Purpose

The purpose of this study is to investigate the unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time power-law-dependent stretching plate. Based on the characteristics of pressure in the boundary layer, the momentum equation with the fractional Maxwell model is firstly formulated to analyze unsteady stagnation-point flow. Furthermore, generalized Fourier’s law is considered in the energy equation and boundary condition of convective heat transfer.

Design/methodology/approach

The nonlinear fractional differential equations are solved by the newly developed finite difference scheme combined with L1-algorithm, whose convergence is verified by constructing a numerical example.

Findings

Some interesting results can be revealed. The larger fractional derivative parameter of velocity promotes the flow, while the smaller fractional derivative parameter of temperature accelerates the heat transfer. The temperature boundary layer is thicker than the velocity boundary layer, and the velocity enlarges as the stagnation parameter raises. This is because when Prandtl number < 1, the capacity of heat diffusion is greater than that of momentum diffusion. It is to be observed that all the temperature profiles first enhance a little and then reduce rapidly, which indicates the thermal retardation of Maxwell fluid.

Originality/value

The unsteady stagnation-point flow model of Maxwell fluid is extended from integral derivative to fractional derivative, which has more flexibility to describe viscoelastic fluid’s complex dynamic process and provide a theoretical basis for industrial processing.

中文翻译：

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广义傅里叶定律的不稳定麦克斯韦流体的滞止点流动和热传递到与时间有关的拉伸板上

目的

这项研究的目的是研究部分麦克斯韦流体向时间幂律相关的拉伸板的非稳态停滞点流动和传热。根据边界层压力的特征，首先采用分数麦克斯韦模型建立了动量方程，以分析非定常滞留点流。此外，在对流换热的能量方程和边界条件中考虑了广义傅立叶定律。

设计/方法/方法

非线性分数阶微分方程是通过新开发的有限差分格式结合L1算法求解的，其收敛性通过构造一个数值示例进行了验证。

发现

可以揭示一些有趣的结果。速度的分数微分参数越大，促进流动，温度的分数微分参数越小，则促进热传递。温度边界层比速度边界层厚，并且速度随着停滞参数的增加而增大。这是因为当Prandtl数<1时，热扩散的能力大于动量扩散的能力。可以观察到，所有温度曲线首先都有一点升高，然后迅速降低，这表明了麦克斯韦流体的热阻滞。

创意/价值

麦克斯韦流体的非稳态驻点流模型从积分导数扩展到分数导数，为描述粘弹性流体的复杂动力学过程提供了更大的灵活性，为工业加工提供了理论依据。