Hayat T, Farooq S, Alsaedi A
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan.
Comput Methods Programs Biomed. 2017 Apr;142:117-128. doi: 10.1016/j.cmpb.2017.02.006. Epub 2017 Feb 22.
The primary objective of present analysis is to model the peristalsis of copper-water based nanoliquid in the presence of first order velocity and thermal slip conditions in a curved channel. Mixed convection, viscous dissipation and heat generation/absorption are also accounted.
Mathematical formulation is simplified under the assumption of small Reynolds number and large wavelength. Regular perturbation technique is employed to find the solution of the resulting equations in terms of series for small Brinkman number. The final expression for pressure gradient, pressure rise, stream function, velocity and temperature are obtained and discussed through graphs. Mathematica software is utilized to compute the solution of the system of equations and to plot the graphical results.
Results indicates that insertion of 30% copper nanoparticles in the basefluid (water) velocity and temperature reduces by almost 3% and 40% respecively. Moreover it is seen that size of the trapped bolus also reduces almost 20% with the insertion of 20% nanoparticles (copper) in the basefluid (water).
It is noted that velocity and temperature are decreasing functions of nanoparticle volume fraction. Moreover the temperature rises when heat generation parameter and Brinkman number are enhanced.
本分析的主要目的是对弯曲通道中存在一阶速度和热滑移条件下铜 - 水基纳米流体的蠕动进行建模。同时考虑混合对流、粘性耗散以及热生成/吸收。
在小雷诺数和大波长的假设下简化数学公式。采用正则摄动技术，针对小布林克曼数，以级数形式求解所得方程。通过图表获得并讨论了压力梯度、压力升、流函数、速度和温度的最终表达式。利用Mathematica软件计算方程组的解并绘制图形结果。
结果表明，在基础流体（水）中插入30%的铜纳米颗粒时，速度和温度分别降低了近3%和40%。此外，还发现当在基础流体（水）中插入20%的纳米颗粒（铜）时，捕获团块的尺寸也减小了近20%。
值得注意的是，速度和温度是纳米颗粒体积分数的递减函数。此外，当热生成参数和布林克曼数增加时，温度会升高。
