In this paper, a series of generalized-formed equations describing the fluid flow, combined with the heat and mass transfer of viscoelastic fluid under the impacts of Dufour and Soret effects are presented. The constitutive relation of viscoelastic fluid, modified Fick’s model and Fourier’s law are all considered as fractional types. Assume that the ultrafiltration process happens in a funnel, and this particular convex domain renders the problem real and more difficult. The highlight of this work is to deal with a series of complex and coupled controlling equations on a funnel-shaped domain. A finite volume method with unstructured grid mesh is adopted, and presented in details. The verified numerical results show that the algorithm is effective, and the numerical method has a good accuracy even with a coarse mesh.

在本文中，提出了一系列描述流体流动的广义形成方程，以及在 Dufour 和 Soret 效应的影响下粘弹性流体的传热和传质。粘弹性流体的本构关系、修正的菲克模型和傅里叶定律都被认为是分数类型。假设超滤过程发生在一个漏斗中，这个特殊的凸域使问题变得真实且更加困难。这项工作的亮点是处理漏斗形域上的一系列复杂且耦合的控制方程。采用非结构化网格的有限体积法，并进行了详细介绍。数值验证结果表明该算法是有效的，该数值方法即使在粗网格下也具有良好的精度。