Stokes flow and heat transfer past a circular cylinder in a square cavity with suction/injection on opposite-side walls

In this paper, we study laminar viscous fluid flow about a circular cylinder placed in a square cavity of uniform cross-section generated by applying injection/suction at the opposite-side walls. Constant temperature is maintained on the walls without suction and on the boundary of the cylinder and constant heat flux is maintained on the walls with suction. In the literature, the problems dealing with flow past a cylinder in a cavity are very a few. The fluid flow pattern in the form of stream lines and temperature distribution in the form of isothermal lines are studied. The flow is assumed to be Stokesian and hence the resulting coupled equations for stream function and vorticity, and the energy equation for temperature are solved numerically by using the standard 5-point formula. Fictitious nodes are introduced for derivative boundary conditions for stream function by using central-difference scheme and 3-point backward difference formula is used for derivative boundary conditions on temperature. It is observed that the temperature increases drastically when a cylinder is kept in the cavity, i.e. it makes the quick heat transfer. Similarly, when a cylinder is placed near to a corner, the heat transfer is more rapid. Suction enhances the heat transfer.