A modern gas turbine must be designed quicker, be more reliable, produce less emissions than its predecessors and yet the engine manufacturer must still make a profit. In order to sell their engines to the airlines, the manufacturer must show that their engines meet strict safety and reliability requirements. The creation of finite element models used for predicting temperatures and displacements of the engine component's is part of this design cycle. This thesis addresses the use of computational fluid dynamics (CFD) as a tool that can help in the prediction of iiietal temperatures for use with "industrial" problems and the associated requirements of accuracy and time-scales. The definition of 'industrial" accuracy and time-scales in this thesis is the accuracy required to enhance the modelling capability of a thermal engineer in design time-scales. A method is developed for using a commercial CFD code. FLUENT, for predicting flow and heat transfer. The code has been validated against several benchmark test cases and has shown good predictive capability and mesh independence for flow and heat transfer in the cavity between a rotating and stationary disc with and without through-flow. For cavities between co-rotating discs with radial througliflow, the predictions are acceptable, but some sensitivity of the heat transfer results to mesh spacing has been identified. The code has also been validated against some "industrial" test cases where experimental data has been available. The effects of buoyancy in the centrifugal force field are discussed and are related to a buoyancy number. The next part of the thesis develops a method of solving the heat transfer problem by coupling a finite element code, SC03, with FLUENT. The ideas are developed on two simple test cases and the problems of what information is to be passed across the coupling boundary and convergence issues are discussed. The results show that passing heat transfer coefficients and local air temperatures achieves the best convergence. The coupled method is their tested against two 'industrial problems. It is concluded that the method has considerable potential for use in design although some difficulties in applying the method are identified. Although not demonstrated, the method developed is not specific to SC03 or FLUENT and ally heat traiisfer/ CFD codes could be used.