Nonlinear Analysis for Non-Newtonian Nanofluid Flow over a Shrinking Plate with Convective Boundary Conditions

Significance: This study addresses critical industrial and biomedical applications including glass blowing (thermal management of shrinking sheets), polymer sheet extrusion (controlled cooling), magnetic drug delivery (nanoparticle targeting), and nuclear reactor cooling (enhanced heat transfer). Aim: We present a novel nonlinear analysis of magnetohydrodynamic (MHD) boundary layer flow of a Jeffery Al2O3 nanofluid over a shrinking permeable plate with convective boundary conditions, uniquely integrating mixed convection, Ohmic dissipation, heat generation, Brownian motion, and thermophoresis within a non-Newtonian nanofluid framework. Methodology: The governing partial differential equations are transformed using similarity transformations and solved via the Adomian decomposition method (ADM). Comprehensive validation against RK4, RK45, and bvp4c demonstrates excellent agreement with maximum relative errors below 5×10−4. Key Contribution: (i) Normal velocity decreases by 15–25% as the Biot number increases from Bi=0.4 to 0.6; (ii) tangential velocity decreases by 20–30% as the magnetic parameter increases from M=5 to 15; (iii) temperature increases by 30–40% as the Eckert number increases from Ec=0.5 to 2.5; (iv) ADM converges within 12–15 terms with L2 errors <10−5; (v) skin friction coefficient increases from Cf=3.02713 to 3.90082 as Q0 increases from 1 to 4; (vi) Nusselt number values: Nu/Re=0.4621 at Pr=0.7, 0.8954 at Pr=2, 3.2890 at Pr=20. These quantitative findings provide design guidelines for engineers in thermal management and biomedical applications.