Articles - Numerical Analysis and Applicable Mathematics

Abstract

The aim of the present work was to study the effects of uniform vertical magnetic field and uniform rotation on the double-diffusive convection in Rivlin-Ericksen viscoelastic fluid through permeable media. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that the stable solute gradient and rotation have stabilizing effects on the system. In the presence of rotation, the medium permeability has a destabilizing (or stabilizing) effect and magnetic field has stabilizing (or destabilizing) effect on the system, whereas, in the absence of rotation, medium permeability and magnetic field have destabilizing effect and stabilizing effect on the system, respectively. The kinematic viscoelasticity has no effect for stationary convection. The kinematic viscoelasticity, rotation, stable solute gradient and magnetic field introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of over stability are also obtained.