Masters Theses

Yeunsik Choi

Date of Award

6-1985

Degree Type

Thesis

Degree Name

Master of Science

Major

Engineering Science

Major Professor

Kenneth H. Kim

Committee Members

J. H. Forrester, M. O. Soliman

Abstract

The purpose of this study is to investigate a steady laminar natural convection plume arising from a horizontal line source of heat. This study also includes a natural convection flow over a vertical adiabatic surface with a heat source concentrated at the leading edge. In each case, particular interest is directed to the examination of the effect of thermal radiation heat transfer. The study is initiated by first determining a set of governing equations for an incompressible, Newtonian fluid in a two dimensional flow field where the no slip condition on the wall is applied. Fluid properties such as viscosity and thermal conductivity are assumed to be constant. Transformation variables, derived by Birkoff's group theory, reduce the governing partial differential equations to ordinary differential equations. The radiation properties of the medium are specified by assuming the medium is optically thick, which is known as the Rosseland approximation. The radiation heat flux which results from the Rosseland approximation is linearized.

The technique of numerical analysis used is the Runge-Kutta algorithm with Gill coefficients. This algorithm is employed in a program designed to generate solutions based on automatic corrections to initial guesses for starting values given to the slopes of the velocity and temperature profiles. The corrections are obtained by satisfying the asymptotic boundary layer conditions so that the mean square error between the computed variables and the asymptotic values is minimized.

Extensive numerical calculations are carried out for Prandtl numbers ranging from 0.01 to 100 in the presence of and in the absence of thermal radiation. The results obtained from this research are plotted and analyzed.

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