This paper presents a theoretical analysis of blood flow incorporating heat and mass transport, influenced by time-dependent magnetism and Casson fluid behavior. The study focuses on the intricate dynamics of unsteady, nonlinear partial differential equations (PDEs) governing blood flow. By employing similarity transformations, the governing nonlinear equations for motion, energy, and concentration are transformed into ordinary differential equations (ODEs). The solution process involves utilizing the Runge-Kutta Fehlberg method and a shooting procedure to solve the resulting ODE system. The study delves into the impact of various physical parameters, including Casson fluid behavior, permeability, Prandtl number, Hartmann number, thermal radiation parameter, chemical reaction parameter, and Schmidt number. These parameters are analyzed graphically with respect to flow variables, namely blood velocity within the vessel, blood temperature, and blood concentration. Key findings from the simulation study include a decrease in blood flow velocity with increasing magnetic and unsteadiness parameters. This research stands out by investigating unsteady blood flow within a slender, permeable vessel, accounting for the influence of time-dependent magnetism. The study's uniqueness lies in its exploration of two-dimensional, unsteady blood flow within a stretched vessel, a novel perspective that has not been previously elucidated.