VELOCITY PROFILE MODELING FOR NON-ISOTHERMAL FLOWS INSIDE A CIRCULAR TUBE

Abstract

This research proposes a new method to establish the velocity field and the dimensionless velocity profile for Newtonian and non-Newtonian flows inside a circular tube. Several studies developed regarding different fluid types (such as potency law fluid, Bingham and Herschel-Bulkley, among others) observed that a rational or irrational polynomial was used for the dependent velocity field variable. Thus, a rational polynomial was established as a starting point for this research as the dependent velocity field variable. Dimensionless velocity profiles obtained from the proposed fluid-dynamics model were experimentally compared only with dimensionless velocity profiles for non-isothermal Newtonian flows of glycerol, in cooling as well as heating. On the other hand, it was possible to calculate that RMS errors found using relative dimensionless velocity data obtained from the proposed fluid-dynamics model creates very small errors, which are comparable to RMS errors found using data obtained from application of a numerical method. Finally, the proposed fluid-dynamics model was validated with a dimensionless velocity profile obtained from the flow of a cooling process, resulting in the validity of the proposed model.