Viscous dissipation and radiation effects on MHD heat transfer copper water nanofluid flow over an exponentially shrinking surface

This research examines the impact of radiation and heat source on MHD heat transfer Nanofluid flow. The flow occurs across a porous exponential stretching sheet with suction/ injection and partial slip circumstances. The nanofluid contains copper (Cu)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Cu)$$\end{document} nanoparticles. Implement the appropriate transformations to convert the controlling mathematical modeled partial differential equations (PDEs) into ordinary differential equation (ODE) models. Several research investigations have shown that the thermal conductivity of conventional fluids increases by 15-40% when nanoparticles are added to the base fluid. However, the effectiveness of this idea relies on the method used to include the nanoparticles. The characteristics of nanoparticles, such as volume fraction, agglomeration, and size, have a significant role in determining their behavior. From this research, it can be inferred that under a magnetic field environment, not only does the fluid flow exhibit more consistency compared to ordinary fluid, but it also leads to an improvement in the rate of heat transfer. The transformed system is examined using the implicit finite difference method known as the Keller Box method with the assistance of MATLAB software. The research focuses on a comparative analysis of magnetic nanoparticles, velocity and thermal slips, viscous dissipation, and radiation impacts related to the specified problem. An analysis is conducted on the physical attributes of several variables in relation to the velocity and temperature fields. Quantitative data about skin friction and Nusselt number have been collected and analyzed. It has been shown that the velocity increases as the heat source and Eckert number is higher. The velocity profile in the presence of a magnetic field is typically reduced by a factor that depends on M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M$$\end{document}. For a nanofluid like copper-water, the velocity near the surface might decrease by about 20-30% as the magnetic field is increased from M=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=1$$\end{document} to M=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=4$$\end{document}. The viscous dissipation caused a 5-8% increase in the temperature near the wall compared to pure water. Elevated suction factor values substantially improve the velocity curve and reduce the temperature. The obtained numerical solutions exhibit a strong correspondence with previously reported studies, although within certain limitations.