Study of magnetoconvection with maxwell cattaneo law /

Study of magnetoconvection with maxwell cattaneo law /

Mathematics

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
presence of external constraints like magnetic field and rotation are studied. The 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 with 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 convection 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 fiveix 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 of instability. In general, it is observed that step function and inverted parabolic temperature profile are the most destabilizing and stabilizing profiles. The range of values of the parameters of the problem for which oscillatory convection in the case of free-free isothermal boundary exists is also discussed. (ii) The effect of temperature modulation on the onset of RayleighBénard-Chandrasekhar convection using Maxwell-Cattaneo law The effect of imposed time-periodic boundary temperature (ITBT, also called temperature modulation) and magnetic field at the onset of Rayleigh-Bénard convection is investigated by making a linear analysis. The classical Fourier heat law is replaced by the non-classical MaxwellCattaneo law. The venezian approach is adopted in arriving at the critical Rayleigh number and wave number for small amplitude of ITBT. Three
cases of 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 lower wall is modulated. The temperature modulation is shown to give rise to sub-critical motion. 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. It is shown that the system is more stable when the boundary temperatures are modulated out of phase.x
(iii) The effect of gravity modulation on the onset of RayleighBénard-Chandrasekhar convection using Maxwell-Cattaneo law The effect of gravity modulation and magnetic field at the onset of Rayleigh-Bénard-Chandrasekhar convection is investigated by making a regular perturbation technique. The stability of the horizontal fluid layer heated from below is examined by assuming time-periodic body acceleration called g-jitter, which normally occurs in satellites and in vehicles connected with microgravity simulation studies. The venezian
approach is adopted in arriving at the critical Rayleigh number and wave number for small amplitude of gravity modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. It is observed that gravity modulation leads to delayed convection. (iv) The effect of suction-injection-combination (SIC) on the onset of Rayleigh-Bénard-Chandrasekhar convection in a micropolar fluid with Maxwell-Cattaneo law The effect of suction-injection-combination (SIC) on the onset of Rayleigh-Bénard-Chandrasekhar convection in a micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic on the spinvanishing boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters on the onset of convection has been analyzed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC beingxi pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. The problem suggests an elegant method of external control of internal convection. (v) The effect of non-uniform temperature gradients on RayleighBénard-Chandrasekhar convection in a micropolar fluid with
Maxwell-Cattaneo law The effect of non-uniform temperature gradient on RayleighBénard-Chandrasekhar convection in a micropolar fluid with MaxwellCattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters on the onset of convection has been
analyzed. Six different non-uniform temperature profiles are considered their comparative influence on onset is discussed. It is observed that the micropolar fluid layer heated from below is more stable compared to the classical Newtonian fluid layer.

Kiran, R.V. - 0944302

CHRIST (Deemed to be University)

2013

English

PhD