Galerkin finite element solution for electromagnetic radiative impact on viscid Williamson two-phase nanofluid flow via extendable surface

Williamson nanofluids (WNF) thermal and flow characteristics were explored in this study using Magnetohydrodynamics (MHD), porous medium, viscous dissipation, thermal radiative, Joule heating, Brownian, thermophoresis diffusion, and convective boundary constraints. To assess the performance of WNF, two different nanoparticles (Aluminum Alloys (AA7072) and Titanium Alloy (Ti6Al4V) are used, coupled with engine oil (EO) as a base fluid. Using a modified Buongiorno nanofluid model with entropy analysis, the mathematical flow modeling of the nanofluid could be completed. The influences of thermal radiation, Joule heating, and viscous dissipation are all considered in the determination of the heating phenomena. Using an exponentially similar parameter, the governing (PDEs) set of equations is translated into the suitable structure of ordinary differential equations (ODEs). The resultant ODE issue is numerically solved using the COMSOL software's Galerkin finite element approach. Graphically depicted are significant results in terms of many variables versus heat, frictional force, Nusselt number, and entropy generation. The work's notable finding is that, in opposed to previous liquids, the heat conductivity in Williamson phenomena progressively rises. The entropy of the system increases as the volume proportion of nanoparticles, thermal radiation, Weissenberg number, Biot number, and Reynolds number increase. The main finding is that aluminum alloys-engine oil based nanofluid is a better heat conductance than titanium alloys-engine oil nanofluid. Moreover, the temperature outline is improved to increase the estimates of the thermal Biot and Weissenberg numbers.