Magnetic field plays a significant role in innumerable fields like mechanical, chemical, biological and medical research. Few examples include power generation systems, magnetohydrodynamic (MHD) accelerators, liquid metal fluids, cooling of nuclear reactors, high-temperature plasmas, chemical processing equipment and electronic components. In view of these facts, the current investigation discusses the fundamental flows of a Casson fluid in horizontal parallel plates (three fundamental situations considered such as the plate walls progresses in the conflicting directions, the progress of lower plate in the flow direction and other is in fixed position, and the progress of the plates in the flow direction respectively). Influences of radiation, velocity slip, porous medium and Joule heating are considered into account. The flow situation is assumed in Cartesian coordinate system. The momentum and energy equations are transformed into non-dimensional system utilizing appropriate non-dimensional parameters. The exact solutions of the non-dimensional differential equations have been obtained. The pictorial representations are provided for the velocity as well as temperature characteristics in all the mentioned cases. It is concluded by graphical approach that velocity is enhanced in the case of increasing Darcy's parameter and boundary slip while reduced for the large magnetic field. On the other hand, it is found that slip factor is reducing the heat transfer rate while magnetic field is giving rise to it.

磁场在机械、化学、生物和医学研究等无数领域中发挥着重要作用。很少有例子包括发电系统、磁流体动力 (MHD) 加速器、液态金属流体、核反应堆冷却、高温等离子体、化学处理设备和电子元件。鉴于这些事实，目前的研究讨论了卡松流体在水平平行板中的基本流动（考虑了板壁在相互冲突的方向上前进、下板在流动方向上的前进等三种基本情况）。固定位置，以及板块在流动方向上的进展情况）。考虑了辐射、速度滑移、多孔介质和焦耳热的影响。流动情况假设在笛卡尔坐标系中。利用适当的无量纲参数将动量和能量方程转化为无量纲系统。已经获得了无量纲微分方程的精确解。在所有提到的情况下，都提供了速度和温度特性的图示。通过图形化方法得出结论，在增加达西参数和边界滑移的情况下，速度提高，而在大磁场下速度降低。另一方面，发现滑移系数降低了传热率，而磁场则增加了传热率。利用适当的无量纲参数将动量和能量方程转化为无量纲系统。已经获得了无量纲微分方程的精确解。在所有提到的情况下，都提供了速度和温度特性的图示。通过图形化方法得出结论，在增加达西参数和边界滑移的情况下，速度提高，而在大磁场下速度降低。另一方面，发现滑移系数降低了传热率，而磁场则增加了传热率。利用适当的无量纲参数将动量和能量方程转化为无量纲系统。已经获得了无量纲微分方程的精确解。在所有提到的情况下，都提供了速度和温度特性的图示。通过图形化方法得出结论，在增加达西参数和边界滑移的情况下，速度提高，而在大磁场下速度降低。另一方面，发现滑移系数降低了传热率，而磁场则增加了传热率。通过图形化方法得出结论，在增加达西参数和边界滑移的情况下，速度提高，而在大磁场下速度降低。另一方面，发现滑移系数降低了传热率，而磁场则增加了传热率。通过图形化方法得出结论，在增加达西参数和边界滑移的情况下，速度提高，而在大磁场下速度降低。另一方面，发现滑移系数降低了传热率，而磁场则增加了传热率。