THE EXISTENCE OF AN ASYMPTOTIC THERMALLY DEVELOPED REGION FOR LAMINARFORCED-CONVECTION IN A CIRCULAR DUCT

With reference to the stationary and laminar forced convection in a ci rcular duct for an incompressible Newtonian fluid having a fully devel oped velocity profile, previous studies on the existence of an asympto tic thermally developed region are improved. A sufficient condition, m uch broader than those previously found in the literature for the exis tence of an asymptotic thermally developed region, is determined. It i s proved that this condition is also necessary if one requires that th e asymptotic value of the Nusselt number is nonzero. A numerical compu tation of the temperature field in the thermal entrance region for two different wall heat flux distributions which Fulfil the sufficient co ndition for the existence of an asymptotic thermally developed region and which yield the same asymptotic value of the Nusselt number is per formed. Copyright (C) 1996 Elsevier Science Ltd.