Numerical simulations of non-Newtonian fluids are indispensable for optimization and monitoring of several industrial processes such as crude oil transportation, nuclear cooling, geothermal and fossil fuel production. The governing equations derived for non-Newtonian fluid models result in nonlinear differential equations. Thus, increasing the complexity even for simple geometries. The cumbersome numerical computation and rudimentary empirical solutions hinder faster analysis over a wide range of parameters. However, machine and deep learning methods have higher accuracy but rely heavily on the quality and amount of training data, and the solution may become inconclusive if data is sparse. In this research, a novel algorithm (Herschel Bulkley Network) is introduced to simulate the non-Newtonian fluid flow in a pipe using data redundant deep neural network (DNN) for fully developed, laminar, and incompressible flow conditions. The objective of this investigation is to develop a physics dominated DNN solely driven by minimizing residuals from the Navier-Stokes based governing equations, establishing benchmark research. Herschel-Bulkley model is used to approximate the complex rheological behavior of a non-Newtonian fluid. The proposed DNN algorithm is structured to incorporate initial/boundary conditions in cylindrical coordinates and approximate the solution without the aid of any simulated or training data. The simulated results and analysis demonstrate an excellent agreement between the proposed algorithm and non-Newtonian fluids flow attributes. The detailed parametric analysis exhibits the competency of the proposed algorithm to explain the rheological features. Monte-Carlo simulation is performed by propagating uncertainty to investigate the dominant parameters affecting simulated results. The uncertainty in fluid consistency index is responsible for higher variance in the calculated flow rate, while the least variation is observed due to fluid behavior index uncertainty. The performance of the algorithm is validated with experimental datasets. The statistical error estimation exhibits a mean absolute error of 11.5%, and root mean squared error of 0.87. A comprehensive analysis on training unsupervised DNN and adjusted hyperparameters is also highlighted to achieve expedite convergence.

非牛顿流体的数值模拟对于原油运输、核冷却、地热和化石燃料生产等多种工业过程的优化和监测必不可少。为非牛顿流体模型导出的控制方程导致非线性微分方程。因此，即使对于简单的几何图形也增加了复杂性。繁琐的数值计算和基本的经验解决方案阻碍了对广泛参数的更快分析。然而，机器和深度学习方法具有更高的准确性，但在很大程度上依赖于训练数据的质量和数量，如果数据稀疏，解决方案可能会变得不确定。在这项研究中，引入了一种新算法（Herschel Bulkley 网络）来模拟管道中的非牛顿流体流动，使用数据冗余深度神经网络 (DNN) 来模拟完全发展的层流和不可压缩流动条件。本次调查的目的是开发一个以物理为主的 DNN，完全通过最小化基于 Navier-Stokes 的控制方程的残差来驱动，建立基准研究。Herschel-Bulkley 模型用于近似非牛顿流体的复杂流变行为。所提出的 DNN 算法的结构是将初始/边界条件合并到圆柱坐标中，并在没有任何模拟或训练数据的帮助下逼近解。模拟结果和分析表明所提出的算法与非牛顿流体流动属性之间具有极好的一致性。详细的参数分析展示了所提出的算法解释流变特征的能力。蒙特卡罗模拟是通过传播不确定性来研究影响模拟结果的主要参数来执行的。流体稠度指数的不确定性导致计算的流速变化较大，而由于流体行为指数的不确定性，观察到的变化最小。该算法的性能通过实验数据集进行验证。统计误差估计的平均绝对误差为 11.5%，均方根误差为 0.87。还强调了对训练无监督 DNN 和调整后的超参数的综合分析，以实现加速收敛。