Study of magnetoconvection with maxwell cattaneo law

Abstract

This thesis deals with the study of Rayleigh-Bénard-convection in a Newtonian fluid and micropolar fluid by replacing the classical Fourier law by non-classical Maxwell-Cattaneo heat flux law. The effects of second sound, non-uniform basic temperature gradients, suctioninjection-combination, temperature modulation and gravity modulation in newlinepresence of external constraints like magnetic field and rotation are studied. newlineThe problems investigated in this thesis throw light on externally controlled convection in Newtonian and micropolar fluids in the presence of Maxwell-Cattaneo law. The problems investigated in this thesis deal newlinewith practical problems with very large heat fluxes and/or short time duration. With this motivation, we investigate in this thesis five problems and their summary is given below. (i) Effects of Coriolis force and non-uniform basic temperature gradients on the onset of Rayleigh-Bénard-Chandrasekhar newlineconvection with Maxwell-Cattaneo law The effect of non-uniform temperature gradient on RayleighBénard-Chandrasekhar convection in a rotating Newtonian fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalues is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset is discussed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones. It is shown that the system having magnetic field will delay in the onset newlineof instability. In general, it is observed that step function and inverted parabolic temperature profile are the most destabilizing and stabilizing profiles.