A uniform two-dimensional magneto-hydrodynamic convection flow of an adhesive incompressible fluid along a vertical stretching surface in accordance with varying thermal conductivity and radiation is analyzed. The uppermost layer temperature, the transverse magnetic field and the stretching velocity are presumed to alter as a power function of the distance from the origin. The non-linear PDE (partial differential equations) which run our examined problem are converted into a set of non-linear ordinary differential equations by the use of a relevant transformations followed by a numerical solution implementing a shooting method together with Runge-Kutta integration formula. We examine the effects of a variety of regulating parameters, viz the magnetic parameter, the velocity and temperature exponents, the variable thermal conductivity parameter, buoyancy parameter and the radiation parameter. The graphs and tables express a powerful impact of these parameters on the behavior of the flow and heat transfer.

中文翻译：

---

非线性拉伸面驱动的磁流体动力均匀自由对流传热二维薄层对流

根据热导率和辐射的变化，分析了粘性不可压缩流体沿垂直拉伸表面的均匀二维磁流体动力对流流动。假定最上层温度、横向磁场和拉伸速度作为距原点距离的幂函数而改变。通过使用相关变换，然后是实现射击方法的数值解以及 Runge-Kutta 积分公式，将运行我们研究的问题的非线性 PDE（偏微分方程）转换为一组非线性常微分方程. 我们检查了各种调节参数的影响，即磁参数、速度和温度指数、可变热导参数、浮力参数和辐射参数。图表和表格表达了这些参数对流动和传热行为的强大影响。