The goal of this study is to determine how Joule heating, magnetic fields, and chemical reactions affect the flow of Maxwell nanofluid over a porous vertical stretching surface. This topic has several practical applications, such as cooling systems, polymer manufacture, and increased industrial efficiency. Heat treatment has several clinical applications, including improving drug delivery and treating cancer. Nanoparticles in the fluid achieve concentration by thermophoresis and move randomly via Brownian diffusion. The partial differential equations that govern flow and their accompanying boundary conditions can be transformed to non-dimensional form using appropriate similarity variables. The Runge-Kutta technique was used to solve transformed ordinary differential equations (ODEs). This shooting method converts the problem to an initial value problem (IVP), which the Runge-Kutta (RK) algorithm then utilizes to solve the boundary value problem. The results for numerous regulating flow factors are shown, and their implications on velocity, temperature, and concentration distributions are discussed. Drag factor, heat transfer coefficient, and mass transfer estimates are presented in a table format. The study's main findings show that increasing the Joule heating parameter improves concentration and temperature profiles while decreasing temperature distribution via an increase in the Prandtl value. The temperature profiles rise as the Lewis number, Brownian motion, and thermophoresis parameters increase. Concentration profiles decrease as the chemical reaction develops. There is remarkable agreement with previously published data.