Linear and non linear electroconvection in a micropolar fluid

Abstract

This thesis presents a theoretical study of linear and non-linear analyses of Rayleigh Bénard Marangoni/Rayleigh Bénard electro newlineconvection in a micropolar fluid. The effects of non-uniform basic temperature gradient, suction injection combination and gravity newlinemodulation have been studied in the presence of electric field. The effect of heat transfer in a micropolar fluid in the presence of electric field is also studied and results are presented graphically and discussed qualitatively. These problems assume greater importance in geophysics, newlineastrophysics, oceanography, and engineering and in space situations with g-jitter connected with gravity stimulation study. newlineKeeping in mind the importance and relevance of externally controlled internal convection in a micropolar liquid. We deal with four newlineproblems, details of which are given below. newline(i) Effect of non uniform basic temperature gradient on the onset of Rayleigh Bénard Marangoni electro convection in a micropolar fluid. The non-uniform temperature gradient finds its origin in the transient heating or cooling at the boundaries and as a result the basic temperature profile depends explicitly on position and time. This has to be determined by solving the coupled momentum and energy equations. This coupling also makes the problem very complicated. In the present study, therefore, we adopt a series of temperature profiles based on a newlinesimplification in the form of a quasi-static approximation that consists of freezing the temperature distribution at a given instant of time. In this method, we assume that the perturbation grows much faster than the newlineinitial state and hence freeze the initial state into some spatial distribution. newlineTherefore the effects of these non-uniform basic temperature gradient and electric field are studied on the onset of Rayleigh Bénard Marangoni convection in micropolar fluid.