In this study, a modified Sisko fluid with Buongiorno model effects over a curved surface was considered. The MHD was applied normally to the flow direction, and the effects of chemical reacted and active energy at the curved surface is also discussed. We chose this pertinent non-Newtonian fluid model since it best represents blood composition, and thus helps us venture into complex blood flow problems. Since the flow is discharged over a curved shape, we therefore commissioned curvilinear coordinates to best portray our envisaged problem. We were also required to define various sundry parameters to make our mathematical equations easily solvable. Mathematical modelling was completed by considering traditional assumptions, including boundary layer approximation. Numerical simulation was conducted using MATLAB solver bvp4c. Several numerical tests were conducted to select the best blend of the linked parameters. We noticed thermal flux upsurged when the chemical reaction parameter was increased with the magnetic indicator parameter caused the flow to slow down, while an increasing amount of activation energy enhanced the concentration of the fluid. The numerical results and impacts of assorted parameters on different profiles are elaborated with the help of graphs and a table.