THERMAL ENTRANCE REGION FOR LAMINAR FORCED-CONVECTION IN A CIRCULAR TUBE WITH A POWER-LAW WALL HEAT-FLUX

Laminar forced convection in a circular tube is investigated with a bo undary condition of prescribed axially varying wall heat flux, under t he assumptions of hydrodynamically developed flow and of negligible ax ial conduction and viscous dissipation in the fluid. A condition on th e asymptotic behaviour of the axial distribution of wall heat flux is established which is fulfilled by power-law varying axial distribution s and which guarantees the existence of a thermally developed regime. It is proved that for all the axial distributions which fulfil this co ndition the asymptotic value reached by the local Nusselt number is 48 /11, i.e. the same which holds for a uniform wall heat Aux. For some p ower-law varying axial distributions of wall heat flux, a finite diffe rence determination of the thermal entrance region is performed. In ev ery numerical solution, the local Nusselt number tends asymptotically to 48/11.