Theses and Dissertations

Date of Award

8-2022

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Dambaru Bhatta

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Paul Bracken

Abstract

Here a study on thermal convection in a porous vertical cylindrical annulus which is heated from below is carried out. The walls are considered to be impermeable that is the velocity is 0 at the boundary walls. The cylindrical annulus is radially insulated. The governing system consists of the continuity equation, Darcy-Boussinesq equation, heat equation and the equation of state. Employing weakly non-linear approach, the basic state system and the perturbed system are derived. After obtaining the solutions to the basic state system, the pressure term in perturbed system is eliminated by taking double curl, and then eliminating the velocity, a partial differential equation in the linearized perturbed temperature is obtained. This partial differential equation is solved in terms of Bessel and trigonometric functions using separation of variables method. For axisymmetric case, the solution contains the zeroth order Bessel functions of the first and second kind. Computational results for the temperature are presented in tabular and graphical forms.

Comments

Copyright 2022 Anirban Ray. All Rights Reserved.

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