Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux

The laminar forced convection in a circular duct is investigated in the case of a sinusoidal axial variation of the wall heat flux. The axial heat conduction in the fluid is neglected, while the effect of viscous dissipation is taken into account. The heat transfer in the thermally developed region, where the temperature is the sum of a linear function and a periodic function of the axial coordinate, is analysed. Both the temperature field and the local Nusselt number are evaluated analytically. Comparisons with the solution in the absence of viscous heating are performed. It is shown that the effect of viscous dissipation on the temperature field may be relevant especially in the case of a sinusoidal wall heat flux distribution with a vanishing mean value.