controls the evaluation of temperature and salinity. Analytically, the onset criteria for stationary and oscillatory convection is derived. Since the onset of stationary (steady case) convection is unaffected by Maxwell-Cattaneo effects as well as visco-elastic parameters, oscillatory convection rather than stationary convection is the key to visualize the effects of different parameters in this paper. Two different scenarios for oscillatory convection have been discussed (i) when Maxwell-Cattaneo coefficient for salinity CS = 0 and
(ii) when Maxwell-Cattaneo coefficient for temperature CT = 0. Also a comparative study for these two cases i.e. CS = 0 and CT = 0 is performed for different controlling parameters like relaxation parameter (λ1), retardation parameter (λ2), diffusion ratio (τ ), solutal Rayleigh number (RaS) and Prandtl number (P r) with the help of graphs.