EFFECT OF HEAT GENERATED BY A FRACTIONAL MAGNETIZE DUSTY FLUID FLOW MODEL IN A SLIT MICROCHANNEL

In this work, the effects of fractional time derivatives on the thermal and flow characteristics of an incompressible, magnetized dusty fluid in a vertical slit microchannel are examined. Temperature and velocity profile dynamics under different magnetic intensity, fractional order, and wall-slip conditions are investigated using both Caputo-Fabrizio (CF) and Atangana-Baleanu in Caputo (ABC) fractional models. The Laplace transform is used to solve the governing equations analytically, and the Riemann Sum Approximation (RSA) is used to invert the equations numerically. The findings indicate that fractional parameters and magnetic fields have a major effect on fluid velocity and heat transmission. In comparison to the CF model, the ABC model continuously displays smoother temperature and velocity profiles, indicating higher memory and damping effects. The study shows that skin friction and heat transfer rate are critically influenced by fractional order, magnetic parameters, and particle inertia. The results improve our knowledge of dusty MHD flows in microscale applications like industrial processing, medicinal devices, and energy systems. A study comparing the CF and ABC models of magnetized dusty flow in a slit microchannel with slip and volumetric heat generation has found consistent, quantifiable model differences. The ABC model predicts larger memory-induced damping, such as higher skin friction and lower Nusselt numbers, compared to the CF model.