Azimuthally inhomogeneous thermal boundary conditions in turbulent forced convection pipe flow for low to medium Prandtl numbers

The effect of azimuthally inhomogeneous surface heat flux on thermal statistics of turbulent forced convection pipe flow is studied via direct numerical and large eddy simulations. Two Prandtl numbers of Pr=0.71 and Pr=0.025 are considered together with bulk Reynolds numbers of Re b =5300,11700,19000,37700. A zero temperature gradient condition is imposed on one half of the pipe's surface, while on the other either a constant or a sinusoidal heat flux distribution is imposed. The azimuthally averaged Nusselt number does not change with the different boundary conditions and is close to the one calculated with an appropriate correlation valid for uniform heat flux. Contrarily, the local Nusselt number depends on the wall thermal condition. The turbulent Prandtl number is anisotropic and strongly dependent on the radial location, especially for low Prandtl number fluids at low Reynolds numbers. For higher Reynolds numbers, the turbulent Prandtl number attains an isotropic state with a value of approximately 1 in the core region of the flow.