Application of the direct operational method to an analysis of unsteady heat flow, between a fluid and a solid body generating heat (Q1096473)

An analysis of unsteady heat flow between a fluid and a solid body generating heat is presented. An appropriate mixed initial and boundary value problem formulated originally by \textit{H. S. Carslaw} and \textit{J. C. Jaeger} [Conduction of heat in solids (1986; Zbl 0584.73001)] has been solved by means of the direct operational method. Using the special functions \(Bes_ n(x,y)\) and \(Bs_ n(x,y)\), the temperature distributions are obtained in the so-called closed form. It has been also adduced a number of formulae from operator calculus in which the functional forms (the inverse Laplace transforms) have been expressed in terms of the mentioned special functions. These formulae can be applied when solving many problems of technical importance.