Numerically solving a transient heat conduction problem with convection and radiation
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Authors
Albert, David J.
Subjects
Numerical analysis
Heat equation
Runge-Kutta
Finite difference
Volterra integral equation
Heat equation
Runge-Kutta
Finite difference
Volterra integral equation
Advisors
Leader, Jeffery J.
Date of Issue
1993-06
Date
June 1993
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
The transient surface temperature distribution is determined for the flat plate and sphere subjected to cooling by combined convection and radiation. In the study, the initial boundary value problem is reduced to a singular nonlinear Volterra integral equation of the second kind using the integral transform method. Several numerical techniques are introduced in an attempt to find an approximate solution of the problem: The method of successive approximations, the Runge-Kutta method, and the finite difference method. The integral equation is solved numerically by the Runge-Kutta method of orders 1, 3, and 5. In addition, the finite difference method is implemented to solve the initial boundary value problem, and the solutions are compared with those generated by the Runge-Kutta method. All the numerical results are presented graphically. Limitations and difficulties involved in these schemes are discussed. At the end, a numerical algorithm for solving the problem is proposed.
Type
Thesis
Description
Series/Report No
Department
Department of Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
93 p.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.