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The heat-transfer problems of combined free and forced convection by a fully developed laminar flow in a vertical channel of constant axial wall temperature gradient with or without heat generations are approached by a new method. By introducing a complex function which is directly related to the velocity and temperature fields, the coupled momentum and energy equations are readily combinable to a Helmholtz wave equation in the complex domain. This greatly reduces the complexities of the problems. For illustrations, the cases of flows between parallel plates and in a rectangular channel are treated. It shows that this method is more direct and powerful than those of previous investigations.
Longbin Tao (Mon,) studied this question.