Influence of magnetohydrodynamics and viscosity ratio on modified tetra-hybrid nanofluid flow under a threshold non-Fourier heat flux framework

This study examines the combined effects of magnetohydrodynamics (MHD), vis-cosity ratio, and thermal radiation on the flow and heat transfer of a water-based tetra-hybrid nanofluid containing Gold, Silver, Titanium dioxide, and Aluminium oxide nanoparticles over a stretching surface. The governing momentum and energy equations are reduced to ordinary differential equations via similar-ity transformations, and closed-form analytical solutions are obtained using Appell hypergeometric functions. Key parameters, including the viscosity ratio, nanoparticle volume fraction, and inverse Darcy number,are analysed and com-pared across di-, tri-, and tetra-hybrid nanofluids. The results show that stronger magnetic fields and higher nanoparticle loadings suppress the velocity field, while changes in the thermal parameters modify the temperature distribution and thermal boundary-layer thickness. Among the formulations considered, the di-hybrid nanofluid exhibits the largest normalized wall-temperature gradient, whereas the tetra-hybrid formulation exhibits higher temperature profiles under the parameter ranges studied.