MHD flow of dissipative ternary nanofluid past a stretching/shrinking sheet: RSM analysis

S. S. Sahranbana¹ - S. N. A. M. Izam¹ - N. S. Anuar¹ - N. A. L. Aladdin²

¹ School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
² Department of Mathematics, Centre for Foundation Defense Studies, Universiti Pertahanan Nasional Malaysia, 57000 Kuala Lumpur, Malaysia

Abstract
Magnetohydrodynamic flow of a dissipative ternary nanofluid over a stretched/ shrinkable sheet was investigated. In a base fluid (water), ternary nanoparticles, silicon dioxide (SiO₂), aluminium oxide (Al₂O₃), and titanium dioxide (TiO₂) were equally dispersed. The governing equations of the ternary nanofluid were simplified by a similarity transformation, resulting in ordinary differential equations. The equations were resolved numerically with the bvp4c function in MATLAB. The validation tests and numerical findings for the local skin friction and local Nusselt number, as well as the velocity and temperature profiles, were visually shown. Optimization was conducted with response surface methodology based on central composite factorial design. Quadratic regression is employed to analyse the data. The findings demonstrate that the local skin friction and the Nusselt number are significantly influenced by several parameters, including the Eckert number, the stretching/shrinking parameter, the nanoparticle volume fraction, and the magnetic field. The Nusselt number shows an increase with the Eckert number, whereas it exhibits an inverse relationship with the nanoparticle volume fraction and magnetic field. The research has also revealed that the incorporation of nanoparticles and an enhancement of the magnetic field lead to a broader range of solutions. The results demonstrate that the stretching/shrinking parameter influences the occurrence of dual solutions. Specifically, the shrinking parameter results in the existence of dual solutions instead of a single solution. Furthermore, a maximum local Nusselt number occurs at lower Eckert number, magnetic and nanoparticle volume fraction parameters. Key words: magnetohydrodynamic, fluid momentum controller, output torque, attitude control. Tables 8, Figs 12, Refs 26.