Joule Heating and Viscous Dissipation Effects on Heat Transfer of Hybrid Nanofluids with Thermal Slip

Hybrid nanofluids are vital in engineering and industrial sectors due to effective thermal conductivity as compared to regular fluids and nanofluids, which result in a high rate of heat transfer. The present article explores the flow analysis of hybrid nanofluid past a shrinking/stretching sheet in the occurrence of a constant magnetic field and suction/injection. Hybrid nanofluid contains water as a base fluid and nanoparticles namely titania TiO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{\text{TiO}}_{2} } \right)$$\end{document}, as well as iron oxide Fe3O4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{\text{Fe}}_{3} {\text{O}}_{4} } \right)$$\end{document} act simultaneously to affect the thermo-transport processes. Further, the energy losses due to Joule heating and viscous dissipation are also considered. A mathematical model is developed and appropriate governing Navier–Stokes equations are derived and transformed to non-linear ordinary differential equations using similarity transformations. The numerical solution is obtained using bvp4c solver with MATLAB code. The important findings are recorded as follows. The heat energy transport accelerates with higher values of Eckert number and thermal radiation but decelerates with higher suction. Thus, the present flow model also favors thinning of the thermal boundary layer. Most importantly, the velocity and temperature in the flow domain increases with an increase in volume fraction of hybrid nanofluid due to faster momentum as well as thermal energy transport. Another striking feature is the decrease in skin friction coefficient on stretching of bounding surface, which adds to flow stability; whereas in the case of shrinking, the opposite effect is observed. The magnitude of skin friction (force coefficient) increases with the rise of volume fraction of titanium dioxide but which is consistent with the fact that there is a progressive thinning of the boundary layer with an increase of ϕ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi_{1}$$\end{document} (volume fraction of titanium dioxide).