Existing solutions of the problem of axi-symmetric stagnation-point flow and heat transfer on either a cylinder or flat plate are for incompressible fluid. Here fluid with temperature dependent density is considered in the problem of axi-symmetric stagnation-point flow and heat transfer on a cylinder with constant heat flux. 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 introducing for the first time. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the solutions above are presented for Reynolds numbers, , ranging from 0.01 to 1000, selected values of compressibility factors, and different values of Prandtl numbers where is cylinder radius and is kinematic viscosity of the fluid. For all Reynolds numbers and surface heat flux, as compressibility factor increases both components of velocity field, heat transfer coefficient, and shear-stresses increase and pressure function decreases.

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