On closed-form analytical solution for circular duct, thermally developing slug flow under mixed boundary condition

Abstract

The present work deals with the problem of steady-state heat transfer in slug flow in a circular pipe with constant physical properties and negligible axial heat conduction. Use both of the Laplace transform with respect to the axial co-ordinate and of Galerkin's technique in the transform domain results in an approximate analytical solution. The calculations have shown that the second approximation thus obtained agrees well with the known exact analytical solution in the form of a series.