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 free stream is steady and with a constant strain - rate . An exact solution of the Navier-Stokes equations and energy equation is 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 the solutions above are presented for Reynolds numbers, , ranging from 0.01 to 1000, selected values of compressibility factor, and different values of Prandtl numbers where is cylinder radius and is kinematic viscosity of the fluid. For all Reynolds numbers and surface temperature, as compressibility factor increases both components of velocity field, heat transfer coefficient, and shear-stresses increase and pressure function decreases.

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