Transient fractional dusty fluid flow in a superhydrophobic microchannel

This study uses fractional derivatives in Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) forms to provide a thorough investigation of heat transfer and flow dynamics in superhydrophobic microchannels with dusty fluid under magnetohydrodynamic (MHD) effects. The precision and flexibility of the model to transient thermal systems are improved by the fractional derivatives, which take nonlocal memory effects into account. The governing equations for temperature and velocity profiles are solved under laminar, incompressible flow conditions using the Riemann sum approximation (RSA) for numerical inversion of Laplace transforms. The findings show that while the ABC model provides longer thermal retention, the CF model is more appropriate for situations needing rapid thermal stabilization. The results of the study demonstrate the important role that fractional parameters play in heat transfer and velocity behaviors, allowing for customized solutions for a range of engineering systems. Applications include energy-efficient designs, cooling systems, and thermal insulation in sectors that need accurate fluid and temperature management.