Exact steady-state solution to air pumping from underground partly covered by an impermeable tarp
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A pipe is located in a semi-infinite two-dimensional porous medium partially covered by a tarp. A constant pressure gradient may be imposed at infinity on the medium while air is pumped into the pipe. The governing Laplace equation is solved by extending the famous Keldysh–Sedov formulae to doubly connected domains by reduction of the mixed problem to a Riemann–Hilbert problem with discontinuous coefficients; the solution is obtained by combining factorization and functional equations. Then, the influence of the various geometrical and flow parameters is presented and discussed.
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- 3.Lavrentiev, M., Shabat, B.: Methods of the Theory of Functions of a Complex Variable. Moscow: Nauka (Russian). German translation: Lawrentjew M, Shabat B 1967 Methoden der komplexen Funktionentheorie. VEB Deutscher Verlag der Wiss., Berlin (1987)Google Scholar
- 4.Leontiou, T., Ikram, M., Beketayev, K., Fyrillas, M.M.: Heat transfer enhancement of a periodic array of isothermal pipes Int. J. Therm. Sci. 104, 480–488 (2016). https://doi.org/10.1016/j.ijthermalsci.2016.02.001 CrossRefGoogle Scholar
- 8.Vasil’ev, V.A.: On the shape of a groundwater mound with infiltration between two drains on an impermeable layer. Prikladnaya Matematika i Mekhanika (PMM) 19, 106–108 (1955). (in Russian)Google Scholar
- 11.Gakhov, F.D.: Boundary Value Problems. 3rd edn. Nauka , Moscow (in Russian) (1977); Engl. transl. of 1st ed. Pergamon Press, Oxford (1966)Google Scholar