Numerical study of unsteady thin film flow and heat transfer of power-law tetra hybrid nanofluid with velocity slip over a stretching sheet using engine oil

Abstract This paper explores the effects of velocity slip and power-law nanofluid flow on tetrahybrid nanofluids across a stretching sheet. Tetrahybrid nanofluids, which combine four distinct nanoparticles Ag , $$SiO_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>i</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> , CuO , and ZnO with engine oil as the base fluid, are investigated for their potential to enhance thermal performance. Engine oil plays a critical role in reducing friction and wear in mechanical systems by forming a protective layer on components such as cylinders, pistons, and bearings. Using MATLAB’s , the study solves a set of ordinary differential equations derived from boundary layer equations, applying appropriate similarity transformations. It is observed that two unique velocity profiles intersect at a specific location, which shifts away from the stretching sheet as the velocity slip parameter increases. The findings indicate that tetrahybrid nanofluids offer superior heat transfer rates compared to standard nanofluids, showing improvements of 7.43, 6.27, and 5.35% over hybrid and tri-hybrid nanofluids, respectively. This study provides graphical representations of how various parameters, including the Prandtl number, power-law index, slip parameter, magnetic field parameter, and Reynolds number, affect temperature and velocity profiles. It is revealed that increasing the value of the solid volume fraction causes the tetrahybrid nanofluid velocity to decrease and its temperature to rise. The innovation of this work lies in its detailed examination of tetrahybrid nanofluids, extending beyond earlier research on simpler nanofluids and offering valuable insights for advanced thermal management solutions.