Anomalous Diffusion in Finite Length Fingers Comb Frame with the Effects of Time and Space Riesz Fractional Cattaneo-Christov Flux and Poiseuille Flow (Journal of Computational Mathematics, 2018)
This paper presents an investigation on the anomalous diffusion in finite length fingerscomb frame, the time and space Riesz fractional Cattaneo-Christov flux is introducedwith the Oldroyds' upper convective derivative and the effect of Poiseuille flow is alsotaken into account. Formulated governing equation possesses the coexisting characteristicsof parabolicity and hyperbolicity. Numerical solution is obtained by the L1-scheme andshifted Grünwald formulae, which is verified by introducing a source item to constructan exact solution. The effects, such as time and space fractional parameters, relaxationparameter and the ratio of the pressure gradient and viscosity coefficient, on the spatialand temporal evolution of particles distribution and dynamic characteristics are showngraphically and analyzed in detail.
Keywords: Anomalous diffusion; Cattaneo-Christov flux; Fractional derivative; Poiseuille flow; Distribution.