Analytical solutions of an unsteady magnetohydrodynamic (MHD) flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting, and Boussinesq fluid over a vertical oscillating plate embedded in a Darcian porous medium in the presence of a thermal radiation are presented. The fluid considered here is a gray, absorbing/emitting radiating, but nonscattering medium. At time t > 0, the plate temperature and concentration near the plate are raised linearly with time t. The dimensionless governing coupled unsteady boundary layer partial differential equations are solved by the Laplace transform technique. An increase in permeability parameter (K) is found to increase fluid velocities and shear stress in the regime. Also it was found that when the conduction-radiation parameter (R) increased, the fluid velocity and the temperature profiles decreased. Applications of the study are found in materials processing and solar energy collector systems.

中文翻译：

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通过无限振动垂直多孔表面的非定常MHD流动的传热和传质

提出了一种不稳定的磁流体动力学（MHD）流动的解析解，该流动具有在存在热辐射的情况下嵌入在Darcian多孔介质中的垂直振荡板上不可压缩，粘性，导电和Boussinesq流体的传热和传质特性。这里考虑的流体是一种灰色的，吸收/发射辐射但不散射的介质。在时间t > 0处，板附近的板温度和浓度随时间t线性增加。用Laplace变换技术求解无量纲控制耦合非定常边界层偏微分方程。渗透率参数增加（K被发现增加了流体速度和剪切应力。还发现当传导辐射参数（R）增加时，流体速度和温度分布降低。该研究的应用发现于材料加工和太阳能收集器系统中。