Masters Theses

Guy H. Lee

Date of Award

12-1987

Degree Type

Thesis

Degree Name

Master of Science

Major

Engineering Science

Major Professor

K. H. Kim

Committee Members

C. J. Remenyik, M. O. Soliman

Abstract

The purpose of this study was to investigate laminar natural convection heat transfer along a thin needle with radiative heat flux. In particular, the investigation centered on the skin friction factor and heat transfer rate as well as the velocity and temperature profiles along the transformed spatial variable η. The radiative heat flux term was linearized after being simplified by means of Rosseland approximation. The study was initiated by finding transformation variables which reduced the original boundary layer equations in cylindrical coordinate into ordinary differential equations. Through this transformation, a certain condition about the needle shape was found to guarantee such a transformation exists. Then the relationships between skin friction factor and transformed velocity function, as well as heat transfer rate and transformed temperature function, were formulated to establish the relationship between these transformed variables and real dimensional values.

These coupled ordinary differential equations were solved by one type of shooting method which took into account the fact that some boundary conditions were prescribed at infinity. This scheme guessed initial conditions such as the slope of velocity and temperature at the wall and examined the convergence of the boundary conditions at infinity by means of integration. This scheme was stable in a sense that any values of initial guesses are automatically corrected for convergence and the error term was well controlled within the tolerance bound.

The values of skin friction factor and heat transfer rate at the wall were calculated in terms of similarity variables for several values of Prandtl numbers and parameters of conduction to radiation ratio. Also several profiles for the momentum and thermal boundary layer were presented in graphs for different values of Prandtl numbers and parameters of conduction to radiation ratio. This information leads to the conclusion about the effect of the degree of radiative influence as well as the role of Prandtl numbers. This study can provide valuable information about the heat transfer and skin friction along the slender wire especially in high temperature.

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