Mixed convection flow in a vertical channel with temperature dependent viscosity and flow reversal: An exact solution

An exact solution of steady fully developed mixed convection flow of viscous, incompressible fluid in a vertical channel having temperature dependent viscosity with asymmetric wall heating is obtained in this article. The Reynold model is used to capture the variation of viscosity as an exponential function of temperature and the governing equations are solved analytically. The solutions obtained are graphical represented and the effects of viscosity variation parameter, mixed convection parameter and wall temperature difference ratio on fluid velocity and skin-friction are investigated. In addition, the condition for occurrence of reverse flow at the channel walls is also established. During the course of numerical computation, it is found that an increase in viscosity variation parameter increases both fluid velocity as well as skin-friction at the heated wall. Furthermore,] the magnitude of flow reversal increases with increase in viscosity variation parameter around the cold region while the role of wall temperature difference ratio is to minimize the occurrence of reverse flow.