Transient thermal stresses in a finite solid circular cylinder due to a cylindrical surface heat source over the lateral surface

An exact solution is given for the determination of transient thermal stresses in a traction-free, finite solid, circular cylinder subjected to a cylindrical surface heat source over the lateral surface and having a heat loss to a surrounding medium over the entire boundary surface. The problem is formulated in terms of thermo-elastic displacement potential and Love's function, and the solution rigorously satisfies traction-free boundary conditions on both the lateral and end surfaces of the cylinder.

The problem is of considerable technological importance, particularly to certain nuclear reactor analyses related to the behavior of fuel elements and control rods during power transients.

Numerical calculations are carried out for various combinations of Biot's number and the ratio of length to diameter of the cylinder. The results obtained are compared with those of an infinite, solid, circular cylinder and of a solid circular disc.