Application of some special functions to the counterflow heat exchanger analysis (Q1820068)

Starting period of a counterflow heat exchanger is considered and closed form as well as compact expressions describing the fluid temperature distributions are presented. This result was obtained owing to the use of the special functions \(Bes_ n\) and \(Bs_ n\), \(n=0,\pm 1,..\). These, related to the Bessel functions depend on two variables and allow to simplify the calculations. The considerations are supplemented by the list of formulae of symbolic calculus which may be used when solving the heat and mass transfer problems described by hyperbolic differential equations by means of the Laplace transformation.