Analysis of laminar fully developed mixed convection in a vertical channel with opposing buoyancy

The problem of laminar fully developed mixed convection in a parallel plate channel is analyzed for the case where buoyancy opposes the flow. Complete, closed-form solutions for the velocity and wall heat transfer are obtained. In the paper, solutions to the fully developed flow energy equations are used to obtain the dimensionless velocity profiles in terms of the Grashof-to-Reynolds number ratio. Criteria for the onset of flow reversal are then developed. Expressions for the mean fluid temperature are developed and used to write wall Nusselt number relations.