Dynamics of nanoparticle radius and inter-particle spacing on the nanofluid flow over an extending sheet with Cattaneo-Christov heat flux and inclined magnetic field impacts

This work investigates the influences of Cattaneo-Christov heat and mass flux on nanofluid flow toward a convectively heated bidirectional elongating sheet. The impacts of space- and thermal-dependent heat sources, Brownian motion, thermophoresis and convective boundary constraints are used in the study. Variable porosity of the sheet's surface has employed to explore how variations in nanoparticles' interspacing and their radius influence momentum of the fluid. The modeled equations have numerically solved using the bvp4c method after being converted to dimensionless form via similarity transformations. It has revealed in this work that, with augmentation in inclination angle, porosity and magnetic factors, there is corresponding reduction in primary and secondary velocities both for interparticle spaces (say h=5/2&7/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h = 5/2\,\,\& \,\,7/2\,$$\end{document}) and radius of nanoparticles (sayRp=3/2&5/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{say}}\;Rp = 3/2\,\& \,5/2)$$\end{document}. This reduction is more significant in case of large interparticle spaces (say h=7/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h = \,\,7/2$$\end{document}) and large radius of nanoparticles (say Rp=5/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Rp = \,5/2$$\end{document}). Thermal characteristics have escalated with growth in thermal Biot number and radiation factor. Concentration characteristics augmented with thermophoresis factor and concentration Biot number while retarded with upsurge in Brownian motion factor and mass relaxation time factor. It is revealed that the retardations in skin frictions CfxRex1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{fx} Re_{x}<^>{1/2}$$\end{document} and CfyRey1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{fy} Re_{y}<^>{1/2}$$\end{document} are more significant for h=7/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h = 7/2$$\end{document} and Rp=5/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Rp = 5/2$$\end{document} in contrast of h=5/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h = 5/2$$\end{document} and Rp=3/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Rp = 3/2$$\end{document}.