The current paper covers the impact of variable thickness and melting transfer of heat on magnetohydrodynamics (MHD) nanofluid motion past a slendering extending surface. Similarity transformations altered the derived equations into ordinary differential equations (ODEs). The mathematical performances were operated by employing the RK-4 method. The study figured out graphs and tables for various parameters as well as sketched out skin friction and Nusselt number for the stream factors; independently for Ag-water nanofluid. The outcomes of the present study were confirmed by comparing previous published results which established a positive agreement.

中文翻译：

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可变厚度和热量的传热对通过细长拉伸片的磁流体动力学纳米流体流动的影响

当前的论文涵盖了变厚的厚度和热量的熔融传递对经过细长延伸表面的磁流体动力学（MHD）纳米流体运动的影响。相似变换将导出的方程式更改为常微分方程式（ODE）。通过使用RK-4方法进行数学运算。研究得出了各种参数的图形和表格，并画出了流因数的皮肤摩擦力和努塞尔数。独立地用于Ag-水纳米流体。本研究的结果通过比较先前发表的证实了肯定协议的结果得到了证实。