Non-Boussinesq analysis of fully-developed mixed convection in an inclined rectangular duct

Mixed convection flow in an inclined rectangular duct is studied by releasing the Boussinesq approximation. The fully-developed regime with a parallel velocity is considered. The boundary conditions are such that two facing walls are adiabatic, while the other two facing walls are isothermal with different temperatures. Temperature-independent values of the dynamic viscosity, of the thermal conductivity and of the thermal expansion coefficient are assumed. The balance equations are solved analytically by employing double finite Fourier transforms. The friction factor, the dimensionless velocity distribution and the dimensionless pressure distribution in a duct cross-section are determined. Comparisons with the results available in the literature are performed either for the limiting case of Boussinesq flow or for the case of forced convection.