The aim of this paper is to present non-similar solutions of a steady laminar compressible boundary layer flow past a long thin circular cylinder including the effects of wall enthalpy and surface mass transfer. The governing equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then the resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. The increase in the value of power law variation of viscosity causes an increase in the boundary layer thicknesses of both the velocity and enthalpy profiles. Skin friction as well as heat transfer at the wall increases with suction and decreases with injection. The increase in viscous dissipation causes an increase in skin friction and decrease in heat transfer at the wall.