Numerical investigation of magnetohydrodynamic blood-based ternary and hybrid nanofluid flow over a bidirectionally stretching surface: thermal radiation, variable viscosity, and non-Darcy effects

The present investigation examines the combined effects of nonlinear thermal radiation, viscous dissipation, and temperature-dependent variable viscosity on the magnetohydrodynamic (MHD) convective heat and mass transfer characteristics of a blood-based ternary nanofluid (Cu–Au–Ag/Blood) flowing over a bidirectionally stretching surface embedded in a non-Darcy porous medium. The principal novelty of this study lies in the simultaneous incorporation of Cattaneo–Christov heat and mass flux relaxation, an exponential variable viscosity model validated for bio-nanofluid systems, and a Forchheimer-extended Darcy framework, which collectively distinguish the present formulation from antecedent investigations in the domain of ternary nanofluid transport. Governing nonlinear partial differential equations are transformed into a coupled system of nonlinear ordinary differential equations (ODEs) via an appropriate set of similarity variables, and the resulting system is numerically resolved employing the Galerkin-weighted residual finite element method (FEM) with quadratic Lagrange shape functions over a discretised domain of 10,000 elements with a convergence tolerance of 10 −6 . The numerical algorithm is validated against established benchmark data for skin-friction coefficients, yielding excellent agreement to five significant figures. Salient quantitative outcomes indicate that an increment in the variable viscosity parameter B from 0.2 to 0.6 engenders a 3.1 % enhancement in axial skin friction, a 4.7 % reduction in the Nusselt number, and a concurrent suppression of the secondary velocity component, attributable to the intensification of fluid viscosity with falling temperature gradients away from the wall. Augmentation of the Eckert number from 0.05 to 0.15 depresses the surface Nusselt number by approximately 4.1 %, reflecting irreversible viscous dissipation that retards interfacial thermal gradients. The ternary nanofluid (Cu–Au–Ag/Blood) consistently exhibits superior Nusselt and Sherwood numbers relative to the hybrid (Cu–Au/Blood) and mono-nanofluid (Cu/Blood) configurations, underscoring the thermophysical synergy of triple-nanoparticle loading. These findings offer quantitative design guidance for biomedical engineering applications encompassing magnetic drug targeting, hyperthermia-based oncological therapy, thermal regulation in blood-contacting microfluidic devices, and magnetically modulated nanoparticle-assisted perfusion systems.