Combined forced and free flow in a vertical annular duct with circumferentially non uniform boundary conditions

The combined forced and free flow in a vertical annular duct is studied. The thermal boundary conditions are non–axisymmetric and such that no axial temperature change takes place. Fully–developed and steady–state laminar flow is considered and the Boussinesq approximation is invoked. The effect of viscous dissipation is neglected. The Fourier series expansion method is employed to obtain the analytical expressions of the dimensionless temperature field, of the dimensionless velocity field and of the Fanning friction factor. To illustrate the general solution, a sample case is described in detail: an annular duct such that the inner wall is half adiabatic and half with a uniform heat flux, while the outer wall is kept at a uniform temperature.