Dimensionless pressure drop number for non-newtonian fluids applied to Constructal Design of heat exchangers

This paper introduces a dimensionless group for pressure drop, named Bejan number (Be), to be used with non-Newtonian fluids. When defining Be for non-Newtonian fluids, it is necessary to choose a characteristic apparent viscosity to compose this dimensionless group. In non-Newtonian fluid dynamics, the viscosity at a characteristic shear rate is usually chosen as reference, with the latter given as the reference velocity divided by the reference length. When the flow rate is not known, a reference velocity may be taken as the square root of the pressure drop divided by the mass density. Thus, a characteristic apparent viscosity may be defined for any non-Newtonian model, even for one that does not present a characteristic viscosity defined explicitly in the viscosity function, such as the power-law model. The non-dimensionalization of motion equations for the crossflow of a power-law fluid between two aligned cylinders was performed using this philosophy. Some numerical tests were performed to corroborate the idea that the introduced form for Be is a good alternative to be used in experiments to predict and evaluate the heat transfer density in the context of Constructal Design of heat exchangers tube bundles. (C) 2017 Elsevier Ltd. All rights reserved.