We study the dependence of low field mobility on various parameters such as well width and interface roughness for a two-dimensional electron gas confined to a AlGaN/GaN quantum well as a function of temperature. The potential profile, the energy levels, electron concentrations and wave functions for each level are found from the self-consistent numerical solution of Schrodinger and Poisson equations for the quantum well. Then the scattering rates for electrons due to acoustic phonons, optical phonons and interface roughness are obtained using the self consistently calculated wave functions. Ensemble Monte Carlo technique is used to find the drift velocities of the two-dimensional electrons along the interface. The mobility of two-dimensional electrons is extracted from these data. Electron transport properties of bulk GaN is also studied in order to compare the two and three-dimensional mobility values. It is seen that electron mobilities upto 40 x 10(3) cm/Vs can be obtained in a 2DEG confined to an AlGaN/GaN hetero interface. The results of simulation are compared with experimental findings and it is seen that the agreement between simulation and experiments in two dimensions is very satisfactory.