On the properties of some special functions related to Bessel's functions and their application in heat exchanger theory

Abstract

Basic properties of Bs n ( x, y) and Bes n ( x, y) functions related to Bessel functions, are presented. The functions are defined by double power series: Bs n(x, y) ▪ ∑ m= max(0,n) ∞ x m m! ∑ k=0 m−n y k k! Bes n(x, y) ▪ ∑ m= max(−n,0) ∞ x m+ny m (m+n)!m! Numerous formulae are given on the origin of identities, differential formulae as well as the ones for calculation of integrals, whose sub-integral functions comprise the foregoing special functions. Some applications of Bs n ( x, y) and Bes n ( x, y) functions are also given with regard to the theory of cross-flow recuperator and to heat transfer analysis of gas-cooled clinker beds. Some cases of boundary conditions and initial boundary conditions are considered. The solutions are of the so-called closed form which is by far better than those achieved by approximate methods. Bs n ( x, y) and Bes n ( x, y) functions may be applied to theoretical analyses of heat and mass exchangers, regenerators, ion exchangers and for different kinds of heavy equipment used in the chemical industry. These functions can also be applied to control and protect various physical processes.