Parallel and non-parallel laminar mixed convection flow in an inclined tube: the effect of the boundary conditions

The necessary condition for the onset of parallel flow in the fully developed region of an inclined duct is applied to the case of a circular tube. Parallel flow in inclined ducts is an uncommon regime, since in most cases buoyancy tends to produce the onset of secondary flow. The present study shows how proper thermal boundary conditions may preserve parallel flow regime. Mixed convection flow is studied for a special non-axisymmetric thermal boundary condition that, with a proper choice of a switch parameter, may be compatible with parallel flow. More precisely, a circumferentially variable heat flux distribution is prescribed on the tube wall, expressed as a sinusoidal function of the azimuthal coordinate with period 2pi. A pi/2 rotation in the position of the maximum heat flux, achieved by setting the switch parameter, may allow or not the existence of parallel flow. Two cases are considered corresponding to parallel and non-parallel flow. In the first case, the governing balance equations allow a simple analytical solution. On the contrary, in the second case, the local balance equations are solved numerically by employing a finite element method.