The present work presents a numerical solution of combined convective and radiation heat transfer from a vertical rectangular air-cooled aluminum fin. There are three governing equations (Continuity, Momentum and Energy equation) are solved numerically by using (TDMA) for fluid and the fin. Heat transfer by both mixed convection and radiation is considered. Mixed convection effect should be appreciable for low speed air flow over the fin. Radiation heat transfer mode is important for large temperature difference between the fin and the surrounding as well as for high emissivity fin material and low speed air-flow. Conjugate heat transfer should be taken into account as it gives rise to non-uniform heat transfer coefficient the consideration of which is more realistic in contrast with the assumption of uniform heat transfer coefficient in conventional fin theory. Results shown at constant of Re with large value for CCP means increased convective cooling and the fin requires shorter time to attain steady stat temperature.
