A numerical scheme based upon a finite difference method combined with a boundary integral method is used to investigate the mixed convection heat transfer from a circular cylinder with a heated core region. Numerical results are given for radius r(c) = O.11, Prandtl numbers Pr = 0.72 and 5, Reynolds numbers Re less than or equal to 40, buoyancy parameters Gr/Re-2 less than or equal to 8 and thermal conductivity ratios lambda less than or equal to 400. The heat transfer and the how field has been found to be primarily affected by both the buoyancy forces and the thermal conductivity ratio, but also depending on the inclination angle alpha and on the Reynolds and Prandtl numbers.