Hamza F, Abd El-Latief A, Khatan W
Department of Mathematics, Faculty of Science, University of Alexandria, Alexandria, Egypt.
Department of Mathematics, Faculty of Science, University of Damanhour, Damanhour, Egypt.
PLoS One. 2017 Jan 3;12(1):e0168530. doi: 10.1371/journal.pone.0168530. eCollection 2017.
In this work, the fractional mathematical model of an unsteady rotational flow of Xanthan gum (XG) between two cylinders in the presence of a transverse magnetic field has been studied. This model consists of two fractional parameters α and β representing thermomechanical effects. The Laplace transform is used to obtain the numerical solutions. The fractional parameter influence has been discussed graphically for the functions field distribution (temperature, velocity, stress and electric current distributions). The relationship between the rotation of both cylinders and the fractional parameters has been discussed on the functions field distribution for small and large values of time.
在这项工作中，研究了在横向磁场存在的情况下，黄原胶（XG）在两个圆柱之间的非定常旋转流动的分数阶数学模型。该模型由两个表示热机械效应的分数阶参数α和β组成。使用拉普拉斯变换来获得数值解。已通过图形讨论了分数阶参数对函数场分布（温度、速度、应力和电流分布）的影响。针对时间的小值和大值，在函数场分布上讨论了两个圆柱的旋转与分数阶参数之间的关系。
