Treatment of Variable Physical Properties by Dimensional Analysis

Treatment of Variable Physical Properties by Dimensional Analysis 

When using dimensional analysis to tackle engineering problems, it is generally assumed that the physical properties of the material system remain unaltered in the course of the process. Relationships such as the heat transfer characteristic of a wire in an air stream (Example 2) or of a mixing vessel 

However, constancy of physical properties cannot be assumed in every physical process. A temperature field may well generate a viscosity field or even a density field in the material system treated. In non-Newtonian (pseudoplastic or viscoelastic) liquids, a shear rate can also produce a viscosity field. 

Although most physical properties (e.g., viscosity, density, heat conductivity and capacity, surface tension) must be regarded as variable, it is particularly the value of viscosity that can be varied by many orders of magnitude under certain process conditions. Besides this, it shows the highest temperature coefficients. In the following, dimensional analysis will be preferentially applied to describe the variability of this one physical property. However, the same approach can be adapted for any other physical property. 

The well-disposed reader will be surprised that this topic is given so much space in this book. An explanation is easy to give A complete similarity requires a geometrical, material and process-related similarity, but the material similarity often cannot be easily obtained. 

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VI. TREATMENT OF VARIABLE PHYSICAL PROPERTIES BY DIMENSIONAL ANALYSIS... 

I 8 Treatment of Variable Physical Properties by Dimensional Analysis... 

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