Pi-space and Requirements Concerning the Model Material System

Pi-space and Requirements Concerning the Model Material System 

We will start by discussing a pi-space in which an optional process in an apparatus of a given geometry takes place and where the hydrodynamics is coupled with a steady-state heat transfer [35]. The target pi-number will be laid down later on (Example 17). In case temperature independent materials take part, the process will be described by the following possible process-related and material pi-numbers  

The Brinkman number, Br, is only relevant if the transformation of the mechanical energy into heat is important. All material properties are related to the characteristic temperature T0. 

If the problem is restricted to the creeping flow, the mass inertia (p) will not play a role. In this case, p must be combined with the quantities Cp 0 and g to give pCp 0 and pg. Consequently, the above pi-framework is reduced by one pi-number  

However, if viscosity is temperature dependent, this has to be taken into account by an appropriate enlargement of the pi-space  

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