Tetra-hybrid nanofluids are appealing for next-generation thermal systems because they have better thermophysical characteristics than mono- or binary nanofluids. This study examines the unsteady magnetohydrodynamic (MHD) flow and heat transfer properties of a Carreau tetra-hybrid nanofluid across an inclined stretching surface. The fluid contains Au, \(\hbox {Al}_2 \hbox {O}_3\) , Ag, and \(\hbox {TiO}_2\) nanoparticles in a CMC-water base fluid. Non-Fourier heat transfer is captured using the Christov heat flux model, and thermodynamic efficiency is evaluated by entropy production. MATLAB’s bvp5c is used to solve the governing vector momentum and energy equations numerically after they have been modified using similarity variables. Simulations were performed over realistic parameter intervals, with the unsteadiness factor varied between 0.1 and 0.5, the elastic Weissenberg number from 0.5 to 2.0, magnetic field strength between 1 and 5, Brinkman number from 0.1 to 0.5, Biot number from 0.2 to 1.0, inclination angle from 0 \(^\circ\) to 60 \(^\circ\) , and thermal relaxation time between 0.1 and 0.5. The results indicate that an increase in magnetic field strength diminishes velocity while raising temperature owing to Joule heating; a bigger We enhances elastic stretching in the flow; and Br amplifies entropy generation. The local Nusselt number escalates with M and \(\gamma _{{\text{T}}}\) . Tetra-hybrid nanofluids exhibit superior heat transfer performance compared to ternary counterparts, highlighting their potential for next-generation thermal management systems.
