Caputo–Fabrizio fractional model on magnetite nanofluid flow with ethylene glycol through a vertical channel

Recent advances in nanotechnology and nanoscience have attracted considerable attention from researchers across various scientific and engineering disciplines. Magnetite–ethylene glycol nanofluids have potential applications in biomedical systems, including drug delivery, medical imaging, and hyperthermia, as well as in industrial applications such as lubrication systems, electric vehicles, bearings, mining machinery, wheel hubs, gearboxes, and construction equipment. In recent years, researchers have incorporated nanoparticles into conventional ethylene glycol to enhance its thermophysical properties and heat transfer performance. The present study investigates the flow characteristics of a Maxwell nanofluid consisting of magnetite nanoparticles suspended in ethylene glycol, with particular emphasis on flow through vertical ducts or channels. The governing equations are formulated using Caputo–Fabrizio time-fractional derivatives, thereby extending the classical partial differential equation model to a fractional framework capable of representing memory effects. The velocity, temperature, and concentration fields are obtained by employing finite Fourier sine and Laplace transform techniques. The resulting analytical solutions are examined graphically to elucidate the effects of the governing physical parameters. Furthermore, the skin-friction coefficient, Nusselt number, and Sherwood number are evaluated and presented in tabular form. The results indicate that the addition of magnetite nanoparticles to ethylene glycol enhances heat transfer by 20.09 % while reducing mass transfer by 2.68 %. Finally, the present results are validated through comparison with previously published findings, demonstrating good agreement.