Unfolding some numerical solutions for the magnetohydrodynamics Casson–Williamson nanofluid flow over a stretching surface

Abstract

Abstract This research focuses on exploring the significance of chemical reactions and thermal radiation on the magnetohydrodynamic (MHD) flow of a Casson–Williamson nanofluid (CWNF) over a stretching sheet. The objective is to comprehend how these factors influence the flow and heat transfer. A mathematical model, comprising partial differential equations adjusted into ordinary differential equations (ODEs) via utilizing some transformation. These ODEs are then tackled by MATLAB’s BVP4C method, which is part of the finite difference technique. Results are verified by comparison with existing literature and are depicted visually and in tabular format. Additionally, the study explores the effects of external factors such as magnetic fields and the Lewis number on parameters like Nusselt number, friction factor, and Sherwood number. Furthermore, heat generation in MHD CWNF is analyzed, along with a thorough evaluation of heat transfer near a stretching sheet with a permeable layer. The findings suggest that growing Brownian motion factor (Nb) and thermophoresis coefficient (Nt) enhance the rate of heat transfer, signifying improved heat transfer rates. Similarly, higher Nt values are associated with enhanced Sherwood numbers, indicating better mass transfer. Conversely, higher Nb values lead in lower local Sherwood numbers. Physically, an increase in Brownian motion causes significant displacement of nanofluid particles, boosting their kinetic energy and thereby enhancing heat generation within the boundary layer. It is noted that the Eckert number (Ec) reflects the impact of different Ec values on temperature distribution. As Ec increases, there is a proportional increase in fluid temperature due to frictional heating, which stores heat energy within the fluid. This effect becomes more pronounced for non-linear stretching surfaces, demonstrating the response of the thermal region to viscous dissipation. Viscous dissipation has the potential to enhance convective heat transfer, leading to amplified temperature distribution and thickening of the thermal layer.