Optimizing a ternary hybrid ferrofluid slip flow with magnetic dipole and viscous dissipation by Response Surface Methodology (RSM)

Abstract

In electromagnetism, a magnetic dipole is a tiny loop of electric current or a pair of magnetic poles. As the loop size decreases to zero while maintaining a constant magnetic moment, it forms a magnetic dipole. Composed by the magnetic particles, ferromagnetic fluids align with magnetic fields and when a magnetic dipole interacts with such fluids, the particles magnetize the fluid and influence the dipole’s field. Hence, this study investigates the magnetic dipole and velocity slip on ternary hybrid ferrofluid flow past a shrinking surface. The model considers three magnetic nanoparticles – iron oxide (Fe₃O₄), cobalt ferrite (CoFe₂O₄), and copper (Cu) – dispersed in a base fluid. The similarity transformation technique is applied to derive mathematical models, which were solved numerically using bvp4c program in MATLAB. The analysis reveals that ferrohydrodynamic interaction reduces the skin friction coefficient and heat transfer rate but enhances velocity and temperature profiles. Additionally, the ternary hybrid ferrofluid is also shown to outperform both conventional ferrofluid and hybrid ferrofluid in fluid flow characteristics. Response Surface Methodology (RSM) is employed to identify the optimal combination of parameters, suggesting that the highest ferrohydrodynamic parameter and viscous dissipation, along with minimal Cu-nanoparticle concentration, maximize the heat transfer rate. Contour and surface plots illustrate these optimal conditions. This study highlights an innovative application of ternary ferrofluid with a magnetic dipole and employs RSM to optimize parameters for enhanced heat transfer performance, addressing a gap in existing literature and providing the way for further advancements in this field.