Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media

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ESLAHI NOOSHIN; VATANKHAH ALIREZA; SEDGHI ASL MOHAMMAD

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Journal: Iranian Journal of Soil and Water Research Year:2020 | Volume:51 | Issue:3 Page(s): 563-574

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Information Journal Paper

Title

Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media

Author(s)

ESLAHI NOOSHIN | VATANKHAH ALIREZA | SEDGHI ASL MOHAMMAD | Issue Writer Certificate

Keywords

Fully developed turbulent flowQ1

fractional-order differential modelQ1

free surface profileQ2

NonDarcian flowQ1

analytical solutionQ2

Abstract

In this study, the fractional-order differential equations in range of (0, 1) were used to model the water surface profile under Darcy's law condition in porous medium for a Fully developed turbulent flow. The developed equation is solved analytically. The laboratory model used in this study consists of a coarse-grained porous medium with 6. 4 m length, 0. 8 m width and 1 m height, including rounded corner materials, which are tested for different flow rates and three longitudinal slopes of 0, 4, 20. 3%. Then, parameters of model and porous media were calibrated based on laboratory data. In order to evaluate the proposed analytical solution, the obtained results from fractional-order differential model were compared with the laboratory data. The results showed a satisfactory agreement with experimental data of water surface profile (seepage line) in all three slopes. The maximum error of the proposed model is 3. 5% compared to the experimental data. It can be concluded that the proposed method can provide better description of water surface profile analysis under nonDarcy flow conditions as compared to Darcy model in porous media.

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APA: Copy

ESLAHI, NOOSHIN, SEDGHI ASL, MOHAMMAD, & VATANKHAH, ALIREZA. (2020). Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media. IRANIAN JOURNAL OF SOIL AND WATER RESEARCH, 51(3 ), 563-574. SID. https://sid.ir/paper/396043/en

Vancouver: Copy

ESLAHI NOOSHIN, SEDGHI ASL MOHAMMAD, VATANKHAH ALIREZA. Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media. IRANIAN JOURNAL OF SOIL AND WATER RESEARCH[Internet]. 2020;51(3 ):563-574. Available from: https://sid.ir/paper/396043/en

IEEE: Copy

NOOSHIN ESLAHI, MOHAMMAD SEDGHI ASL, and ALIREZA VATANKHAH, “Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media,” IRANIAN JOURNAL OF SOIL AND WATER RESEARCH, vol. 51, no. 3 , pp. 563–574, 2020, [Online]. Available: https://sid.ir/paper/396043/en

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