Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary conditions

•DNS of heat transfer in a turbulent pipe flow with non-homogeneous thermal boundary conditions.•The temperature statistics are characterized for Reτ=180Reτ=180, 360 and Pr=0.7Pr=0.7, 4.•Eddy diffusivities compared to the values predicted by simple models.•Simplified models provide reasonable predictions far from the wall.•Corrections to the models are needed near the pipe wall.

Direct numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.