Study of single and two component convection in micropolar liquid

Abstract

In this thesis, we study linear and non-linear analysis of RayleighBénard and double diffusive convection in a micropolar liquid. The effect of non-uniform basic temperature gradient, non-uniform basic concentration gradient, temperature modulation at the boundary and gravity modulation are studied. newlineThe problem investigated in this thesis through a light on externally controlled internal convection in a micropolar liquid. The problems investigated in this thesis have possible application in geophysics, newlineastrophysics, oceanography engineering and in space situations with gjitter connected with gravity stimulation study. With this motivation, we investigate in this thesis four problems and their summary is given below one by one. (i) EFFECT OF GRAVITY MODULATION ON HEAT TRANSFER BY RAYLEIGH-BÉNARD CONVECTION IN A MICROPOLAR LIQUID newlineThe vertical oscillation, or g-jitter or gravity modulation, is known to appear in the situation of the satellite. In the laboratory, Rayleigh-Bénard system subjected to time-periodic vertical oscillations may be useful in regulating the onset of convection and heat transfer. This aspect is also in newlinefocus in the thesis. In this problem the effect of time-periodic body force or grtavity modulation on the onset of Rayleigh-Bénard convection in a micropolar liquid is investigated. The linear and non-linear analyses are performed. The linear theory is based on normal mode analysis and perturbation method. The expression for correction Rayleigh number is obtained as a function of frequency of modulation and other micropolar liquid parameters. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenzvii model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat newlinetransfer. (ii) LINEAR AND WEAKLY NON- LINEAR STABILITY ANALYSIS OF DOUBLE-DIFFUSIVE CONVECTION IN A MICROPOLAR LIQUID.