Entropy generation optimization in a radiative hybrid nanofluid (engine oil + NiZnFe2O4 + MnZnFe2O4) flow through a convectively heated microchannel with cross-diffusion effects

The vertical microchannels phenomenon is useful in the cooling process of microelectronic devices, fuel cells and MHD (magnetohydrodynamic) micro-pumps. The understanding of this phenomenon makes these flows crucial in industries and engineering products. Objective of this paper is how Dufour, Soret and chemical reaction affect the characteristics of hybrid nanofluid (engine oil + manganese zinc ferrite ((MnZnFe2O4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{MnZnFe}}_{2} {\text{O}}_{4} )$$\end{document} + nickel zinc ferrite (NiZnFe2O4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{NiZnFe}}_{2} {\text{O}}_{4} )$$\end{document})) flow in a microchannel with two vertical parallel plates. The irreversibility analysis is considered. The bvp4c solver in MATLAB is implemented to compute the transformed system derived from the equations used to describe the present problem. The heat transfer rate and other physical parameters of relevance near both plates are explained using graphs. It has been observed that as the Brinkman number and Dufour numbers increased, the entropy production rate is significantly changed. It is noticed that there is a reduction in Bejan number with the escalation in volume fraction of NiZnFe2O4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{NiZnFe}}_{2} {\text{O}}_{4}$$\end{document} (ϕNi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi_{{{\text{Ni}}}}$$\end{document}). The skin-friction factor declined with the rate of 0.03114 at 0≤Mn≤3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \le {\text{Mn}} \le 3$$\end{document} (near left plate) and decreased in the friction factor is 2.45896 when ϕNi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi_{{{\text{Ni}}}}$$\end{document} is in the range 0≤ϕNi≤0.09\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \le \phi_{{{\text{Ni}}}} \le 0.09$$\end{document} (near right plate). It is detected that when Dufour number (Du\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Du}}$$\end{document}) is at 0≤Du≤0.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \le {\text{Du}} \le 0.6$$\end{document}, heat transmission rate cuts down by 0.06935 (near the left plate). Sherwood number risen by 0.043153 (near the left plate) when Soret number (Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Sr}}$$\end{document}) is set to 0≤Sr≤0.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \le {\text{Sr}} \le 0.6$$\end{document}.