ANALYSIS ON TRANSIENT THERMAL STRESSES IN AN ANNULAR FIN

Transient thermal stresses are an important consideration in production processes involving large temperature changes. Recently, thermal stresses have also become significant in design problems related to microelectronic devices through their effects on material properties and system parameters. To calculate the thermal stresses, three kinds of methods are available. The first is the analytical method, in which the elastic theory is used to find the exact solution. The second approach consists of some kind of approximate technique, such as a perturbation procedure. The third method is the use of a numerical process, such as a finite-difference or a finite-element method.

This article investigates the transient thermal stresses in an annular fin with its base subjected to a heat flux of a decayed exponential function of time. In order to obtain the solution of the governing equation, which is a partial differential equation, the following procedures of analysis are used.

1. Normalize the governing partial differential equation subject to appropriate initial and boundary conditions.

2. Take the Laplace transform of the resulting equation with respect to time.

3. Utilize the exponential-like solutions introduced by Keller and Keller to solve the transformed system.

4. Achieve the inverse Laplace transform by means of complex contour integration and the residue theorem.

5. Substitute the temperature distribution function into the governing equation of thermal stresses. Then use Simpson's rule to obtain the thermal stress distribution as a function of time and position of the fin.