Mixed convection in an unequally heated loop: steady solutions

We consider a one-dimensional mixed convection of liquid metal with forced circulation and unequal heating. The steady solution of the corresponding heat equation with proper boundary conditions is obtained analytically. The solution shows formation of a local circulation loop by unequal heating and deformation of the circulation loop by the forced circulation. It is also found that the heat transfer characteristics are almost independent of the unequal heating condition, although the deformation occurs more easily for a more symmetric case.