Mathematical investigation has been presented to examine the magnetohydrodynamic boundary layer flow of viscous nanofluids bygone a nonlinear stretched plate among cumulative impact of viscous dissipation and joule heating. Physical formulation produced a system of partial differential equations which has been converted into a set of ordinary differential equations through employing suitable similarity variables. For numerical solutions of resulting governing equations of flow, a Keller-box method has been addressed. Results of dimensionless velocity and dimensionless temperature for impacts of various types of nanoparticle along with water base fluid and effects of physical parameters, namely solid volume fraction, nonlinear stretching parameter, magnetic parameter and Brinkmann number have been deliberated via graphs. Additionally, surface shear stress and surface heat flux for selected suitable values of pertinent parameters have been computed and explicated via table.

中文翻译：

---

考虑粘性耗散和焦耳热，传热和磁流体动力学纳米流体通过非线性拉伸表面的流动行为

已经进行了数学研究以检查粘性消散和焦耳热的累积影响中非线性拉伸板所产生的粘性纳米流体的磁流体动力学边界层流动。物理公式产生了一个偏微分方程组，该系统已通过采用适当的相似性变量转换为一组常微分方程。对于由此产生的流动控制方程的数值解，已经提出了一种Keller-box方法。无量纲的速度和与水基流体沿着不同类型的纳米粒子的影响和物理参数，即固相体积分数，非线性拉伸参数的影响因次温度的结果，磁性参数和布林克曼数目已经审议通过图。此外，已计算了相关参数的选定合适值的表面剪切应力和表面热通量，并通过表格进行了说明。