In the present study, the potential of rectangular fins with a 30 degrees and 60 degrees angle and 10 mm offset from the horizontal direction perpendicular to flow for heat transfer enhancement in a plate fin heat exchanger is numerically evaluated with the use of a conjugated heat transfer approach. The rectangular fins are mounted on a flat plate channel. Numerical computations are performed by solving a steady, three-dimensional Navier-Stokes equation and an energy equation by using the Fluent software program. The study is carried out at Re=400 inlet temperatures, velocities of cold and hot air are fixed at 300 K, 600 K and 1.338 m/s, 0.69 m/s, respectively. The results show that heat transfer is increased by about 9 % at the exit of the channel with a fin angle of 60 degrees when compared to the channel without fins for parallel flow. The heat transfer enhancement with fins of 30 degrees and 60 degrees for different values of the Reynolds number with 300 and 800 and for varying fin heights, fin intervals and also temperature distributions on the hot and cold fluid sides of the channel outside surface are investigated in the parallel and counter flow arrangement.