Abstract In this paper, two-phase flow of blood is considered through a circular tube along with magnetic properties. The tube is considered as a circular cylinder form and the blood is flowing through it under the influence of uniform magnetic field and an external oscillating pressure gradient. Exact solutions for the fluid and magnetic particles velocities are obtained by means of integral transforms. The velocity of the fluid is presented as a sum of post transient and transient solutions. Moreover, a semi-analytical solution based on the Bessel equation and Tzou’s algorithm for the inverse Laplace transform is obtained. A comparison among the profiles of the fluid’s velocity determined with both solutions is also made. Furthermore, in order to study the influence of the material parameters, numerical simulations and graphical illustrations are used and useful conclusions are summarized.

中文翻译：

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血液通过具有磁性的圆形管的两相流

摘要 本文考虑了血液通过圆管的两相流以及磁性。该管被认为是一个圆柱体形式，血液在均匀磁场和外部振荡压力梯度的影响下流过它。流体和磁性粒子速度的精确解是通过积分变换获得的。流体的速度表示为后瞬态和瞬态解的总和。此外，还获得了基于贝塞尔方程和拉普拉斯逆变换的Tzou 算法的半解析解。还对两种解决方案确定的流体速度分布进行了比较。此外，为了研究材料参数的影响，