Impact of temperature-dependent viscosity on linear and weakly nonlinear stability of double-diffusive convection in viscoelastic fluid

The impact of temperature-dependent viscosity on the double-diffusive viscoelastic convective fluids is investigated, with applications in heat transfer, polymer processing, food industry, biomedical engineering, etc. Both linear and weakly nonlinear analyses are carried out to determine the stability of fluids using the Oldroyd-B model. Analytical criteria for the onset of linear stationary and oscillatory convection are derived. The effects of rheological parameters, linearly and exponentially varying viscosity, salinity Rayleigh number and Prandtl number on the system's stability are investigated. Linear stability analysis reveals that the interaction between thermal and solute diffusions with rheological parameters favours oscillatory convection over stationary convection. In weakly nonlinear theory, a power series expansion derives a Landau amplitude equation, allowing heat and mass transfer analysis in viscoelastic fluids with temperature-dependent viscosity. Numerical results highlight the effects of variable viscosity on heat and mass transfer rates, represented by Nusselt and Sherwood numbers. Further, the weakly non-linear stability analysis evaluates the impact of the Prandtl number, rheological parameters and salinity Rayleigh number on heat and mass transfer rates. These findings are compared with existing results to validate and enhance our understanding of fluid behaviour under different conditions.