Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on a Cylinder

The steady-state, viscous, compressible flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite stationary cylinder with constant wall temperature are investigated. The impinging freestream is steady and with a constant strain rate (k) over bar. Exact solutions of the Navier-Stokes equations and energy equation are derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced for the first time. The general self-similar solution is obtained when the wall temperature of the cylinder is constant. All of the aforementioned solutions are presented for Reynolds numbers Re = (k) over bara(2)/2 nu ranging from 0.01 to 1000, selected values of compressibility factor, and different values of Prandll numbers where a is cylinder radius and nu is kinematic viscosity of the fluid. For all Reynolds numbers and surface temperatures, as the compressibility factor increases, both components of the velocity field, heat-transfer coefficient, and shear stresses increase, whereas the pressure function decreases.