Viscous dissipation effects on turbulent heat transfer in pipes with uniform wall heat flux

An analysis is made of the turbulent Graetz problem with viscous energy dissipation effects in pipes with uniform wall beat flux. The effects of viscous dissipation on fully developed Nusselt numbers are studied for fluids with Prandtl numbers 1, 10, 10², 10³ for Reynolds numbers between 5 × 10³ and 5 × 10⁵ with both cooling and heating conditions at the pipe wall. The viscous dissipation effects on convective turbulent heat transfer in arctic hot oil pipelines are discussed.