Influence of Stefan blowing on the flow and heat transfer of non-Newtonian Jeffrey nanofluid over an unsteady stretching sheet

• Impact of Unsteadiness on Transport Properties : Increasing unsteadiness in the flow system significantly reduces heat transfer, mass transfer, and wall shear stress coefficients, underscoring its critical role in modulating transport phenomena. • Thermal Behavior Under External Influences : Fluid temperature rises with enhanced radiation, magnetic field strength, and porosity, highlighting the interplay of these parameters in dictating thermal dynamics in non-Newtonian nanofluids. • Jeffrey Parameter's Dual Effect : While higher Jeffrey fluid parameters suppress flow velocity, they concurrently elevate fluid temperature, emphasizing the inverse relationship between viscoelasticity and momentum/thermal profiles. • Practical Relevance for Cooling Systems : Insights into heat transfer optimization under Stefan blowing/suction and MHD effects offer valuable guidance for designing efficient cooling technologies in heat exchangers, solar collectors, and electronic devices. This study investigates the unsteady boundary layer flow and heat transfer of a non-Newtonian Jeffrey nanofluid over a stretching sheet with the influence of Stefan blowing or suction, magnetic field, thermal radiation and porous medium. The two-phase Buongiorno model is employed to account for nanoparticle effects, including Brownian motion and thermophoresis. The governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs) using similarity transformations and solved numerically using the fourth-order Runge-Kutta (RK-4) method combined with the shooting technique. The model provides insight into the physical behavior of nanofluids in porous media under time-dependent and magnetohydrodynamic (MHD) effects, which are critical for industrial applications such as heat exchangers, solar thermal collectors, and electronic cooling systems.