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Exact solution of flow in a composite porous channel

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article concerns fully developed laminar flow of a viscous incompressible fluid in a long composite cylindrical channel. Channel consist of three regions. Outer and inner regions are of uniform permeability and mid region is a clear region. Brinkman equation is used as a governing equation of motion in the porous region and Stokes equation is used for the clear fluid region. Analytical expressions for velocity profiles, rate of volume flow and shear stress on the boundaries surface are obtained and exhibited graphically. Effect of permeability variation parameter on the flow characteristics has been discussed.
Rocznik
Strony
97--110
Opis fizyczny
Bibliogr. 20 poz., rys., tab., wykr.
Twórcy
  • Department of Mathematics and Astronomy, University of Lucknow, India.
  • Department of Mathematics and Astronomy, University of Lucknow, India
Bibliografia
  • [1] A.K. Al-Hadhrami, L. Elliot, D.B. Ingham, and X. Wen. Analytical solutions of fluid flows through composite channels. Journal of Porous Media, 4(2), 2001. doi: 10.1615/JPorMedia.v4.i2.50.
  • [2] A.K. Al-Hadhrami, L. Elliot, D.B. Ingham, and X. Wen. Fluid flows through two-dimensional channel of composite materials. Transport in Porous Media, 45(2):281–300, 2001. doi: 10.1023/A:1012084706715.
  • [3] A. Haji-Sheikh and K. Vafai. Analysis of flow and heat transfer in porous media imbedded inside various-shaped ducts. International Journal of Heat and Mass Transfer, 47(8-9):1889–1905, 2004. doi: 10.1016/j.ijheatmasstransfer.2003.09.030.
  • [4] A.V. Kuznetsov. Analytical investigation of Couette flow in a composite channel partially filled with a porous medium and partially with a clear fluid. International Journal of Heat and Mass Transfer, 41(16):2556–2560, 1998. doi: 10.1016/S0017-9310(97)00296-2.
  • [5] C.Y. Wang. Analytical solution for forced convection in a semi-circular channel filled with a porous medium. Transport in Porous Media, 73(3):369–378, 2008. doi: 10.1007/s11242-007-9177-5.
  • [6] D.A. Nield, S.L.M. Junqueira, and J.L. Lage. Forced convection in a fluid-saturated porous medium channel with isothermal or isoflux boundaries. Journal of Fluid Mechanics, 322:201–214, 1996. doi: 10.1017/S0022112096002765.
  • [7] H.C. Brinkman. On the permeability of media consisting of closely packed porous particles. Applied Scientific Research, 1:81–86, 1949. doi: 10.1007/BF02120318.
  • [8] I. Pop and P. Cheng. Flow past a circular cylinder embedded in a porous medium based on the Brinkman model. International Journal of Engineering Science, 30(2):257–262, 1992. doi: 10.1016/0020-7225(92)90058-O.
  • [9] K. Hooman and H. Gurgenci. A theoretical analysis of forced convection in a porous saturated circular tube: Brinkman-Forchheimer model. Transport in Porous Media, 69:289–300, 2007. doi: 10.1007/s11242-006-9074-3.
  • [10] K. Vafai and S.J. Kim. Forced convection in a channel filled with a porous medium: An exact solution. Journal of Heat Transfer, 111(4):1103–1106, 1989. doi: 10.1115/1.3250779.
  • [11] M. Kaviany. Laminar flow through a porous channel bounded by isothermal parallel plates. International Journal of Heat and Mass Transfer, 28(4):851–858, 1985. doi: 10.1016/0017-9310(85)90234-0.
  • [12] M. Parang and M. Keyhani. Boundary effects in laminar mixed convection flow through an annular porous medium. Journal of Heat Transfer, 109(4):1039–1041, 1987. doi: 10.1115/1.3248179.
  • [13] P. Vadasz. Fluid flow through heterogenous porous media in a rotating square channel. Transport in Porous Media, 12(1):43–54, 1993. doi: 10.1007/BF00616361.
  • [14] S. Chikh, A. Boumedien, K. Bouhadef, and G. Lauriat. Analytical solution of non-Darcian forced convection in an annular duct partially filled with a porous medium.International Journal of Heat and Mass Transfer, 38(9):1543–1551, 1995. doi: 10.1016/0017-9310(94)00295-7.
  • [15] S. Govender. An analytical solution for fully developed flow in a curved porous channel for theparticular case of monotonic permeability variation. Transport in Porous Media, 64:189–198, 2006. doi: 10.1007/s11242-005-2811-1.
  • [16] S.K. Singh and V.K. Verma. Flow in a composite porous cylindrical channel covered with a porous layer of varaible permeability. Special Topics & Reviews in Porous Media – An International Journal, 10(3):291–303, 2019.
  • [17] V.K. Verma and S. Datta. Flow in a channel filled by heterogeneous porous mediuum with a linear permeability variation. Special Topics & Reviews in Porous Media – An International Journal, 3(3):201–208, 2012. doi: 10.1615/SpecialTopicsRevPorousMedia.v3.i3.10.
  • [18] V.K. Verma and S.K. Singh. Flow in a composite porous cylindrical channel of variable permeability covered with porous layer of uniform permeability. International Journal of Pure and Applied Mathematics, 118(2):321–334, 2018.
  • [19] V.K. Verma and H. Verma. Exact solutions of flow past a porous cylindrical shell. Special Topics & Reviews in Porous Media – An International Journal, 9(1):91–99, 2018. doi: 10.1615/SpecialTopicsRevPorousMedia.v9.i1.110.
  • [20] M. Abramowitz and I.A. Stegun. A Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Dover Publications, New York, 1972.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bf781260-ebf1-458a-a990-fe06990f32d5
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