摘要
利用生物磁流体动力学(BFD)原理,在生物磁流体经由遭受磁场作用的多孔介质时,研究其流动的基本理论.所研究流体的磁化强度随温度而变化.流体被认为是非Newton流体,其流动由二阶梯度流体方程所控制,并考虑了流体的粘弹性效应.假设管道壁是能够伸展的,管壁表面的速度与到坐标原点的纵向距离成正比.首先将问题简化为包括7个参数的、耦合的非线性微分方程组的求解.将血液看作生物磁流体,并用上述方法分析,目的是计算某些血液的流动参数,并配以适当的数值方法,导数用差分格式近似.计算结果用图形给出,从而在磁场作用下,得到过热状态中关系血液的、血流动力学流动的理论预测.结果清楚地表明,在电磁过热治疗进程期间,磁偶极子对动脉中血液流动特征的影响起着重大作用.该研究引起了临床医学的关注,其结果有益于癌症病人采用电磁过热的治疗.
The theoretical investigation of a fundamental problem of flow of a biomagnetic fluid through a porous medium subjected to a magnetic field by using the principles of Biomagnetic Fluid Dynamics（BFD） was dealt with.The study pertains to a situation where magnetization of the fluid varies with temperature.The fluid was considered to be non-Newtonian,its flow being governed by the equation of a second-grade fluid,which takes into account the effect of fluid visco-elasticity.The walls of the channel were assumed to be stretchable,where the surface velocity was proportional to the longitudinal distance from the origin of coordinates.The problem was first reduced to that of solving a system of coupled nonlinear differential equations that involve seven parameters.Considering blood as a biomagnetic fluid and using the present analysis,an attempt had been made to compute some parameters of blood flow,by developing a suitable numerical method and by devising an appropriate finite difference scheme.The computational results were presented in graphical form and thereby some theoretical predictions were made in respect of the hemodynamical flow of blood in a hyperthermal state,under the action of a magnetic field.The results reported here clearly indicate that presence of a magnetic dipole bears the potential to affect the characteristics of blood flow in arteries to a significant extent during the therapeutic procedure of electromagnetic hyperthermia.The study should attract the attention of clinicians and the results should be useful to them in their treatment of cancer patients by the method of electromagnetic hyperthermia.
出处
《应用数学和力学》
CSCD
北大核心
2010年第11期1330-1343,共14页
Applied Mathematics and Mechanics
关键词
生物磁流体
血液
伸展壁
多孔介质
电磁过热疗法
biomagnetic fluid
blood
stretching walls
porous medium
electromagnetic hyperthermia
