On the choice of the reference temperature for fully-developed mixed convection in a vertical channel

The effect of the choice of the reference fluid temperature on the solutions of fully-developed mixed-convection problems in a plane vertical channel is studied. First, the boundary conditions of either uniform wall temperatures or a uniform temperature at a wall and a uniform heat flux on the opposite wall are considered. It is shown that, in these cases, the choice of the reference temperature affects both the velocity profiles and the axial change of the difference between the pressure and the hydrostatic pressure. A general method to choose the reference fluid temperature for the fully developed mixed convection in ducts is proposed. Finally, an analytical solution for the boundary condition of uniform wall heat fluxes is obtained by choosing the mean fluid temperature in each cross section as the local reference temperature.