The Linear and Non-linear Study of Effects of Temperature Modulation on Double Diffusive Convection in Oldroyd-B Liquids

Abstract

The problem aims to find the effects of temperature modulation in viscoelastic fluids, namely Oldroyd-B liquids, subjected to double diffusive convection. Both linear as well as a non-linear study has been carried out. A regular perturbation technique has been employed to determine the correction Rayleigh number. The results show that the Lewis number and strain retardation parameter induces stability to the system whereas stress relaxation parameter destabilizes the system for synchronous modulation. Truncated Fourier series represents the non-linear analysis. Nusselt number and Sherwood number are used to quantify the heat and mass transfer respectively. Strain retardation parameter and the Lewis number decrease the heat and mass transfer for synchronous modulation while stress relaxation parameter increases them. The opposite results are obtained for asynchronous and lower wall modulations. Modulation is shown mostly to give rise to super-critical motion.