EFFECT OF TIME-DEPENDENT TRANSPIRATION ON AXISYMMETRIC STAGNATION-POINT FLOW AND HEATTRANSFER OF A VISCOUS FLUID ON A MOVING CIRCULAR CYLINDER

Effect of time dependent normal transpiration on the problem of unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder moving simultaneously with time-depended angular and axial velocities and with time-dependent wall temperature or wall heat flux are investigated. The impinging free stream is steady with a strain rate . A reduction of Navier-Stokes equations and energy equation is obtained by use of appropriate transformations. The general semi-similar solutions are obtained when angular and axial velocities of the cylinder and also its wall temperature or its wall heat flux vary as certain functions of time. The cylinder may perform different types of motions. It may move or rotate with constant speed, with exponentially increasing/decreasing axial/angular velocity, with harmonically varying axial/angular speed, or with accelerating/decelerating oscillatory axial/angular speed. The cylinder surface temperature or its surface heat flux may have the same type of behavior as the cylinder motion. Semi-similar solutions of the unsteady Navier-Stokes and energy equations are obtained numerically using a finite-difference scheme. All the solutions above are presented for different Reynolds numbers ( ) and different functions of dimensionless transpiration rate,  , where  is cylinder radius and  is kinematic viscosity of the fluid. Shear stresses corresponding to all the cases increase with the increase of Reynolds number and decrease with the increase of suction rate. The maximum value of shear stress increases with increase of oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain angular/axial velocity function and at particular values of Reynolds number is azimuthally/axially stress-free. Heat transfer rate increases with the increase of the rate of suction, Reynolds number, and Prandtl number. Interesting means of heating and cooling processes of cylinder surface are obtained using different rate of transpiration.