Some explicit analytical solutions of field synergy for steady 2D incompressible laminar flow in cylindrical coordinates

In this paper, several analytical solutions for the steady 2D incompressible laminar flow including the heat source, the mass flow source or no any sources in cylindrical coordinates are derived and analyzed based on the field synergy theory. The physical meanings of the solutions are discussed and explained, which are valuable to further develop the field synergy principle and understand how to improve or to weaken the field synergy in practice. The method of separating variables with addition and another extraordinary method are used to obtain analytical solutions in the process of derivation. Besides theoretical meaning, the solutions can serve as the benchmark problems for developing the numerical heat transfer.