One most common K-Σ model is used for study of the turbulence in the off-set jet problem. Finite Volume based SIMPLE algorithm is used for solving the discretized equations and power-law scheme is used for discretizing the convection terms The flow and heat transfer characteristics in the wall jet cooling that had already been done experimentally, is also shown. The regions of study are the recirculating zone, impingement and developing wall jet zones. Thermal characteristic of each zone is studied. The numerical results are compared with the experimental results. Computational details of various mean flow and turbulent parameters are presented and described for different offset ratios. The results include reattachment length, velocity profile, the axial velocity decay curve and wall static pressure distribution. The spatial distributions of turbulent intensities show a high turbulent recirculating flow between the jet and the off-set plate. The results obtained are satisfactory with the experimental results.