Engineers desire to be able to predict natural convection flow and heat transfer in high Rayleigh number flows, such as those found in gas and steam turbines during shutdown. Numerical simulations are used in order to predict these natural convection flows. The simulations must have a relatively low computational cost which is why the bulk of engineering simulations are Reynolds Averaged Navier Stokes (RANS) simulations. In order to improve the predictions of natural convection heat transfer, new models for the turbulent heat flux have been implemented into a commercial solver. It was found that the newly implemented Generalised Gradient Diffusion Hypothesis (GGDH) and Algebraic Flux Model (AFM) were able to give improved predictions over the baseline model. The implemented models were then able to give predictions of wall heat transfer to within 20% of experimental values, making them suitable for engineering design calculations. A modification to the GGDH model was also developed, the GGDH+ model, in order to give improved predictions in regions with thermally stratified flow. The models were validated using data from a rig representative of a large industrial gas turbine during shutdown. Experimental data from the casing rig was complemented by Large Eddy Simulations (LES) of the rig, giving a larger validation dataset. A fundamental investigation into vortex flow structures that occurred in the rig was also conducted. The RANS simulations were also validated using literature experimental data which was again complemented by Direct Numerical Simulations (DNS) of the literature cases. An investigation was conducted into methods to control the natural convection flow and heat transfer inside of a gas turbine. The aim was to reduce the non-uniformity of heat transfer around the engine casing which would reduce casing distortion during shutdown. It was shown that flow extraction methods could improve the heat transfer distribution.