Mehmood Rashid, Tabassum Rabil, Ali Mohamed R, Muhammad Taseer
Department of Mathematics, Faculty of Natural Sciences, HITEC University, Taxila Cantt, Taxila 47080, Pakistan.
Department of Mathematics, Faculty of Basic and Applied Sciences, Air University, Islamabad 44000, Pakistan.
Nanomaterials (Basel). 2023 Jan 24;13(3):471. doi: 10.3390/nano13030471.
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 transformations 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 acquire results numerically. Micropolar coupling parameter, microelements concentration and nanoparticles 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 presented through bar graphs. Outcomes revealed that material constant has increasing effects on normal 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 magnitude 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%.
本研究聚焦于在一个伸长（拉伸）表面上横向流动的含液纳米颗粒流。将微小的铜颗粒添加到基础液体（水）中。还考虑了微旋转现象的影响。通过适当的变换，得到了控制流动问题的非线性耦合常微分方程。采用龙格 - 库塔 - 费尔贝格格式结合打靶法进行数值求解。研究了微极耦合参数、微量元素浓度和纳米颗粒体积分数对速度、温度和微旋转分布的影响。此外，针对相关参数计算了热通量和剪应力，并通过柱状图展示。结果表明，材料常数对流速的法向分量有增强作用；然而，它对切向速度、微旋转分量和温度分布的影响逐渐减小。微量元素浓度较低时，温度分布似乎更高。还进一步注意到，微量元素浓度高（n = 0）时，法向速度分布的幅值更高，而微量元素浓度低（n = 0.5）时，切向速度分布在表面附近更高。当纳米颗粒体积分数从1%增加到5%时，热通量增加了3.74%。
