Khan Masood, Alshomrani Ali Saleh
Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan.
Department of Mathematics, Faculty of Science, King Abdul-Aziz University, Jeddah, 21589, Saudi Arabia.
PLoS One. 2016 Jun 20;11(6):e0157180. doi: 10.1371/journal.pone.0157180. eCollection 2016.
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
在本研究中，我们分析了磁场对广义牛顿卡雷奥流体驻点流动的影响。考虑对流表面边界条件来研究热边界层。通过采用局部相似变换，将当前问题的主导偏微分方程转化为一组常微分方程。在将其转化为初值问题后，利用龙格 - 库塔 - 费尔贝格方法对所得到的非线性常微分方程进行数值积分。本研究发现，动量和热边界层受到各种相关参数的显著影响，如哈特曼数M、速度剪切比参数α、魏森贝格数We、幂律指数n、毕奥数γ和普朗特数Pr。分析还表明，速度剪切比参数会提高流体速度以及表面摩擦。此外，哈特曼数的较大值对应于动量边界层厚度的变薄，而热边界层厚度的情况则相反。另外，可以看出数值计算结果与先前报道的研究结果非常吻合。
