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Fractional modeling of heat and mass transfer in Maxwell ternary hybrid nanofluid flow with Dufour effect over an oscillating vertical plate

Muhammad RamzanDepartment of Mathematics, Bahauddin Zakariya University, Multan, PakistanIram HassanDepartment of Mathematics, Bahauddin Zakariya University, Multan, PakistanHakim AL GarallehZuhair JastaneyahDepartment of Mathematical Science, College of Engineering, Universty of Business and Technology, Jeddah, 21361, Saudi ArabiaIbrahim MahariqDepartment of Mathematics, Mutah University, Mutah, JordanA. Az ZobiMuhammadShahryarAbbasDepartment of Mechanical Engineering, university of Education, Lahore, PakistanMustafa BayramDepartment of Chemistry and Its Teaching Methods, Tashkent State Pedagogical University, Tashkent, UzbekistanDilsora AbduvalievaDepartment of Chemistry and Its Teaching Methods, Tashkent State Pedagogical University, Tashkent, Uzbekistan
2026en

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This study investigates unsteady magnetohydrodynamic free-convection heat and mass transfer in a Maxwell ternary hybrid nanofluid over an oscillating vertical plate. The fluid model incorporates heat generation, chemical reaction, diffusion-thermo (Dufour) effects, and magnetic field influences. The governing momentum, energy, and concentration equations are formulated in dimensional form and subsequently transformed into a dimensionless system using appropriate characteristic scales. To incorporate memory and hereditary effects in heat and mass transport, the classical Fourier and Fick constitutive laws are generalized through the Atangana-Baleanu fractional derivative, resulting in fractional heat and mass flux models. The influences of the fractional parameters, Dufour number, Grashof number, Prandtl number, Schmidt number, heat source parameter, chemical reaction parameter, and nanoparticle volume fractions on the velocity, temperature, and concentration distributions are examined graphically. In addition, the thermal performance of engine-oil- and water-based ternary hybrid nanofluids is compared using their thermophysical properties. The results demonstrate that the fractional model captures stronger memory effects than the corresponding classical model. Furthermore, the engine-oil-based ternary hybrid nanofluid exhibits superior heat-retention characteristics compared with the water-based ternary hybrid nanofluid under the considered conditions. These findings highlight the importance of fractional modeling in describing nonlocal transport phenomena and provide useful insights for advanced thermal management and energy-transfer applications involving electrically conducting non-Newtonian nanofluids.

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