
 An approximate method for computing transient thermal stresses in hollow cylinders, plates, and hollow spheres is presented. The method makes use of polynomial approximations to the temperature distribution by means of which the partial differential equation of the problem is reduced to a set of first-order ordinary differential equations. Nonuniform initial temperature distribution and heat transfer from both surfaces can be treated without difficulty making possible the practical solution of problems with relatively little labor for which an exact solution requires a great expenditure of labor and time. Several examples are presented and compare favorably with more accurate solutions.

This method provides an approximate solution for transient thermal stresses in hollow cylinders, plates, and spheres with heat transfer at two surfaces, reducing labor and time compared to exact solutions.

Approximate Solution to Thermal-Shock Problems in Plates, Hollow Spheres, and Cylinders With Heat Transfer at Two Surfaces

Key Takeaway: This method provides an approximate solution for transient thermal stresses in hollow cylinders, plates, and spheres with heat transfer at two surfaces, reducing labor and time compared to exact solutions.