Masters Theses

Ceylung Chu

Abstract

"This report presents numerical methods for calculating temperature distributions in any physical system in which heat transfer is taking place. The syste.11 may be at either a steadystate condition or a transient condition. The temperature distribution may itself be or primary interest, or it may be used further to calculate the flow or heat or thermal stress.

The system under investigation is divided into a certain number of subdivisions, or so-called "regions". A reference point (node point) will be taken as representative for the region which includes that point. The temperature at the "node point11 is taken to be the temperature throughout the region. An energy balance for each region yields a system of first order differential equations. The number of equations is identical with the number of regions. This system of first order differential equations is first solved by Runge-Kutta method, then by explicit method.

In the Runge-Kutta method a set of formulas are used to calculate the temperatures at the end of the time interval at each step. 1 In the explicit method the temperature of a region at the end of the time interval is calculated explicitly from the temperatures at the beginning of the time interval or this region and its neighbor regions.

If the system is at steady state, a system of fourth degree non- linear algebraic equations is normally obtained when radiation is considered. Newton-Raphson Iteration Method is used to solve this set of equations simultaneously.

The programs given in this report are applicable to one-, two-, and three-dimensional. problems. The number of equations, and thus the number of subdivisions is limited by the storage capacity of the computer.

Before the programs can be applied, a calculation of the coefficients or the polynomial in the program must be carried out. These coefficients are evaluated from the subdivisions chosen, the physical properties or the system and the heat transfer phenomena involved.

Two demonstrative problems are given in the Appendix to show the procedure of applying the programs given in this report to physical systems" -- Abstract, pp. 1-2

Advisor(s)

Sauer, Harry J., Jr., 1935-2008

Committee Member(s)

Culp, Archie W.
Antle, Charles E.
Pagano, Sylvester J., 1924-2006

Department(s)

Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering

Publisher

University of Missouri at Rolla

Publication Date

1964

Pagination

83 pages

Note about bibliography

Includes bibliographical references (pages 46-47)

Rights

© 1964 Ceylung Chu, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Thesis Number

T 1602

Print OCLC #

5959097

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