Cooling of a cylindrical container blasted into the rock

An upright cylindrical container blasted into the rock is filled instantaneously with a warm liquid. Heat is transferred from the liquid into the surrounding rock and the open air. The temperature of the liquid and the surrounding rock is determined as a function of time.The differential equation and the auxiliary conditions of the transient heat conduction problem are Laplace transformed, the subsidiary equations are solved by two-dimensional relaxation, and the resulting temperature is obtained by means of numerical inversion of the Laplace transform.The results are presented numerically and graphically.