Stability Analysis on Double Diffusive Convection for a Non Newtonian Fluid with Relaxation Stress, Thermal Diffusion and Internal Heat Generation

Abstract

The investigation, Stability Analysis on Double Diffusive Convection with relaxation stress, Thermal Diffusion and Internal Heat Generation was carried out for non-Newtonian fluid systems. The Boussinesq approximation was used for the density variation with temperature and concentration. Also, the Rosseland approximation was adopted for the radiative flux. Governing equations that incorporate the coupling effect of relaxation stress, thermal diffusion and internal heat generation is developed. The governing equations are non-dimensionalised, and the emerging nonlinear partial differential equations governing the flow are solved using the regular perturbation, normal mode representation and linear stability analysis processes. In order to compare our mathematical solutions to findings from existing literature, profiles were developed using Mathematica software to test for the sensitivity of the pertinent parameters on the onset of instability in the system. The results showed that for stationary convection in non-Newtonian fluids: an increase in the radiation and relaxation stress parameters translates into a more stable system by delaying the onset of instability in the system while, an increase in Prandtl number, growth rate parameter, porosity, Soret, internal 1.1 Introduction heat and Lewis number instigates the onset of instability in the system. In conclusion, we’ve been able to investigate the stability behaviour of Double Diffusive Convection for non Newtonian fluid systems experiencing the coupling effects of relaxation stress, thermal diffusion and internal heat generation using linear stability analysis.