The aerodynamic and thermodynamic performance of an aircraft gas turbine directly affects the fuel consumption of the engine and the life of the turbine components. Hence, it is important to be able to understand and predict the fluid flow and heat transfer in turbine blades to enable the modifications and improvements in the design process. The use of numerical experiments for the above purposes is becoming increasingly common. The present thesis is involved with the development of a flow solver for turbine flow and heat transfer computations. A 3-D Navier-Stokes code, the Moore Elliptic Flow Program (MEFP) is used to calculate steady flow and heat transfer in turbine rotor cascades. Successful calculations were performed on two different rotor profiles using a one-equation q-L transitional turbulence model. A series of programs was developed for the post-processing of the output from the flow solver. The calculations revealed details of the flow including boundary layer development, trailing edge shocks, flow transition and stagnation and peak heat transfer rates. The calculated pressure distributions, losses, transition ranges, boundary layer parameters and peak heat transfer rates to the blade are compared with the available experimental data. The comparisons indicate that the q-L transitional turbulence model is successful in predicting flows in transonic turbine blade rows. The results also indicate that the calculated loss levels are independent of the gridding used while the heat transfer rate predictions improve with finer grids. / Master of Science