The purpose of this paper is to focus on the transient flow and heat transfer of a non-newtonian fluid (Casson fluid) between parallel disks in the presence of an external magnetic field. The bottom disk is considered to be porous and fixed, whereas the upper disk moves down. Also, the influence of the heat source/sink and viscous dissipation is taken into account. The conservative partial differential equations have been transformed into dimensionless ones and are solved semi-analytically using Least Square Method. Besides, applying a numerical solution, the accuracy of analytical results is verified using the fourth-order Runge–Kutta method. The effects of various physical parameters such as suction/injection, heat source/sink, Prandtl number, magnetic field, slip condition, and Casson fluid parameter on velocity and temperature distribution as well as skin-friction coefficient and Nusselt number are examined and discussed. The results have shown that higher values of the Casson fluid parameter decrease the Nusselt number and shear stress. Also, it is observed that the Hartmann number augmentation decreases the heat transfer rate. What is more, it is shown that the intensity of injection/suction affects how streamlines behave against the central vertical axis.

本文的目的是关注在存在外部磁场的情况下平行圆盘之间非牛顿流体（卡森流体）的瞬态流动和热传递。底部圆盘被认为是多孔且固定的，而上部圆盘向下移动。此外，还考虑了热源/散热器和粘性耗散的影响。将保守偏微分方程转化为无量纲方程，并使用最小二乘法进行半解析求解。此外，应用数值解，使用四阶龙格-库塔方法验证分析结果的准确性。各种物理参数的影响，如吸力/注入、热源/汇、普朗特数、磁场、滑移条件、检查和讨论了关于速度和温度分布的 Casson 流体参数以及皮肤摩擦系数和 Nusselt 数。结果表明，较高的 Casson 流体参数值会降低 Nusselt 数和剪切应力。此外，据观察，哈特曼数增加会降低传热率。更重要的是，它表明注入/抽吸的强度影响流线对中心垂直轴的行为。