Nanomaterials 2023, 13, 471. https://doi.org/10.3390/nano13030471 www.mdpi.com/journal/nanomaterials Article Crosswise Stream of Cu-H2O Nanofluid with Micro Rotation Effects: Heat Transfer Analysis Rashid Mehmood 1 , Rabil Tabassum 2 , Mohamed R. Ali 3, * and Taseer Muhammad 4, * 1 Department of Mathematics, Faculty of Natural Sciences, HITEC University, Taxila Cantt, Taxila 47080, Pakistan 2 Department of Mathematics, Faculty of Basic and Applied Sciences, Air University, Islamabad 44000, Pakistan 3 Center of Research, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt 4 Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia * Correspondence: mohamed.reda@fue.edu.eg (M.R.A.); tasgher@kku.edu.sa (T.M.) Abstract: The present study focuses on a crosswise stream of liquid-holding nano-sized particles over an elongating (stretching) surface. Tiny particles of copper are added into base liquid (water). The influence of the micro rotation phenomenon is also considered. By means of appropriate trans- formations non-linear coupled ordinary differential equations are attained that govern the flow problem. The Runge–Kutta–Fehlberg scheme, together with the shooting method, is engaged to ac- quire results numerically. Micropolar coupling parameter, microelements concentration and nano- particles volume fraction effects are examined over the profiles of velocity, temperature and micro- rotation. Moreover, heat flux and shear stress are computed against pertinent parameters and pre- sented through bar graphs. Outcomes revealed that material constant has increasing effects on nor- mal components of flow velocity; however, it decreasingly influences the tangential velocity, micro- rotation components and temperature profile. Temperature profile appeared to be higher for weak concentration of microelements. It is further noticed that normal velocity profile is higher in mag- nitude for the case of strong concentration (n = 0) of microelements, whereas tangential velocity profile is higher near the surface for the case of weak concentration (n = 0.5) of microelements. An increase of 3.74% in heat flux is observed when the volume fraction of nanoparticles is increased from 1 to 5%. Keywords: micro-rotation; copper nanoparticles; oblique flow; numerical scheme 1. Introduction Heat transferal properties of fluids are highly influenced by their thermal conductiv- ity. Metals have higher thermal conductivity than liquids. This property of metals in- spired Choi et al. [1] to suggest the insertion of metallic nanoparticles in traditional fluids to improve their rate of heat transfer. Over the past decade or so, nanofluids have become an essential feature in almost all modern day industrial and technological devices and procedures. Nano particles are easily suspended within base fluids to keep the mixture homogenous while making it a lot more effective when it comes to their thermal capabil- ities. Several manufacturing procedures operating at high temperatures are required to dissipate heat at a reasonably rapid pace. Nanofluids can be a promising solution to all these aspects and challenges. Keeping this interesting property in view, many researchers pondered over the flow of nanoliquid. A flow phenomenon in which fluid strikes a solid wall or surface is called stagnated flow. This type of flow can be orthogonal or transverse. For the first time Hiemenz [2] reported the flow problem towards point of stagnation. Mustafa et al. [3] reported flow characteristics of nanoliquid in the neighborhood of the Citation: Mehmood, R.; Tabassum, R.; Ali, M.R.; Muhammad, T. Crosswise Stream of Cu-H2O Nanofluid with Micro Rotation Effects: Heat Transfer Analysis. Nanomaterials 2023, 13, 471. https://doi.org/10.3390/ nano13030471 Academic Editor: Henrich Frielinghaus Received: 7 December 2022 Revised: 6 January 2023 Accepted: 14 January 2023 Published: 24 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/license s/by/4.0/).