Constructal Design of tube arrangements for heat transfer to non-Newtonian fluids

Abstract

Non-Newtonian fluids, because of their complex rheology, behave quite differently from Newtonian fluids in flows and heat transfer. Pseudoplastic fluids suffer viscosity reduction in shear flows, which considerably affects convection heat transfer in heat exchangers. In the present work, we focus on searching for optimal spacing between two aligned tubes of elliptical cross-section subjected to forced heat convection from shear thinning (pseudoplastic) fluids. We employed Constructal Design Method to search numerically for best system configurations. The performance indicator here adopted was the maximum heat transfer density for a fixed total volume and a fixed pressure drop, i.e., the heat transfer density for a fixed Bejan number (Be). We relied on Constructal Design associated with Design of Experiments and Response Surface methodologies, using numerical results obtained with a finite volume method code. Thus, the effect of the power-law index, n, ranging from 0.4 to 1, on optimal geometries (obtained for Be = 105 and Pr = 1) has been investigated. The optimal geometries differ much from those found in literature for Newtonian fluids: a great enhancement in heat transfer with the decrease of n has been highlighted, confirming that shear thinning is a key parameter for heat transfer increase using non-Newtonian fluids. The maximum heat transfer density proved to be strongly dependent on the power-law index. The heat transfer density was higher for more shear thinning fluids. We observed that the optimal aspect ratio increases as n increases, suggesting that, for non-Newtonian fluids, the tubes should be more slender for better heat transfer performance. In the meantime, the global optimal distance was the same for all values of the power-law index.