The paper is aimed at studying fluid flow heat transfer in the axisymmetric boundary layer flow of a viscous incompressible fluid, along the axial direction of a vertical stationary isothermal cylinder in presence of uniform free stream with momentum slip. The equations governing the flow i.e. continuity, momentum and energy equation are transformed into non-similar boundary layer equations and are solved numerically employing asymptotic series method with Shanks transformation. The numerical scheme involves the Runge-Kutta fourth order scheme along with the shooting technique. The flow is analyzed for both assisting and opposing buoyancy and the effect of different parameters on fluid velocity, temperature distribution, heat transfer and shear stress parameters is presented graphically.