The multizone model described in the previous section provides a solution for the radiation component of the overall furnace heat transfer problem. However, some additional means must be provided to obtain the other components in the heat balance, such as convection and heat generation due to combustion and the influence of mixing between the fuel, oxidant and combustion products. These may be calculated by solving the equations governing conservation of mass, momentum, chemical species, and energy in a turbulent, chemically reacting flow. The task of solving the coupled governing conservation equations is formidable. Fortunately, there are a number of commercially available programmes now available to carry out these Computational Fluid Dynamic (CFD) calculations. These programmes apply advanced numerical solution techniques to solve the governing partial differential equations. With advances in processing speed and memory, these programmes can now be run on reasonably low cost computers. These models are becoming increasingly useful, especially for predicting flame shape, the formation, emission and control of oxides of nitrogen, and for predicting temperature uniformity in critical applications such as metal heat treatment. They are applied to gas, liquid and solid fuel combustion problems.

The time necessary to solve an industrial problem is dependent on the level of complexity and accuracy required. If the problem can be simplified and the flow assumed to be two-dimensional, then a CFD analysis can be as short as one day. However, the times required for problem definition and machine computation significantly increases with complexity.

The geometry is discretised into a fine grid structure (finite volumes) with sometimes as many as a million intersecting grid points. The partial differential equations are solved for each point. Good grid generation is essential to minimise the risk of numerical errors and to ensure predictive quality. The user should repeat the simulations using a finer discretisation, to ensure that the predicted results are grid independent.

The extent of model evaluation by comparison of predictions with measurements remains limited with too few comparisons for full-scale combustion chambers.

Despite the difficulties and complexities of the problem, the development of models for combustion and heat transfer engineering applications has advanced significantly in recent years with the introduction of: