ItemPhD

Study of linear and non-linear analyses of rayleigh-benard chandrasekhar convection in micropolar fluid with saturated porous medium

Title
Study of linear and non-linear analyses of rayleigh-benard chandrasekhar convection in micropolar fluid with saturated porous medium
Creator
Anncy, Maria S.
Contributor
Joseph, T V and Pranesh, S
Description
Thermal instability of Chandrasekhar convection in a micropolar fluid, saturated porous layer is being investigated in this study. The model is confined between two horizon- tal plates of infinite length and separated by a fixed distance. A uniform temperature gradient is provided at the lower plate, while the upper plate is cooled. The study is analysed for both linear as well as non-linear cases to understand the stability, transfer of heat and mass within the model. The study is carried out in extending the model for Rayleigh-Benard and double diffusive convection with external constraints such as in-ternal heat, concentration source, gravity modulation, temperature modulation, coupled cross diffusion and throughflow. The outcome of the study is discussed in detail and presented pictorially through graphs. Linear and Non-linear Analyses of Double Diffusive Chandrasekhar Convection with Heat and Concentration Source in Micropolar Fluid with Saturated Porous Media under Gravity Modulation. A thermosolutal convective study is carried out in the presence of externally imposed magnetic field and gravity modulation together with heat and concentration source in a micropolar fluid. This problem is analysed for both linear and non-linear cases by as- suming the strength of heat and concentration source same. The expression for critical thermal Rayleigh number and correction thermal Rayleigh number are obtained using regular perturbation method to understand the stability of problem. The transfer of heat and mass transport is investigated by deriving the eighth order Lorentz equation. It is found that internal Rayleigh number and Darcy number speeds up the onset of instabil-ity while the coupling parameter and Chandrasekhar number has a reverse effect. Also, the transfer of mass is more compared to the transfer of heat. Linear and Non-linear Analyses of Double Diffusive Chandrasekhar Convection Coupled with Cross-diffusion in Micropolar Fluid over Saturated Porous Medium The problem aims to find the effects of coupled cross-diffusion in a micropolar fluid over a porous medium, subjected to double-diffusive-Chandrasekhar convection. The usual stability analysis has been employed to determine the critical thermal Rayleigh number. Non-linear analysis is carried out by deriving the Lorentz equations using trun- cated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood number respectively. Analysis related to the effect of various parameter are plotted and the result for the same are interpreted. As Dufour parameter increases, the diffusion of heat and solute takes place which increases the temperature difference and thereby delays the onset of convection by making the system stable. It is observed from the results that Dufour parameter and Soret parameter have opposite influence on the stability of the problem. Linear and Non-linear Analyses of Throughflow Effect on the Onset of Rayleigh-Benard-Chandrasekhar Convection in Micropolar Fluid with Porous Medium. The Rayleigh-Benard convection over a porous medium saturated with micropolar fluid is simulated via externally imposed magnetic effect. The stability of the system is ex- amined using linear analysis by the method of normal mode. The rate of heat and mass transport within the system is examined by deriving sixth order Lorentz equation using non-linear analysis. It is observed that by regulating the throughflow effect, the con- vection of the system can be controlled. Also, the pro-gravity and anti-gravity cases has a stabilizing effect on the system. From mathematical calculation, it can be seen that heat transfer rate is same for both pro-gravity and anti-gravity cases, because of the symmetric nature of the boundaries considered. Linear and Non-linear Analyses on the Effect of Time Periodic Boundary Temper- ature and Internal Heat Source in a Micropolar Fluid on the Onset of Rayleigh- Benard-Chandrasekhar Convection with Porous Medium The impact of temperature modulation at the boundaries over a surface containing voids that is soaked in micropolar fluid is investigated to understand the thermal instability of the convection exposed to magnetic effect and internal heating of the system. A small amplitude of perturbation is given to the system to analyse the thermal instability by performing a linear study through the method of regular perturbation, which yields Rayleigh number for unmodulated and modulated system. Three cases of study is car-ried out to inspect the vibrating temperature field at the boundaries, namely symmetric case where the temperature is modulated in-phase, asymmetric case where the temper-ature is modulated out-phase and the case where only the bottom wall temperature is modulated. The non-linear analysis is employed to find the heat in the system, using Lorentz model. The outcome of the study conveys that sub critical motion occurs dur- ing in-phase modulation while the out-phase modulation leads to a more stable system. Moreover, internal Rayleigh number hastens the onset of convection.
Source
Author's Submission
Date
2021-01-01
Publisher
Christ(Deemed to be University)
Subject
Mathematics and Statistics
Rights
Open Access
Relation
61000156
Format
PDF
Language
English
Type
PhD

Collection

PHD

Citation

Anncy, Maria S., “Study of linear and non-linear analyses of rayleigh-benard chandrasekhar convection in micropolar fluid with saturated porous medium,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 23, 2025, https://archives.christuniversity.in/items/show/12118.

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