Publication Date

9-10-1969

Abstract

The one-dimensional time-dependent equation of heat conduction is solved analytically for an infinite two-layer circular cylinder whose core may be either hollow or solid. On the outer surface of the cylinder, which has no heat loss due to convection, a constant heat flux from an external source of heating is applied uniformly. The layers are in perfect thermal contact, and there is no heat loss at their interface. At the smaller radius of the inner layer is a perfect insulator so that the heat flux on the inner surface of the two-layer cylinder is zero. The temperature is uniform initially throughout the layers, and the thermal and physical properties of each layer remain constant.

Equations for predicting the transient temperature distribution within each layer are determined from the heat-conduction equation by using a method of separation of variables, by homogenizing the boundary conditions, by applying the boundary conditions, and by determining eigenvalues and eigenfunctions. The constants or integration are determined by applying the boundary conditions to the general solutions. The solutions for the temperature distribution in layers 1 and 2, respectively, are

and

The various terms in these equations are defined in the text. These final solutions are shown analytically to satisfy the heat-conduction equation and the boundary conditions. Appendix A contains a discussion of Bessel functions of the first and second kinds of orders zero and one. Appendix B contains listings of computer programs to determine values of Beta which satisfy the “root equation” and to verify the initial conditions. Some values of Beta are given for a steel-phenolic cylinder. Subroutines are given for computing the Bessel functions of the first and second kinds of orders zero and one. The results may be of general academic interest to those working in heat conduction or studying thermal environments.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Sarah Lee Meyer

Second Committee Member

George Milton Wing

Third Committee Member

Julius Rubin Blum

Language

English

Document Type

Thesis

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