Solving generalized fractional problem on a funnel-shaped domain depicting viscoelastic fluid in porous medium. (December 2022) - Li, Jia; Li, Botong; Meng, Yahui
Abstract: 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.