“Nyuggel” Lunabister, Donrossness, Shetland ZE2 9JH, U. K.
ABSTRACT
The investigation of eigenvalues of random mechanical vibrations of a cooling system involving the circular-cylindrical shell and its contents, namely a circular-cylindrical mass of fluid, is nearly of some importance. This is particularly pertinent relative to such cooling systems involved in nuclear reactors. In this study, explicit solutions of the governing differential equations are presented in the form of double hypergeometric functions, while two degenerate solutions are obtained in the form of hypergeometric functions of one variable.
The method of attack consists of the application of Laplace transform to a specially constructed linear differential system. Namely, an auxiliary system of non-linear algebraic equations can be shown to be consistent and numerically implemented by the use of the computer algebra package MAPLE V.
AMS Subject Classification. 33C20, 33C50, 33E15, 33E20, 34A05, 76A05
Keywords: Bessel-Clifford equations; hypergeometric functions; Laplace transformation