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The unsteady, viscous flow and mixed convection heat transfer of an incompressible fluid within a vertical concentric cylindrical annulus with time-dependent moving walls are investigated. Fluid is suctioned/injected through the cylinders' walls. Role of movement of the walls on flow and heat transfer inside the vertical annulus is sought. An exact solution of the Navier-Stokes and energy equations is obtained in this problem, for the first time. Here, the transfer of heat is from the hot cylinder walls with constant temperature to the cooler moving fluid. It is interesting to note that the results indicate that the time-dependency of the cylinder walls movement has no effect on the temperature profile. The results also indicate that, compared to other time functions, usage of inverse of time for velocity movement causes significant increase in velocity, stress tensor, and Nusselt number in the vicinity of the moving wall. Also, increasing the mixed convection and suction/injection parameters would increase the Nusselt number and decrease the stress tensor on the inner and outer cylinders no matter what the velocity function is chosen. Therefore, the flow and heat transfer is controllable using the velocity function of the wall movement and change of the other non-dimensional parameters.

Role of movement of the walls with time-dependent velocity on flow and mixed convection in vertical cylindrical annulus with suction / injection