Anomalous Diffusion in Finite Length Fingers Comb Frame with the Effects of Time and Space Riesz Fractional Cattaneo-Christov Flux and Poiseuille Flow

Authors

  • Lin Liu School of Mathematics and Physics and School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China
  • Liancun Zheng School of Mathematics and Physics and School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China
  • Fawang Liu School of Energy and Environmental Engineering, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
  • Xinxin Zhang School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China

DOI:

https://doi.org/10.4208/jcm.1702-m2016-0627

Keywords:

Anomalous diffusion, Cattaneo-Christov flux, Fractional derivative, Poiseuille flow, Distribution.

Abstract

This paper presents an investigation on the anomalous diffusion in finite length fingers comb frame, the time and space Riesz fractional Cattaneo-Christov flux is introduced with the Oldroyds' upper convective derivative and the effect of Poiseuille flow is also taken into account. Formulated governing equation possesses the coexisting characteristics of parabolicity and hyperbolicity. Numerical solution is obtained by the L1-scheme and shifted Grünwald formulae, which is verified by introducing a source item to construct an exact solution. The effects, such as time and space fractional parameters, relaxation parameter and the ratio of the pressure gradient and viscosity coefficient, on the spatial and temporal evolution of particles distribution and dynamic characteristics are shown graphically and analyzed in detail.

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Published

2018-09-17

Issue

Vol. 36 No. 4 (2018)

Section

Articles