Interaction between nonuniform heat source/sink, magnetic field and thermal radiation with heat flux through the flow of non-Newtonian power-law fluid due to a linearly stretching sheet was studied numerically using an implicit finite difference method (FDM). The heat flux is assumed to depend on both the thermal conductivity and the thermal radiation. Besides, the effects of all governing parameters, such as the magnetic parameter, thermal conductivity parameter, the power-law index parameter, Prandtl number, the space-dependent heat source/sink parameter, the temperature-dependent heat source/sink parameter, and the radiation parameter, on the profiles of velocities and temperature are studied and discussed. In particular, thermal radiation was found to play a key role in the heat transfer characteristics and in the formation of thermal boundary layer. Generally, our numerical results reveal that both the velocity and temperature distributions are marginally influenced by both the magnetic parameter and power-law index. A good agreement is observed between our results via finite difference method and the previously published numerical results for some special case.

中文翻译：

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求解流体流动物理问题的有限差分法

使用隐式有限差分法 (FDM) 数值研究了非均匀热源/汇、磁场和热辐射与通过非牛顿幂律流体流动的热通量之间的相互作用。假设热通量取决于热导率和热辐射。此外，所有控制参数的影响，如磁参数、热导率参数、幂律指数参数、普朗特数、空间相关热源/散热器参数、温度相关热源/散热器参数，以及对速度和温度剖面上的辐射参数进行了研究和讨论。特别是，研究发现热辐射在传热特性和热边界层的形成中起关键作用。一般来说，我们的数值结果表明，速度和温度分布都受到磁参数和幂律指数的轻微影响。在我们通过有限差分法得到的结果与之前发表的一些特殊情况的数值结果之间观察到了很好的一致性。