Two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid passing through the shrinking sheet is considered. With the impact of thermal slip, thermal radiation and heat source-sink conditions, the UCM fluid model is integrated. The method of the Lie scaling group is used to transform the strongly nonlinear governing partial differential equations (PDEs) into the ordinary differential equations (ODEs). The transformed ODEs are numerically solved using NDSolve command of MATHEMATICA and graphically presented with their results. The Deborah number’s influence on the velocity profile \(f^{\prime } (\eta )\) is studied for different values and different behavior observed. The Hartmann number M and the mass transfer parameter S have decreased the boundary layer thickness. The Prandtl number has increased the temperature profile \(\theta (\eta )\). In contrast, the thermal boundary layer thickness was decreased by the heat source-sink parameter Q , the radiation parameter R and the thermal slip parameter L. Table 1 shows the verification of the results.

考虑通过收缩片的上对流麦克斯韦（UCM）流体的二维磁流体动力学（MHD）边界层流。在热滑移，热辐射和热源散热条件的影响下，UCM流体模型被集成。李标度组的方法用于将强非线性控制的偏微分方程（PDE）转换为常微分方程（ODE）。使用MATHEMATICA的NDSolve命令对转换后的ODE进行数值求解，并以图形方式显示其结果。对于不同的值和观察到的不同行为，研究了黛博拉数对速度分布\（f ^ {\ prime}（\ eta）\）的影响。哈特曼数M和传质参数S减小了边界层的厚度。普朗特数增加了温度曲线\（\ theta（\ eta）\）。相反，热边界层厚度通过热源-散热器参数Q，辐射参数R和热滑动参数L减小。表1显示了结果验证。