Analysis of steady-state forced convective turbulent heat transfer in concentric annuli with arbitrarily varying boundary conditions of second kind

Turbulent flow heat transfer in concentric annuli is analyzed for the general three-dimensional case in which the wall heat flux varies arbitrarily in both the circumferential and axial directions. The assumptions are those of steady, incompressible, constant-property, fully developed flow of Newtonian fluids in smooth concentric circular annuli. Asymptotic expansions were developed to determine the higher eigenvalues and eigenfunctions. Solutions include the limiting cases with respect to channel geometry (circular tube, plane duct) as well as Reynolds-number (laminar flow, slug flow). Extensive comparison with experimental results is performed for the following boundary conditions: thermally fully developed situation (heat flux independent of axial direction) at circumferentially both constant and varying heat flux; and entrance heat transfer at circumferentially constant and axially both constant and varying heat flux. Agreement was found at both low and high Prandtl numbers. The effect of a spacially varying heat flux distribution on temperature distribution is demonstrated.