Exploration of magnetically influenced flow dynamics of a dusty fluid induced by the ramped movement of a thermally active plate

The study of magnetically influenced flows in conjunction with non-Newtonian dusty fluids finds wide-ranging applications in minerals processing, environmental engineering, and biomedical sciences. These include, but are not limited to, wastewater management, soil remediation and groundwater treatment, removal of contaminants from water or soil, magnetic separation techniques, controlled and site-specific drug delivery, and biomedical diagnostic procedures. This research focuses on the dynamic behaviour of a conducting dusty fluid, modelled using the Casson framework, in the presence of a thermally active plate with ramped movement and the effects of a magnetic field. The model also incorporates several key physical phenomena, including thermal radiation, heat generation, and Newtonian heating wall conditions. To describe the time-dependent flow behaviour mathematically, partial differential equations are employed. Analytical solutions are derived using mathematical approach, notably the Laplace transform (LT). The results, including changes in flow profiles and various physical quantities due to various influencing factors, are depicted through graphs and tables, offering a clear visual representation of the findings. The research concludes that a higher thermal relaxation time parameter significantly improves thermal characteristics. Higher levels of particle concentration parameter correspond to slower fluid flow. Both the heat transfer rate and shearing stress on the plate exhibit temporal variations for a range of physical parameters. The particle concentration parameter has a notable impact on thermal transmission. The study’s findings may be applied in climate modelling, weather prediction, contaminant transport, and studying phenomena such as dust storms, air pollution, and dispersion of volcanic ash clouds.