doiSerbia

Anomalous diffusion and heat transfer on comb structure with anisotropic relaxation in fractal porous media

Wang Zhaoyang (School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China)
Zheng Liancun (School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China), liancunzheng@ustb.edu.cn
Ma Lianxi (Department of Physics, Blinn College, Bryan, Texas, USA)
Chen Goong (Department of Mathematics and Institute for Quantum Science and Engineering, Texas A&M University, College Station, USA)

A kind of anomalous diffusion and heat transfer on a comb structure with anisotropic relaxation are studied, which can be used to model many problems in bio-logic and nature in fractal porous media. The Hausdorff derivative is introduced and new governing equations is formulated in view of fractal dimension. Numerical solutions are obtained and the Fox H-function analytical solutions is given for special cases. The particles spatial-temporal evolution and the mean square displacement vs. time are presented. The effects of backbone and finger relaxation parameters, and the time fractal parameter are discussed. Results show that the mean square displacement decreases with the increase of backbone parameter or the decrease of finger relaxation parameter in a short of time, but they have little effect on mean square displacement in a long period. Particularly, the mean square displacement has time dependence in the form of tα/2 (0 < α ≤ 1)when t>τ, which indicates that the diffusion is an anomalous sub-diffusion and heat transfer.

Keywords: Hausdorff derivative, anomalous diffusion and heat transfer, particles transport, mean square displacement, anisotropic relaxation