Method of moments solution to ethylene glycol based

In this study, we present a comprehensive analysis of the laminar time-dependent magnetohydrodynamic (MHD) flow of ethylene glycol-based aluminum oxide nanofluid through a rectangular channel with contracting/expanding porous walls. We investigate the influence of aggregation/non-aggregation of nanoparticles, as well as the presence of thermal radiation. By imposing self-similarities in space and time, we obtain a system of nonlinear ordinary differential equations governing the flow. To solve these equations, we employ a well-known semi-analytical technique known as the Method of Moments (MoM). Additionally, we compare our results with the outcomes achieved through an application of another commonly utilized numerical approach (shooting technique with the Runge-Kutta-Fehlberg scheme). The comparison shows an excellent agreement that endorses the accuracy of the calculated solutions. The velocity and temperature profiles obtained from our analysis exhibit variations due to the changes in involved dimensionless parameters. We present these variations through graphical representations along with their explanations. Interestingly, our study reveals that the aggregation of nanoparticles influences the fluctuations caused by other parameters, and to some extent, suppresses them. Consequently, we observe less deviation among the velocity and temperature curves for the aggregation case compared to the non-aggregation case. These findings have significant implications in real-world engineering and industry. The understanding of the flow behavior of nanofluids through expanding/contracting rectangular channels can aid in the design and optimization of various engineering systems, such as heat exchangers and microfluidic devices. Additionally, our study provides valuable insights into the effects of nanoparticle aggregation and thermal radiation in such systems, offering opportunities for enhancing their efficiency and performance.