(untitled) (Contemporary Mathematics, 2025)
This study examines the unsteady free convection flow of Casson dusty fluid within an inclined microchannel under the influence of wall shear stress and an inclined magnetic field. The fluid is assumed to contain uniformly dispersed electrically conductive dust particles, and heat is applied via Newtonian heating at one boundary. The governing partial differential equations representing the motion of both fluid and dust phases are derived and solved using the Poincaré-Lighthill Perturbation Technique (PLPT). Key physical parameters such as the Casson fluid parameter, Grashof number, magnetic field inclination, radiation, and dusty fluid interaction parameter are varied to analyze their effect on velocity and temperature profiles. Results reveal that increasing the Casson parameter reduces fluid velocity, while higher Grashof numbers and radiation levels enhance it. The magnetic field generates Lorentz forces that oppose the motion, thereby reducing both fluid and dust particle velocities. The inclined magnetic field and Newtonian heating significantly influence thermal and flow behavior. These findings have practical implications in microfluidics, industrial coatings, biomedical flows, and heat management systems, where controlling dusty fluid dynamics under external fields is crucial.