Rayleigh benard and benard marangoni convection in micropolar fluid

Abstract

We study in this thesis, Rayleigh-Bénard and Bénard-Marangoni convection in a micropolar fluid. We study the effects of temperature modulation at the boundary and gravity modulation in the presence of porous medium. The effects of rotation and internal heat generation are also investigated and results are presented graphically and discussed qualitatively. The problem presented in this thesis throws light on externally controlled internal convection in a micropolar fluid. These problems have many possible applications in geophysics, astrophysics, oceanography engineering and in space situations with g-jitter connected with gravity stimulation study. With this motivation, we examine in this thesis five problems and their summary is given below one by one. (i) THE EFFECT OF IMPOSED TIME-PERIODIC BOUNDARY TEMPERATURE AND POROUS MEDIUM ON THE ONSET OF RAYLEIGH-BÉNARD CONVECTION IN A MICROPOLAR FLUID The analysis of buoyancy driven convection in a micropolar fluid saturated porous layer heated from below and subject to temperature modulation is presented. In addition to a steady temperature difference between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. The small amplitude of the modulation is used to compute the critical Rayleigh number and critical wave number. Three cases of the oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of-phase modulation, and (c) only the bottom wall is modulated. Possibilities of the occurrence of subcritical instabilities are also discussed. The shift in the critical Rayleigh number is calculated as a function of frequency and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures. (ii)LINEAR AND NON-LINEAR ANALYSES OF GRAVITY MODULATION ON THE ONSET OF RAYLEIGH-BÉNARD CONVECTION IN A MICROPOLAR FLUID WITH POROUS MEDIUM.