Forced convection in a circular duct with periodic boundary conditions and axial heat conduction

An investigation of the effect of axial heat conduction in the fluid on laminar forced convection is performed in a cylindrical duct with circular cross section. Two different kinds of boundary conditions are analyzed: (a) a wall temperature distribution which undergoes a sinusoidal axial variation; (b) a wall heat flux distribution which undergoes a sinusoidal axial variation and such that its mean value is equal to the modulus of the amplitude. Reference is made to the hydrodynamically and thermally developed region, where the temperature distribution is given in case (a) by an axially periodic function and in case (b) by the sum of an axially periodic function and a linear function of the axial coordinate. The temperature distribution within the fluid and the local and mean Nusselt number have been evaluated analytically.