Local Similar Solution of Magnetized Hybrid Nanofluid Flow Due to Exponentially Stretching/Shrinking Sheet

The importance of thermal efficiency in major industrial and engineering sectors cannot be overstated. Numerous processes within these domains require substantial heat transfer, and conventional fluids often fall short in generating the necessary amount of heat for these operations. Recognizing this limitation, there arose a need to enhance the thermal conductivity of ordinary liquids. In response to this challenge, researchers and scientists proposed a groundbreaking idea: the introduction of metallic and non-metallic nano additives into the base fluid to improve its thermal effectiveness. This innovative approach gave rise to a new category of liquids known as hybrid nanofluids. In this article, we delve into the analysis of the 2D steady flow of SWCNT-Fe₃O₄/H₂O and MWCNT-Cu/H₂O-based hybrid nanofluid over a stretching and shrinking sheet, taking into account factors such as suction/injection and thermophysical impacts. The utilization of similarity variables enables the reduction of partial differential equations to a more manageable system of ordinary differential equations. To solve these transformed ordinary differential equations, a numerical technique, specifically the shooting algorithm with the bvp4c solver, is employed. The results are presented and elucidated through graphical representations, providing valuable insights into the behavior of the system under consideration.