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.