Study of effect of modulations on the onset of rayleigh benard convection in a couple stress fluid

Abstract

In this thesis we study the linear and non-linear analyses of Rayleigh-Benard convection in a couple stress fluid. The effect of rotational modulation, temperature modulation and gravity modulation in the presence of external constraints like magnetic field and electric field are studied. The problems investigated in this thesis throw light on externally controlled convection in a couple stress fluid. The problems investigated in this thesis have possible applications in geophysics, astrophysics, oceanography engineering and experiment/ space situations with g-jitter connected with gravity simulation studies. with this motivation, we investigate in this thesis four problems and, their summary is given below one by one. (i)Linear and non-liner analyses of rotational modulation on Rayleigh-Benard convection in a couple stress fluid. The linear and non-linear analyses of Rayleigh-Benard convection in a couple stress fluid with rotational modulation is studied. The linear and non-linear analyses are, respectively based on normal mode technique and truncated representation of fourier series. The expression for Rayleigh number and correction Rayleigh number are obtained using regular perturbation method in the case of liner theory. The resulting no-autonomous lorenz model obtained in no-linear analysis is solved numerically using the Runge-Kutta-Fehlberg45 method to quantify the heat transport. The effect of rotational modulation is shown to be stabilizing there by leading to a situation of reduced heat transfer. The problem suggests an elegant method of controlling internal convection.(ii) Linear and non-linear analyses of gravity modulation on Rayleigh-Benard convection in a weakly electrically conducting couple strss fluid.The effect of time-periodic body force on the onset of Rayleigh-Benard convection in weak electrically conducting couple stress fluid is investigated. The stability of the horizontal fluid layer heated from below is examined by assuming time periodic body acceleration. newline