The incompressible, steady and laminar fluid boundary flow and heat transfer through a moving plate subject to a kind of novel constitution relationships containing the relaxation time parameters and distributed order time fractional operators are originally introduced. Formulated distributed order time fractional equations governing the flow and heat consider the relaxation characteristic and a spectrum of memory and nonlocal characteristics. Solutions are obtained numerically that distributed order integrals are approximated by the summation of multi-fractional terms and the fractional derivatives are discretised by the L1 scheme and L2 scheme. Two source items are introduced and, consequently, the exact solutions are defined. Afterward, the comparison between the exact solutions and numerical solutions is given which verifies the correctness of the computed results. The repercussion of dynamic parameters on boundary layer flow and heat transfer is deliberated and shown by graphical illustrations. Results show that the velocity and temperature boundary layers become thicker with the increase of time parameter or with the decrease of relaxation time parameter. For a larger Prandtl number, the temperature boundary layer becomes thinner. Besides, the comparisons between the distributed order time fractional governing equation possessing the monotone decreasing gamma function distributed order and the uniformly distributed order with the classical time fractional governing equation are discussed and analysed.

中文翻译：

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具有分布式有序时间分数本构模型的广义麦克斯韦流体在移动板上的流动和传热


首次介绍了不可压缩、稳定、层流流体边界流动和通过动板的传热，其受到一种包含弛豫时间参数和分布序时间分数算子的新型构成关系的影响。制定的控制流动和热量的分布式有序时间分数方程考虑了弛豫特性以及记忆和非局部特性的频谱。数值上得到了分布阶积分通过多项分数项求和来近似以及分数阶导数通过L1格式和L2格式离散化的数值解。引入了两个源项，因此定义了精确的解决方案。然后将精确解与数值解进行比较，验证了计算结果的正确性。讨论了动态参数对边界层流动和传热的影响并通过图形说明显示。结果表明，随着时间参数的增大或弛豫时间参数的减小，速度和温度边界层变厚。对于较大的普朗特数，温度边界层变得更薄。此外，还讨论和分析了具有单调递减伽马函数分布阶和均匀分布阶的分布阶时间分数阶控制方程与经典时间分数阶控制方程的比较。