This paper investigates the flow behavior of a viscous, incompressible and electrically conducting fluid in a long channel subjected to a time-varied oblique magnetic field $B_0\left(t\right)=B_{0}f\left(t\right)$. The time-dependent MHD equations are solved by using the dual reciprocity boundary element method (DRBEM). The transient level velocity and induced magnetic field profiles are presented for moderate Hartmann number values, several direction of applied magnetic field and for several functions f(t) as polynomial, exponential, trigonometric, impulse and step functions. It is observed that, when f(t) is a polynomial or exponential function, the velocity magnitude increases up to a certain time level where the flow shows an elliptical elongation and then starts to decrease for all values of Hartmann numbers. For the trigonometric function f(t), the flow repeats its behavior with a period. An impulse function changes flow behavior with an elongation at the level where the impulse is applied to the magnetic field. Then, it behaves as if a uniform magnetic field is applied. Having a step function f(t), the behavior of the flow shows both impulse and polynomial functions features. This study shows that time-varied magnetic field changes the flow behavior significantly at all the transient levels.

本文研究了时变倾斜磁场作用下长通道中粘性，不可压缩和导电流体的流动行为 ${乙}_0（Ť）={乙}_{0}F（Ť）$。时间依赖的MHD方程是通过使用对等互惠边界元方法（DRBEM）求解的。给出了适度的Hartmann数值，瞬态水平速度和感应磁场的分布图，施加的磁场的多个方向以及多项函数f（t）的多项式，指数，三角函数，脉冲和阶跃函数。可以看出，当f（t）是多项式或指数函数时，速度幅值增加到一定的时间水平，在该时间水平处，流量显示出椭圆伸长率，然后对于哈特曼数的所有值开始减小。对于三角函数f（t），则该流程会以句点重复其行为。脉冲函数在将脉冲施加到磁场的水平上以伸长率改变流动特性。然后，其表现就好像施加了均匀的磁场一样。具有阶跃函数f（t），流的行为同时显示了脉冲函数和多项式函数的特征。这项研究表明，时变磁场在所有瞬态水平都会显着改变流动特性。