Enhancing heat transfer in MHD Falkner's-Skan flow with thermal radiation, free convection and dusty fluid between parallel plates

Falkner's-Skan flows are one-dimensional flows widely used in fluid dynamics and boundary layer theory. They optimize heat exchangers and cooling systems, enhance turbine and compressor blades in turbomachinery, and provide consistency and quality in semiconductor fabrication. Additionally, they assist in pollution management and environmental impact assessments. The variety of Falkner's-Skan flows clarifies fluid flow phenomena and their practical applications. This article aims to explore the impact of surface temperature on the flow behavior of dusty fluid in Falkner's-Skan flow. The study focuses on the flow of dust particles in a channel formed by two infinite parallel plates. The study assumes that the particles are round and uniformly dispersed in the fluid. Furthermore, the article takes into account the effect of radiation on the energy equation. With the findings of this study, we hope to gain a better understanding of the dynamics of Falkner's-Skan flow and contribute to the development of effective strategies for managing the flow of dusty fluids. The right plate's movement at free stream velocity $U_e=a{x}^n$ causes the fluid to flow. Partial differential equations are used to represent the behavior of the flow. The Poincare-Light Hill Technique yields exact answers. Visual representations of the temperature and velocity curves show the effects of different factors. It is possible to create graphic pictures of the fluid and dust particles using Mathcad-15. Furthermore, critical fluid characteristics for engineers, such as skin friction and heat transfer rate, are analyzed and tabulated. These evaluations include the heat transfer rate at the wedge surface and the influence of this enhancement on surface viscous drag forces.