Numerical study of unsteady thin film flow of power-law tetra hybrid nanofluid with velocity slip effect over a stretching sheet using sodium alginate as base fluid

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This study examines the influence of power-law nanofluid flow and velocity slip on the heat transfer performance of tetrahybrid nanofluids over a stretching sheet, with the objective of enhancing thermal efficiency in industrial applications. The tetrahybrid nanofluids, consisting of Al2O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Al_2O_3$$\\end{document}, TiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$TiO_2$$\\end{document}, Cu, and Fe3O4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Fe_3O_4$$\\end{document} nanoparticles suspended in a sodium alginate base fluid, represent a novel combination of materials whose collective thermal properties have not been extensively studied. The performance of these tetrahybrid nanofluids is compared to that of hybrid and tri-hybrid nanofluids to evaluate their relative heat transfer capabilities. The boundary layer equations are solved using MATLAB’s bvp4c solver, applying similarity transformations to investigate temperature and velocity profiles under varying parameter conditions. The results indicate that tetrahybrid nanofluids significantly enhance heat transfer rates compared to standard nanofluids, with improvements of 7.43%, 6.27%, and 5.35% over hybrid and tri-hybrid nanofluids, respectively. Furthermore, the analysis reveals that velocity profiles intersect at a specific point, and as the velocity slip parameter increases, the profiles move further away from the stretching sheet. Key factors, such as the Prandtl number, power-law index, slip parameter, magnetic field, and Reynolds number, are also examined for their effects on flow and thermal behavior. The key innovation of this research lies in the introduction of tetrahybrid nanofluids as an advanced medium for heat transfer, providing superior thermal efficiency compared to previously studied nanofluids. This study not only builds upon existing research but also provides new computational insights into the potential applications of tetrahybrid nanofluids in areas like food processing and other industries requiring effective thermal management.