SOLUTION FOR HEAT TRANSFER WITH AXIAL CONDUCTION IN A CIRCULAR TUBE BY THE LINEAR OPERATOR METHOD

Abstract

Heat transfer problems with axial conduction in a circular tube for an arbitrary velocity field and a semi-infinite axial domain are investigated by the linear operator method. Since the domain of the linear operator is dense in a Hilbert space, an approximation method in a Hilbert space is applied and an algebraic characteristic equation for calculating the eigenvalues is obtained. Recursive formulas for computing the expansion coefficients with alternative forms are also presented. The computational procedures are straightforward and simple. The computational results show that the asymptotic Nusselt number is insensitive to the Peclet number provided Pe is larger than about 10.