Thermoflow multiplicity in a cooled tube

Abstract

The coupling between the momentum and energy balances and the change of physical properties with temperature can give rise to situations in which the pressure drop vs. flow rate curve is nonmonotonic. This can lead to thermoflow multiplicity-the existence of different flow rates in a tube under the same overall pressure drop. A two-dimensional model is used to analyze the conditions leading to thermoflow multiplicity for an incompressible non-lrlewtonian fluid flowing in a cooled tube. First, the multiplicity features of various limiting models are determined. These results are later used to gain an understanding of the asymptotic multiplicity features of the general model. The results show that the temperature sensitivity of the viscosity necessary for thermoflow multiplicity to occur decreases with increasing Brinkman number or p (modified Stanton number), or with decreasing cooling temperature, Biot number, or power law parameter. Multiple flow rates for a prescribed pressure drop are unlikely to occur in heat exchangers in which the Brinkman numbers are usually low and Biot numbers are high but may be found in polymer processing applications.