Heat transfer in duct flow of non-Newtonian fluids with axial conduction

A special eigenfunction expansion is used to derive an exact solution for heat transfer in laminar flow of a non-Newtonian fluid inside a circular or parallel-plate duct, including axial heat conduction, where the wall is either maintained at a constant temperature or convects heat. The flow is hydrodynamically fully-developed and the velocity distribution may have an arbitrary dependence on the cross flow coordinate. The main features of the present solution are: the eigenfunctions are the same for a given geometry, independent of the velocity distribution; separation of variables of the seemingly non-separable governing partial differential equation; and any velocity distribution, complicated as it may be, is handled easily. The solution accuracy is validated against many published results. It is shown that, as expected, axial heat conduction is significant at the duct inlet. (C) 1998 Elsevier Science Ltd.