Laminar flow through fractal porous materials: The fractional-order transport equation
- Authors: Alaimo, G.; Zingales, M.
- Publication year: 2014
- Type: Articolo in rivista (Articolo in rivista)
- Key words: Fractals; Fractional calculus; Transport equations; Modeling and Simulation; Numerical Analysis; Applied Mathematics
- OA Link: http://hdl.handle.net/10447/215529
Abstract
The anomalous transport of a viscous fluid across a porous media with power-law scaling of the geometrical features of the pores is dealt with in the paper. It has been shown that, assuming a linear force-flux relation for the motion in a porous solid, then a generalized version of the Hagen-Poiseuille equation has been obtained with the aid of Riemann-Liouville fractional derivative. The order of the derivative is related to the scaling property of the considered media yielding an appropriate mechanical picture for the use of generalized fractional-order relations, as recently used in scientific literature.