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Numerical solution of buoyancy MHD flow with magnetic potential

机译：具有磁势的MHD浮力流的数值解

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摘要

In this study, dual reciprocity boundary element method (DRBEM) is applied for solving the unsteady flow of a viscous, incompressible, electrically conducting fluid in channels under the effect of an externally applied magnetic field and buoyancy force. Magnetohydrodynamics (MHD) equations are coupled with the energy equation due to the heat transfer by means of the Boussinessq approximation. Then, the 2D non-dimensional full MHD equations in terms of stream function, temperature, magnetic potential, current density and vorticity are solved by using DRBEM with implicit backward Euler time integration scheme. Numerical results are obtained utilizing linear boundary elements and linear radial basis functions approximation for the inhomogeneities, in a double lid-driven staggered cavity and in a channel with backward facing step. The results are given for several values of problem parameters as Reynolds number (Re), magnetic Reynolds number (Rem), Hartmann number {Ha) and Rayleigh number (Ra). With the increase in Rem, both magnetic potential and current density circulate near the abrupt changes of the walls. The increase in Ha suppresses this perturbation, and forces the magnetic potential lines to be in the direction of the applied magnetic field. The boundary layer formation through the walls emerge in the flow and current density for larger values of Ha.
机译：在这项研究中，采用双向互易边界元方法（DRBEM）解决了在外部施加磁场和浮力的作用下通道中粘性，不可压缩，导电流体的不稳定流动。由于热传递，磁流体力学（MHD）方程与能量方程通过Boussinessq逼近法耦合。然后，通过使用具有隐式后向欧拉时间积分方案的DRBEM求解流函数，温度，磁势，电流密度和涡度方面的二维无量纲完整MHD方程。利用线性边界元素和线性径向基函数逼近非均匀性，可在双盖驱动的交错腔中和朝后台阶的通道中获得数值结果。给出了问题参数的几个值的结果，例如雷诺数（Re），磁雷诺数（Rem），哈特曼数{Ha）和瑞利数（Ra）。随着Rem的增加，磁势和电流密度都在壁的突然变化附近循环。 Ha的增加抑制了这种扰动，并迫使磁势线朝向所施加的磁场的方向。对于较大的Ha值，穿过壁的边界层形成出现在流量和电流密度中。

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