Exact solutions of double diffusive convection in cylindrical coordinates with Le = 1

The unsteady geometrical 2D governing equation set for the double diffusive convection—a very complicated nonlinear partial differential equation set with 4 variables—is solved analytically in the cylindrical coordinates. Two special exact solutions describing the convection in a cylindrical tube and a circular tube respectively are derived with an extraordinary method of separating variables and some other skills. The solutions are valuable for the development of heat and mass transfer theory. Moreover, as benchmark solutions, they are very useful for the computational heat and mass transfer to check the accuracy, convergence and effectiveness of various numerical computation methods.