Numerical Exploration of Magneto-Convection and Diffusion in Gravity-Influenced Jeffrey Fluid Flow With Suction/Injection Over a Stretching Sheet

Fluids composed of Jeffrey are collectively known as non-Newtonian fluids. Some of the application areas include electronic cooling, and designing along with optimizing of Magnetohydrodynamic pump and generator coupled with their heat transfer in different industrial processes. The aim of the present study is to investigate the gravity-driven unsteady magnetohydrodynamic transport of Jeffrey fluid over the stretching sheet. It deals with an electrically conducting fluid that is incompressible and has a uniform magnetic field that is applied perpendicular to the flow. The proposed physical context is represented by the partial differential equations covering boundary conditions. To solve the boundary value problem, the system of nonlinear equations is reduced to first-order form and efficiently solved using the Runge–Kutta based BVP4c technique in MATLAB. The graphical representations of velocity, temperature and concentration profiles are provided to illustrate their variations in response to changes in several parameters whereas the numerical computation of Nusselt number, shear stress and Sherwood number in reaction to different input parameters is shown in tabular form. The results of the study indicate that increasing the magnetic parameter M and chemical reaction rate K₁ significantly suppresses velocity due to enhanced Lorentz and resistive forces, while increasing the temperature and concentration profiles due to reduced convective and diffusive transport. The Jeffrey parameter ${\lambda }_1$ intensifies fluid retardation and heat accumulation. Higher values of Sc and Pr reduce concentration and temperature respectively due to lower diffusivity. The numerical results are validated by comparing limiting cases with existing benchmark solutions and show excellent agreement. The outcomes of this study are applicable to magnetically controlled thermal systems, non-Newtonian polymer processing, biomedical transport modeling, and high-performance electronic cooling, where precise control of flow, heat and mass transfer is critical.