HEAT-TRANSFER IN LAMINAR AND TURBULENT FLOWS IN THE THERMAL ENTRANCE REGION OF CONCENTRIC ANNULI - AXIAL HEAT-CONDUCTION EFFECTS IN THE FLUID

The present analytical study investigates the influence of axial heat conduction within the flow on the heat transfer in the thermal entranc e region of a concentric annular duct with laminar and turbulent inter nal flow. The solution is based on a decomposition of the elliptic ene rgy equation into a pair of first order partial differential equations . By using a new defined vector norm it is possible to obtain a selfad joint eigenvalue problem for the extended Graetz problem even though t he original convective diffusion operator is non-selfadjoint. The obta ined exact analytical solutions for the Graetz problem with axial heat conduction are as simple to compute as the related solutions of the p arabolic problem.