Impact of chemical interactions and thermal emission on fractional MHD Casson flow through fractional derivatives

Abstract This study examines the magnetohydrodynamic (MHD) flow of Casson fluid over a vertical plate, accounting for the combined effects of Newtonian heating, internal heat generation, thermal radiation, and chemical reactions. The physical model is formulated through three key components: the momentum, energy, and concentration equations, incorporating Newtonian heating at the boundary. These equations are transformed into a dimensionless form using appropriate nondimensional parameters. The analysis employs the generalized Fourier's law and the Caputo–Fabrizio fractional derivative with a non‐singular kernel to capture memory effects in the system. Exact analytical solutions for velocity, temperature, and concentration are derived using the Laplace transform technique. The effects of various physical parameters on the fluid dynamics are visualized and analyzed through graphical results generated using MATLAB. The results indicate that temperature decreases with an increasing Prandtl number, while velocity enhances with larger thermal and solutal Grashof numbers. Moreover, higher values of the fractional parameter lead to increased temperatures, whereas concentration decreases with an increasing Schmidt number. The novelty of this work lies in its unified treatment of multiple interacting physical mechanisms using a non‐singular fractional calculus framework, which provides a more realistic and general description of practical MHD flows. This approach offers direct relevance to engineering applications such as polymer processing, biomedical fluid modeling, chemical reactor design, metallurgical operations, and MHD‐based energy systems, where precise control of heat and mass transfer in non‐Newtonian fluids is essential. This study has practical relevance to a range of engineering and industrial applications, such as thermal management in cooling systems, optimization of heat exchangers, chemical reactor control, and processes involving non‐Newtonian fluids. The combined influence of heat generation, radiation, and chemical reactions is especially relevant to polymer processing, biomedical flows (e.g., blood analogues), and metallurgical operations that require precise control over thermal and concentration fields, particularly in the context of the Caputo–Fabrizio derivative.