One of the challenging problems in the plasma spray technique is reproducibility of the coating quality. This problem is mainly associated with arc behavior inside the torch, plasma-particles interaction and coating built-up that includes plasma-substrate interaction. To improve the understanding of the same, in this study, three-dimensional models are developed to simulate the plasma arc inside the torch and plasma-substrate interaction under various operating conditions. The effects of arc current and gas flow rate on characteristics of the arc and temperature and velocity distributions both inside and outside of the torch are explained. Using the nozzle exit profile predicted from the plasma arc model, the Ar-N2 plasma jet and conjugate heat transfer between the plasma and substrate are simulated by using plasma-substrate interaction model. The effects of arc current, gas flow rate, stand-off distance, substrate material and environment around the substrate on the temperature and velocity fields of the impinging plasma jet and thermal flux to the substrate are clarified. This model is validated by comparing the results of present model with previous predictions and measurements.