STUDY OF DIFFERENT TYPES OF MODULATIONS ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYD-B LIQUIDS

Abstract

THE STUDY OF EFFECTS OF TEMPERATURE MODULATION ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYD-B LIQUIDS 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. Mean Nusselt number and mean 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. THE STUDY OF EFFECTS OF GRAVITY MODULATION ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYD-B LIQUIDS The effect of gravity modulation is analysed in Oldroyd-B liquids subjected to double diffusive convection. Both linear and non-linear analysis has been done. A regular perturbation technique has been employed to arrive at the thermal Rayleigh number. The results show that stress relaxation destabilises the system whereas strain retardation parameter and Lewis number stabilises the system. Truncated Fourier series expansion gives a system of Lorentz equations that represent the nonlinear analysis. Mean Nusselt and mean Sherwood numbers are used to quantify the heat and mass transfer respectively. It is observed that Lewis number and strain retardation parameter decreases heat and mass transfer and stress relaxation parameter increases them. It is seen that modulation gives rise to sub-critical motion. THE STUDY OF EFFECTS OF ROTATION MODULATION ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYD-B LIQUIDS The effect of rotation modulation is analysed in Oldroyd-B liquids subjected to double diffusive convection. Both linear and non-linear analysis has been done. A regular perturbation technique has been employed to arrive at the thermal Rayleigh number. The results show that stress relaxation destabilises the system whereas strain retardation parameter and Lewis number stabilises the system. Truncated Fourier series expansion gives a system of Lorentz equations which helps in performing the non-linear analysis. Mean Nusselt and mean Sherwood numbers are used to quantify the heat and mass transfer respectively. It is observed that Lewis number and strain retardation parameter decreases heat and mass transfer and stress relaxation parameter increases them. It is seen that modulation gives rise to subcritical motion. THE STUDY OF EFFECTS OF INTERNAL HEAT SOURCE MODULATION ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYDB LIQUIDS The effect of internal heat source modulation on double diffusive convection in Oldroyd-B liquids is studied. The linear study is done using a regular perturbation technique. It is observed that stress relaxation parameter causes acceleration in convection whereas strain retardation parameter and Lewis number delays it. The non-linear analysis is based on truncated Fourier series expansion. The transport of heat and mass are analyzed using mean Nusselt and mean Sherwood numbers. Modulation is seen to give rise to super-critical motion.