Fully developed mixed convection flow in an inclined circular duct with non-axisymmetric boundary conditions

Laminar mixed convection flow in an inclined circular duct is analyzed in the fully developed region. Non-axisymmetric thermal boundary conditions of the third kind are considered, such that the wall heat flux has a vanishing circumferential average. More precisely, convection towards two environments with unequal temperatures is assumed for the two semicircular halves of the duct wall. The solution is determined numerically by employing a Galerkin finite element method. A check on the numerical results is performed by comparison with the analytical solution available in the special case of vertical duct (vanishing tilt angle). The numerical solution reveals that secondary flow arises whenever the tilt angle is non vanishing. This secondary flow displays a four cells pattern, each cell occupying one quadrant of the circular duct cross section. The special case of horizontal duct is also investigated.