Two-phase Agrawal hybrid nanofluid flow for thermal and solutal transport fluxes induced by a permeable stretching/shrinking disk

Nanofluid is one of the modern heat transfer fluids that offer the potential to substantially enhance the heat transfer efficiency of conventional fluids. Extensive research has been undertaken to explore its fundamental thermophysical properties specifically viscosity and as well as thermal conductivity. This research emphasizes the significance of hybrid nanofluids and investigates the effect of Brownian motion and thermophoretic phenomena on the characteristics of the Agrawal flow that tends to a stagnation point adjacent to a moving porous disk. The model also accounts for the effects of Smoluchowski temperature and Maxwell velocity slip conditions. Through the utilization of similarity ansatz, the governing partial differential equations are simplified into a class of ordinary differential (similarity) equations. Subsequently, these simplified equations achieved numerical solutions by employing the bvp4c solver, which is specifically designed for fourth-ordered boundary value problems. The study delves into the remarkable impacts of the pertinent embedded parameters on key parameters such as mass transfer rate, heat transfer rate, and shear stress. These effects are brilliantly depicted through a combination of graphs and tables. Graphical analyses disclose the presence of dual solutions within a particular range of the stretching/shrinking parameter. Also, enhancing the solid volume fraction of nanoparticles leads to a notable rise in the shear stress and heat transfer for both solution branches, whereas the mass transfer rate experiences a reduction.