Abstract
A generalized equation for the transient temperature response of a body, initially in equilibrium with the surroundings, subjected to a step change in the temperature of the two faces and with a constant rate of internal generation of energy, is developed in dimensionless form for uni-directional heat conduction. The equation is arranged in suitable forms for solution by classical mathematics, analog computer and explicit finite difference methods. Calculations for the classical mathematics and finite difference methods were performed on an IBM 360/65 digital computer and the computer programs used are included in the Appendix. Two Pace TR 10 Analog Computers were used to obtain a solution to the problem and a circuit diagram is included in the report. A major finding of the study is that the temperature at a specific location in the body and at a specific time after the step change in face temperature is composed of two components, one due to the change in face temperature and one due to internal energy generation. In addition, the temperature effect contributed by the energy generated internally is shown to be the product of one factor, dependent only on time and location, and a second factor which is dependent on the actual rate of energy generation, the half width of the body and the thermal conductivity of the material. The arrangement into temperature components permits the evaluation of only two generalized factors which can be used in the solution of a wide range of problems. Each temperature component can be evaluated independently, using any of the solution methods employed in the study. Numerical results determined for each of the temperature components are presented in graphical form. Tables are used to present numerical results obtained from each of the solution methods used. An example of the application of the temperature component factors is given in the report.
Alter, Alan Brian (1971). Solutions of the general heat conduction equation by comparative methods. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -213315.