This thesis documents the application of a computer code developed by the author which makes possible the coupling of heat transfer between fluid and solid thermal models. The code was written using FORTRAN and couples the commercial computational fluid dynamics (CFD) software FLUENT with the Rolls-Royce finite element analysis program, SC03. The thermal modelling of a solid domain bounded by a fluid typically uses heat transfer correlations to define the heat flux at those boundaries. Considerable engineering judgement is required to appropriately select and apply these correlations, so that they accurately model the flow and geometry being considered. The objective of the coupling code is to replace the correlations with a CFD model of the fluid. The coupling is achieved by extracting metal temperatures determined from the finite element solver, using them to define CFD boundary conditions, and passing heat fluxes from the resulting CFD solution back to the finite element model. The finite element model then solves the newly defined problem and the process is repeated until a converged solution is obtained. The coupling code was evaluated through its application to two test cases. The first was an axisymmetric representation of a compressor stator well rig, the experimental apparatus or which comprised a two stage axial compressor, driven by a single stage axial turbine. The coupling code was used to model a temperature transient generated in the rig by injecting liquid nitrogen into the mainstream annulus, upstream of the compressor stages. For the second test case, an industrial application was chosen with real engine geometry. Using an axisymmetric finite element whole engine model of the Rolls-Royce Trent 500 aero-engine the code was employed to couple both axisymmetric and three dimensional representations of the fluid domain surrounding the pre-swirl system. Following the successful completion of these two test cases, the coupling code (now known as SC89) was production released by Rolls-Royce in July 2004 and is now available to their engineering community, as a design tool worldwide.