An extended similarity theory applied to heated flows in complex geometries

In the traditional similarity theory the influence of temperature- and pressure-dependent fluid properties on the flow field and heat transfer is not described by the basic dimensionless parameters, i.e. Prandtl, Reynolds, Rayleigh, . . . number. We present an extended similarity theory that not only takes into account the variable material properties but also can handle small variations in other parameters of the physical model like small changes in the (reference) Prandtl number. The method has general applicability that is suitable for a wide variety of fluid dynamic and heat transfer situations in which variable properties with a strong dependence on temperature and pressure play a significant role. It is especially useful in predicting the behaviour of a certain fluid based on the results for a different one. As an example the Nuelt number of a lid driven heated cavity is determined with fluid properties being temperature dependent.