Analytic modeling of laminar forced convection in a circular duct for arbitrary boundary conditions and inlet temperature profile

Abstract

Although steady forced laminar convection in a circular duct is a classical problem in heat transfer, analytical solutions are only available in a quite limited set of boundary conditions. In this work, a general analytic solution is derived, which is valid for arbitrary wall boundary conditions as well as arbitrary inlet temperature profiles. Solution covers thermally developing as well as thermally fully developed domains, but is limited to hydrodynamically fully developed flow. As a result, the concept of thermally fully developed flow, hence thermal entrance length, had to be revisited. A new general definition is proposed here, which englobes classical definition and generalizes it to arbitrary boundary conditions. The new entrance length concept, which is of fundamental nature, is introduced for a rather general duct cross-section, although remaining analysis to obtain temperature field is presented for the circular cross-section only.