Analysis of Magnetized Free Convective Flow of Casson-Type Fluid Over A Vertical Plate: A Caputo–Fabrizio Fractional Model Approach

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The purpose of this investigation is to examine the impacts of fractional calculus on fluid dynamics and heat transfer of a nanofluid in drilling applications. More specifically, the study explores how free convection and electrical conductivity impact clay nanoparticles dispersed in engine oil—which is modeled as a Casson fluid—as they pass over a flat vertical plate. The key objectives are to: (1) determine the effects of memory effects at different timescales on temperature and momentum profiles via the Caputo–Fabrizio fractional derivative; and (2) analyze the consequences of varying different physical parameters such as magnetic field, Grashof number, nanoparticle volume fraction and Prandtl number. The objective of the investigation is to provide insight into controlling these parameters to optimize drilling processes. The Laplace method is applied to find solutions to the governing equations, and MathCad15 is utilized for illustrating the physical results. The results expose that the temperature and momentum fields are enhanced (at large times) when the fractional parameter is increased and both profiles show opposite behavior at small times. The heat transmission is enlarged with growing estimations of the volume fraction for clay nanoparticles, whereas the momentum field is declined by growing estimations of the volume fraction of nanoparticles. Further, the nanofluid motion declines by growing the magnetic field but accelerates by increasing the Grashof number. Further, this model has applications in engineering to optimize drilling operations, where performance and efficiency in refining depend upon controlling fluid flow and heat transmission. It can also be applied in fields where nanofluids are utilized to enhance heat transfer and fluid dynamics, such as petrochemicals, manufacturing and material engineering. Overall, this study establishes a vigorous foundation for further research and delivers a structure for exploring non-Newtonian NF systems from the perspective of magnetized-driven free convection flow.