TY - JOUR
TI - Anomalous diffusion and heat transfer on comb structure with anisotropic relaxation in fractal porous media
AU - Wang Zhaoyang
AU - Zheng Liancun
AU - Ma Lianxi
AU - Chen Goong
JN - Thermal Science
PY - 2021
VL - 25
IS - 1
SP - 733
EP - 742
PT - Article
AB - 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.