This study aims to express an optimize temperature profile with the most heat transfer and least work loss by minimizing the total entropy generation of a pipeline under external magnetic field. This study has investigated in low Stokes number and low Reynolds number conditions. It shows that, the fluid’s shear stress increases around the wall (r* > 0.8), due to presence of magnetic field. As a consequence, the magnetic field boosts the dissipation term. However, the velocity gradient over a wide range of radius 0 < r^∗ < 0.8 decreases and hence the mean flow velocity increases. Our goal is to use this analysis to manage our magnetic energy better. The entropy generation for fluid flow is minimized in the circular tube with a fix wall temperature under constant magnetic field effect and considering heat dissipation, by applying the calculus of variations. By solving the normalized energy and momentum equations with added source terms due to magnetic field, the real temperature distribution is obtained. Taking the variational of the entropy generation function in the integral form, a nonlinear differential equation with respect to temperature is obtained, which is difficult to be solved analytically. However, series method used to obtain approximate optimize temperature profile.

中文翻译：

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低斯托克斯数下磁场作用下产生最小熵的高粘性管道流

这项研究旨在通过最大程度减少外部磁场下管道的总熵产生来表达具有最大传热和最小功损失的最佳温度曲线。本研究在低斯托克斯数和低雷诺数条件下进行了研究。它表明，由于磁场的存在，流体在壁周围的切应力增加（r *> 0.8）。结果，磁场提高了耗散项。但是，半径0 < r ^∗的宽范围内的速度梯度  <0.8会降低，因此平均流速会增加。我们的目标是使用此分析更好地管理我们的磁能。通过应用变化演算，在恒定磁场作用下并考虑散热的情况下，在具有固定壁温的圆管中，使流体流动的熵产生最小化。通过使用归因于磁场的附加源项求解归一化的能量和动量方程，可以获得真实的温度分布。以积分形式的熵产生函数的变化量，获得关于温度的非线性微分方程，这在解析上很难解决。但是，用于获得近似最佳温度曲线的串联方法。