Numerical analysis of tube arrangements with one, two, and four degrees of freedom for heat transfer with pseudoplastic fluids

Abstract

The association of the Constructal Design Method and Response Surface Methodology was used to investigate the best configuration of tube arrangements for heat transfer with pseudoplastic fluids, aiming to maximize heat transfer density. Systems consisting of a row of tubes and additional smaller tubes were analyzed. The problem consisted of three cases, characterized by one, two and four degrees of freedom. The effect of the sizes of the additional cylinders and the distances between cylinders were investigated. The systems were modeled and solved with Computational Fluid Dynamics (CFD). The power-law model was employed to predict the viscosity of Newtonian and pseudoplastic fluids. An open-source code was used to design the experiments by the Central Composite Design method and to adjust the Response Surfaces via polynomial regression. Considering both Newtonian and pseudoplastic fluids, the results showed that the heat transfer density was highly dependent on the distance between cylinders and that most pseudoplastic fluids had higher performance in terms of heat transfer density. The optimal configurations differed considerably for non-Newtonian fluids – as the pseudoplasticity increased, the geometry tended to be more packed, lower spacing and bigger cylinders. Adding degrees of freedom allowed the system to evolve to increase the heat transfer density, guaranteeing the best performance compared to simpler designs.