Unsteady Casson Fluid Flow in a Superhydrophobic Microchannel in the Presence of Magnetic Field

Abstract

In this Study, fractional calculus is used to investigate unsteady MHD flow and heat transfer of a non-Newtonian Casson fluid in a superhydrophobic microchannel. Transient transport behavior is modeled using the Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives, taking into account magnetic field effects. The results may contribute to better fluid control, less friction, increased pumping efficiency, and optimized performance in medication delivery, industrial processing, microcooling systems, and biomedical microfluidics. The Laplace transform approach is used to solve the resultant equations, and the Riemann-sum approximation (RSA) is used to get numerical solutions in the time domain. The study examines the impact of the Casson parameter, magnetic field parameter, Prandtl number, and fractional-order parameter on velocity, temperature distributions, skin friction, and Nusselt number. Key findings include that increasing the magnetic field parameter reduces fluid motion due to the Lorentz force, while the Casson parameter enhances velocity distribution. A higher Prandtl number corresponds to lower temperature and velocity distributions. The ABC formulation yields slightly higher values for velocity and temperature compared to the CF formulation, and the Nusselt number increases with both the Prandtl number and fractional-order parameter, whereas skin-friction magnitude tends to decrease with stronger magnetic fields. These results highlight the significance of magnetic-field control and fractional modeling in describing transitory Casson fluid movement.