The work presented in this thesis develops techniques, employing the Finite Volume discretisation method, which allow the numerical simulation of three dimensional heat transfer and fluid flow problems using unstructured meshes. The method solves and stores all variables at the element centres which lowers storage requirements and generally shortens run times compared with the Control Volume-Finite Element approach. Correction terms are formulated which address two of the main forms of errors caused by mesh skewness. To allow a generic handling of any unstructured mesh the Cartesian components of velocity are solved under all circumstances. This leads to the requirement to adjust the discretisation of the momentum equations when there is significant flow curvature. The changes are presented in this study both when the position of the flow axis is known prior to the simulation and when its position is known only as a result of the simulation, this being the case when there is more than one source of swirling flow. These original features contribute to a Computational Fluid Dynamics code which is capable of solving swirling, turbulent fluid flow and reactive, radiative heat transfer on highly complex geometries. Specifically the techniques are applied to the simulation of processes occurring in the direct smelting of iron. The use of the Finite Volume method makes it relatively easy to employ many techniques and physical models developed for structured codes. The evaluation of the face convective fluxes is effected through the Rhie - Chow interpolation method. The SIMPLE algorithm is used in the pressure - velocity coupling. In the simulation of swirling flows it is shown that both the standard and ReNormalisation Group k-e models fail to accurately predict turbulent effects. An anisotropic hybrid (k-e and mixing length) model is developed which produces excellent numerical results for the flows of interest. The Simple Chemical Reaction Scheme is used to evaluate the transport of the various chemical species. Radiation effects are simulated through the use of the radiosity model. A series of simulation results are presented which show the capabilities of the methods in test cases ranging from simple heat transfer problems through to the simulation of two swirling jets in a three dimensional unstructured mesh.