The heat transfer coefficient is dependent on many factors such as fluid pressure, velocity, density, specific heat (ratio of specific heats if the fluid is compressible), viscosity & conductivity. It is also dependent on surface properties such as roughness & geometry. Due to the extreme non-linear nature of convection type phenomena, solutions are usually based on imperical relations such as log laws.

In order to implement convective heat transfer in FEA, boundary conditions for specific cases have been developed. Examples of which are Vertical Plate in horizontal flows, flow over isothermal inclined flat plates, flow through horizontal cylinders, flow over an inclined surface, vertical enclosed space flow, flow in horizontal tubes & ducts, generic convection as a function of temperature difference or grashof & prandtl numbers, flow along a rotating disk, etc.. Each boundary condition may have automatic implementation for each of the three flow types, laminar, transition & turbulent.

Non-Linear & Transient Analyses.

If temperatures are much higher or lower than the average temperature in certain locations of the model, there is a good chance that the heat transfer coefficients & conductivity will themselves become temperature dependent. The problem becomes non-linear, as the heat transfer rate is not directly proportional to temperature. The approach to a solution is similar to that of a non-linear displacement analysis, the load is divided into a number of smaller ones that are applied incrementally. The solution becomes an iterative procedure rather than one of matrix factorisation alone.

If the thermal load is impulsive in nature (time dependent), then a solution through time is required. This is carried out by dividing the overall time range into a number of smaller time steps & applying time integration techniques to handle the evaluation of the solution from one time step to the next. As with structural analyses, there are three main types of time integration techniques, Implicit, explicit & central difference (Crank-Nicholson). Implicit analyses are stable but computationally expensive, explicit integration is fast but unstable, and Crank-Nicholson is a mix of the two, but is also unstable.

Thermal - transient