Abstract
I have obtained the similarity between oil cooling-pipe and oil heating-pipe, where the oil flows in a stream-line flow and its viscosity changes by temperature only and the other physical properties are constant. As a relation of viscosity and temperature, I have applied the Vogel's equation (29). I have reduced the similarity of (32) from the foundamental equations, by dimensional analysis, where θm is dimensionless mean temperature of issued oil and Wc/kN is Graetz number and s'is a dimensionless groupe which are defined by (34), and tv is a proper temperature of oil. As general liquids, these viscosities are not so large, always we can take -273 instead of tv. Then Vogel's equation becomes Andrade's equation (2) and s'becomes s (24) and similarity is (26). When change of viscosity is taken into consideration, θm is not only affected by Graetz number, but affected by dimensionless quantity s'.
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