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RAYLEIGH-BENARD CONVECTION IN COUPLE STRESS FLUID WITH MAXWELL-CATTANEO LAW

Thomas, Maria (2019) RAYLEIGH-BENARD CONVECTION IN COUPLE STRESS FLUID WITH MAXWELL-CATTANEO LAW. PhD thesis, CHRIST(Deemed to be University).

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Abstract

The onset of thermal instability in horizontal layers of fluid heated from below illustrates many physical and mathematical features of the general theory of hydrodynamic stability. The effect of non-Fourier heat transfer in couple stress in a Rayleigh-Benard configuration is analyzed theoretically in this thesis. Broad range of applications of couple stress fluid and the need for its characterization at a relatively small scale of time and length act as a motivation for the study of buoyancy-driven convection in such fluids under the influence of magnetic field and under various modulations such as temperature, gravity, rotation and magnetic field by employing Maxwell-Cattaneo law. Linear and non-linear magneto-convection in couple stress fluid with Maxwell–Cattaneo law The interesting facets brought about by the interactions between convection and magnetic fields in a Rayleigh-Benard configuration for free- free boundaries are analyzed in ´ this chapter. Linear and weakly non-linear stability analysis are carried out to study the system. It is proved that the oscillatory mode is not the preferred mode of instability. The couple stresses in the fluid and magnetic field are found to enhance the stability of the system whereas non-Fourier effects destabilized the system. Effect of temperature modulation on the onset of Rayleigh–Benard ´ convection in a couple stress fluid with Maxwell–Cattaneo law The effect of externally imposed time-periodic boundary temperature on the setting in of convection is examined using linear stability analysis. The Venezian approach is applied to deduce the critical Rayleigh number and critical wave number. The stability of the system is characterized by a correction Rayleigh number and is obtained as a function of the Cattaneo number, couple stress parameter, Prandtl number and the frequency of modulation. The study analyzes three types of temperature modulations, viz. in-phase, out-of-phase and only lower wall modulation. Out-of-phase temperature modulation is observed to be a more stable system. The non-Fourier parameter is found to stabilize the system for a range of values of the modulating frequency. Couple stress parameter enhances the stability whereas the effect of Prandtl number is observed to be insignificant. Effect of gravity modulation on the onset of Rayleigh–Benard convection in a couple stress fluid with Maxwell–Cattaneo law The study of time-dependent gravity throws light on the fluid processes under microgravity conditions. The effect of gravity modulation on the onset of thermal convection in a horizontal couple stress fluid layer is studied analytically using linear stability theory. The regular perturbation method based on a small amplitude of modulation is employed to compute the critical value of Rayleigh number and wavenumber. The correction to critical Rayleigh number is derived as a function of Cattaneo number, couple stress parameter, Prandtl number and frequency of the modulation. It is shown that in general, the gravity modulation produces a stabilizing effect. Effect of rotational speed modulation on the onset of Rayleigh–Benard convection in a couple stress fluid with Maxwell–Cattaneo law An externally imposed vertical magnetic field in an electrically conducting horizontal fluid layer of couple stress fluid in a Rayleigh-Benard configuration is considered. A weakly non-linear stability analysis of thermal convection using the Lorenz model is considered to investigate heat transfer in the fluid layer. The Nusselt number is obtained in terms of Cattaneo number, couple stress parameter, Chandrasekhar number, Prandtl number, magnetic Prandtl number and frequency of modulation. The effect of each parameter on heat transport is discussed. A detailed mathematical formulation, graphical representations of the results and the analysis of the results are presented in this thesis. Mathematica is used for the calculation of the critical Rayleigh number, correction to critical Rayleigh number in the case of modulations, Nusselt number and for the plotting of the streamlines. OriginPro is used for the plotting of the remaining graphical representations.

Item Type:Thesis (PhD)
Subjects:Thesis > Ph.D > Mathematics
Thesis
Thesis > Ph.D
ID Code:7858
Deposited By:Shaiju M C
Deposited On:27 May 2019 16:12
Last Modified:27 May 2019 16:12

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