Nanofluid flow with slip condition over a moving surface: buoyancy and heat source effects at the separated stagnation point

Nanofluid dynamic properties have varied consequences in several contexts, including those of cooling, building environments, heat transfer structures, microwave flow cytometry, energy generation, hyperthermia therapies, and related activities. This work presents a numerical examination of the unsteady separated stagnation point flow of Al2O3/H2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{Al}}_{2}{\mathrm{O}}_{3}/{\mathrm{H}}_{2}\mathrm{O}$$\end{document} nanofluid. The study examines the combined impact of buoyancy and heat source effects, as well as mass suction and slip conditions, on the behavior of the system. In this study, we establish a new mathematical model for nanofluids, which we use to derive similarity solutions in the form of a system of ordinary differential equations (ODEs). The bvp4c technique in MATLAB is used to find approximations to the solutions of certain reduced ODEs. A comprehensive analysis has been undertaken to investigate many physical parameters, revealing that the skin friction coefficient exhibits an upward trend with increasing nanoparticle volume percentage and an unsteadiness parameter for opposing flow. The pattern is also evident in the fluid's heat transfer rate. In addition, the influence of the stagnation and unsteadiness parameters on the heat transfer performance is significant. The incorporation of the melting heat parameter results in a broader variety of temperature profiles, hence leading to a spontaneous decrease in the rate of heat transmission. Furthermore, the paper incorporates a validation process to substantiate the suggested model and reinforce the conclusions.