Numerical Solution of N-S Equations in the case of Unsteady Axisymmetric Stagnation-point Flow on a Vertical Circular Cylinder with Mixed Convection Heat Transfer

Abstract

The unsteady problem of impulsive stagnation-point flow on a vertical circular cylinder along with mixed convection heat transfer is solved numerically for the first time. This is because of limitations of similarity solution techniques when we encounter various physical conditions such as time-dependent states. Initially, the fluid is considered to be at rest and with a uniform temperature . At t=0 this fluid starts flowing toward a vertical cylinder at the strength rate of and the cylinder surface's temperature rises to Tw, simultaneously. The Navier-Stokes and energy equations in cylindrical coordinate system have been descritized and solved in a 2-D domain by using a SIMPLE based algorithm. The solution has been obtained in three cases. Firstly, when cylinder's wall temperature Tw is constant. Secondly, when Tw varies linearly along cylinder's axis. And thirdly, when it has parabolic variations. Considering a sample case of incompressible flow with Re=1 and , the results of Nusselt number, wall shear- stress and dimensionless velocity and temperature have been obtained at different states of cylinder's wall temperature and for some selected values of Grashof numbers. An entropy generation analysis for the case of constant wall temperature is performed which is also for the first time in this subject.