In the present study, the potential of rectangular fins with 30A degrees and 90A degrees angle and 10 mm offset from the horizontal direction for heat transfer enhancement in a plate fin heat exchanger is numerically evaluated with conjugated heat transfer approach. The rectangular fins are mounted on the flat plate channel. The numerical computations are performed by solving a steady, three-dimensional Navier-Stokes equation and an energy equation by using Fluent software program. Air is taken as working fluid. The study is carried out at Re = 400 and inlet temperatures, velocities of cold and hot air are fixed as 300, 600 K and 1.338, 0.69 m/s, respectively. Colburn factor j versus Re design data is presented by using Fluent. The results show that the heat transfer is increased by 10 % at the exit of channel with fin angle of 30A degrees when compared to channel without fin for counter flow. The heat transfer enhancement with fins of 30A degrees and 90A degrees for different values of Reynolds number with 300, 500 and 800 and for varying fin heights, fin intervals and also temperature distributions of fluids on the top and bottom surface of the channel are investigated for parallel and counter flow.