A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector $N(\eta )$ .

中文翻译：

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非线性扩散的数值解。拉伸域中微极性流体的传热方程

试图基于有限差分近似进行数值研究，以分析通过达西多孔介质的微极性流体动力学的总流量，微自旋流和传热现象。流体流动机制被认为是在可移动的可渗透片上。传热与两组不同的边界条件相关，即等温壁和等流量边界。基于介质的孔隙率，利用相似度函数来利用一组常微分方程。非线性耦合ODE已通过非常稳定和可靠的数值方案求解，该方案涉及Simpson规则和逐次松弛法。通过在三种不同的网格大小上进行迭代，可以提高结果的准确性，并且通过Richardson外推法可以实现结果的更高阶精度。这项研究通过适当考虑微极性流体理论，提供了现实而有区别的结果。微极性材料参数显示出降低了整体流体速度，热分布和皮肤摩擦系数，但是增加了局部传热速率和耦合应力。微观结构的自旋行为也通过微旋转矢量表现出来 $ñ（\eta ）$ 。