Axial conduction with boundary conditions of the mixed type

A method is proposed for obtaining nearly analytical solutions to laminar flow thermal entrance region problems with axial conduction when the wall boundary conditions are of the mixed type. The method involves the utilization of Green's functions and the solution of a Fredholm integral equation using the Wiener–Hopf procedure. The method is illustrated by obtaining expressions for the temperature field for laminar flow in a circular tube in the zero Peclet number limit for Robin–Dirichlet wall boundary conditions.