Stagnation slip flow of ternary hybrid nanofluid over an exponentially shrinking/Stretching sheet with joule heating, MHD, and thermal radiation effects

Abstract

The stagnation point flow of a ternary hybrid nanofluid (THNF) over a sheet that stretches or shrinks exponentially is investigated in this study. The primary goal is to assess the implication of Joule heating, magnetohydrodynamics (MHD), thermal radiation, and boundary slips on the physical quantities and flow profiles. Besides, attention is also given to the occurrences of multiple solutions in this fluid flow situation. The continuity, momentum and energy equations that described the fluid flow problem are converted into a simpler form of ordinary differential equations (ODEs). This is achieved by applying a similarity transformation, which make the equations easier to solve. Solving the resulting equations using the bvp4c solver in MATLAB software yields results that are analyzed and illustrated through a combination of tables and graphical representations. The analysis reveals that, for a shrinking sheet, an increase in Joule heating reduces the heat transfer. Similarly, a higher thermal slip factor leads to a decreased heat transfer rate in this case. In contrast, parameters such as magnetic field strength, radiation, velocity slip and suction contribute to enhancing the heat transfer rate of THNF. Furthermore, the results indicate that the THNF used in this study exhibits a better heat transfer rate compared to nanofluid (NF) and hybrid nanofluid (HNF). Notably, a shrinking sheet is observed to exhibit multiple solutions when the shrinking parameter falls within a defined range, specifically when $\lambda >{\lambda }_c$. By scrutinizing the analysis of stability, the first solution (upper solution) was determined to be consistently stable and applicable in real-world settings. These findings offer insightful information into the optimization of heat transfer processes in nanofluid-based systems under complex flow conditions. However, these findings apply only to a THNF mixture of alumina, copper, and titania. THNFs may have different flow dynamics and thermal properties depending on the mixtures of nanoparticles.