6533b7defe1ef96bd1275dde

RESEARCH PRODUCT

Laminar flow through fractal porous materials: the fractional-order transport equation

Gianluca AlaimoMassimiliano Zingales

subject

Numerical AnalysisApplied MathematicsMathematical analysisLaminar flowViscous liquidFractional calculuFractional calculusPhysics::Fluid DynamicsTransport equationFractals; Fractional calculus; Transport equations; Modeling and Simulation; Numerical Analysis; Applied MathematicsFractalModeling and SimulationFractalSettore ICAR/08 - Scienza Delle CostruzioniConvection–diffusion equationPorosityPorous mediumNumerical AnalysiScalingMathematics

description

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.

yearjournalcountryeditionlanguage
2015-05-01Communications in Nonlinear Science and Numerical Simulation
https://doi.org/10.1016/j.cnsns.2014.10.005