Rayleigh benard convection in couple stress fluid with maxwell cattaneo law

Abstract

The onset of thermal instability in horizontal layers of fluid heated from below illustrates many physical and mathematical features of the general theory of hydrodynamic stability. The effect of non-Fourier heat transfer in couple stress in a Rayleigh Benard configuration is analyzed theoretically in this thesis. Broad range of applications of couple stress fluid and the need for its characterization at a relatively small scale of time and length act as a motivation for the study of buoyancy driven convection in such fluids under the influence of magnetic field and under various modulations such as temperature, gravity, rotation and magnetic field by employing Maxwell Cattaneo law. newlineLinear and non linear magneto convection in couple stress fluid with Maxwell Cattaneo law newlineThe interesting facets brought about by the interactions between convection and magnetic fields in a Rayleigh Benard configuration for free free boundaries are analyzed in this chapter. Linear and weakly non linear stability analysis are carried out to study the system. It is proved that the oscillatory mode is not the preferred mode of instability. The couple stresses in the fluid and magnetic field are found to enhance the stability of the system whereas non-Fourier effects destabilized the system. newlineEffect of temperature modulation on the onset of Rayleigh Benard convection in a couple stress fluid with Maxwell Cattaneo law newlineThe effect of externally imposed time-periodic boundary temperature on the setting in of convection is examined using linear stability analysis. The Venezian approach is applied to deduce the critical Rayleigh number and critical wave number. The stability of the system is characterized by a correction Rayleigh number and is obtained as a function of the Cattaneo number couple stress parameter Prandtl number and the frequency of modulation. The study analyzes three types of temperature modulations viz. in phase, out of phase and only lower wall modulation.