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), viscosity 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 similarity 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 compared 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.