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NSM analysis of time-dependent nonlinear buoyancy-driven double-diffusive radiative convection flow in non-Darcy geological porous media

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Abstract

A network numerical simulator is developed and described to simulate the transient, nonlinear buoyancy-driven double diffusive heat and mass transfer of a viscous, incompressible, gray, absorbing–emitting fluid flowing past an impulsively started moving vertical plate adjacent to a non-Darcian geological porous regime. The governing boundary-layer equations are formulated in an (X *, Y *, t *) coordinate system with appropriate boundary conditions. An algebraic diffusion approximation is used to simplify the radiation heat transfer contribution. The non-dimensionalized transport equations are solved in an (X, Y, t) coordinate system using the network simulation model (NSM) and the computer code, Pspice. A detailed discussion of the network design is provided. The effects of Prandtl number, radiation–conduction parameter (Stark number), thermal Grashof number, species Grashof number, Schmidt number, Darcy number and Forchheimer number on the transient dimensionless velocities (U, V), non-dimensional temperature (T) and dimensionless concentration function (C) are illustrated graphically. Additionally, we have computed plots of U, V, T, C versus time and average Nusselt number and Sherwood number versus X, Y coordinate, for various thermophysical parameters. The model finds applications in geological contamination, geothermal energy systems and radioactive waste-repository near-field thermo-geofluid mechanics.

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References

  1. Bear J., Bachmat Y.: Introduction to Modelling of Groundwater Pollution. Dordrecht, Netherlands (1987)

    Google Scholar 

  2. Bég, O.A.: Advanced Mathematical Modelling in Fire Safety Engineering Science, p 400 (2007, in press)

  3. Armstead H.C.: Geothermal Energy. EN Spon, London (1982)

    Google Scholar 

  4. Bég O.A., Takhar H.S., Kumari M.: Computational analysis of coupled radiation convection dissipative flow in a porous medium using the Keller-Box implicit difference scheme. Int. J. Energy Res. 22, 141–159 (1998)

    Article  Google Scholar 

  5. Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media. Elsevier Science, Oxford (1998)

    MATH  Google Scholar 

  6. Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (1992)

    Google Scholar 

  7. Bathe K.J.: Finite Element Procedures. Prentice-Hall, USA (1996)

    Google Scholar 

  8. Bég O.A., Prasad V., Takhar H.S., Soundalgekar V.M.: Thermo-convective flow in an isotropic, homogenous porous medium using Brinkman’s model: numerical study. Int. J. Numer. Methods Heat Fluid Flow 8, 59–89 (1998)

    Article  Google Scholar 

  9. Ligget J.A., Liu P.L.F.: The Boundary Integral Equation Method for Porous Media Flow. Allen & Unwin, London (1983)

    Google Scholar 

  10. Bég O.A., Bhargava R., Rawat S., Takhar H.S., Bég T.A.: Finite element modelling of laminar flow of a third grade fluid in a Darcy-Forchheimer porous medium with suction effects. Int. J. Appl. Mech. Eng. 12(1), 215–233 (2007)

    Google Scholar 

  11. Bég O.A., Takhar H.S., Bég T.A., Chamkha A.J., Nath G., Majeed R.: Modelling convection heat transfer in a rotating fluid in a thermally-stratified high-porosity medium: numerical finite difference solutions. Int. J. Fluid Mech. Res. 32(4), 383–401 (2005)

    Article  MathSciNet  Google Scholar 

  12. Zueco J., Alhama F.: Simultaneous inverse determination of the temperature-dependent thermophysical properties of fluids using the network simulation method. Int. J. Heat Mass Transf. 50, 3234–3243 (2007)

    Article  MATH  Google Scholar 

  13. Zueco Jordan J.: Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to constant heat flux. Int. J. Eng. Sci. 44, 1380–1393 (2006)

    Article  Google Scholar 

  14. Zueco, J.: Unsteady free convection–radiation flow over a vertical wall embedded in a porous medium. Commun. Numer. Method Eng. (in press)

  15. Singh P., Misra J.K., Narayan K.A.: Free convection along a vertical wall in a porous medium with periodic permeability variation. Int. J. Numer. Anal. Methods Geomech. 13(4), 443–450 (1989)

    Article  MATH  Google Scholar 

  16. Thomas H.R., Li C.L.W.: Modelling transient heat and moisture transfer in unsaturated soil using a parallel computing approach. Int. J. Numer. Anal. Methods Geomech. 19(5), 345–366 (1989)

    Article  Google Scholar 

  17. Chen G.J., Ledesma A.: Coupled solution of heat and moisture flow in unsaturated clay barriers in a repository geometry. Int. J. Numer. Anal. Methods Geomech. 31(8), 1045–1065 (2007)

    Article  Google Scholar 

  18. Bég, O.A., Bég, T.A., Takhar, H.S., Warke, A.S., Das, S.K.: Mathematical modeling of subsurface contaminant transport with simultaneous first order chemical reaction and second order decay using the ADI scheme. In: HEFAT 2005, 4th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Cairo, Egypt, September (2005)

  19. Dybbs A., Edwards R.V.: A new look at porous media fluid mechanics: Darcy to turbulent. In: Bear, Corapcioglu(eds) Fundamentals of Transport Phenomena in Porous Media. NATO Applied Science Series E, pp. 199–256. Martinus Nijhoff, The Netherlands (1984)

    Google Scholar 

  20. Chamkha A.J., Takhar H.S., Bég O.A.: Numerical modeling of Darcy–Brinkman–Forcheimmer magneto hydro-dynamic mixed convection flow in a porous medium with transpiration and viscous heating. Int. J. Fluid Mech. Res. 29(1), 1–26 (2002)

    Google Scholar 

  21. Skejtne E., Auriault J.L.: New insights on steady, nonlinear flow in porous media. Eur. J. Mech. B Fluids 18, 131–145 (1999)

    Article  MathSciNet  Google Scholar 

  22. Mei C.C., Auriault J.L.: The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222, 647–663 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  23. Firdaouss M., Girermond J.L., Le Quere P.: Nonlinear corrections to Darcy’s law at low Reynolds numbers. J. Fluid Mech. 343, 331–350 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  24. Rasoloarijaona M., Auriault J.L.: Nonlinear seepage flow through a rigid porous medium. Eur. J. Mech. B Fluids 13, 1770195 (1994)

    MathSciNet  Google Scholar 

  25. Lage J.L.: The fundamental theory of flow through permeable media from Darcy to turbulence. In: Ingham, D.B., Pop, I.(eds) Transport Phenomena in Porous Media, pp. 1–30. Elsevier Science, Oxford (1998)

    Chapter  Google Scholar 

  26. Kumari, M., Takhar, H.S., Nath, G.: Non-Darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media. Thermo Fluid Dynamics. Wärme-und Stoffübertragung, vol. 23, pp. 267–273 (1988)

  27. Takhar H.S., Bég O.A.: Non-Darcy convective boundary layer flow past a semi-infinite vertical plate in saturated porous media. Heat Mass Transf. J. 32, 33–44 (1996)

    Article  Google Scholar 

  28. Bég, O.A., Bhargava, R., Rawat, S., Halim, K., Takhar, H.S.: Computational modeling of biomagnetic micropolar blood flow and heat transfer in a two-dimensional non-Darcian porous medium. Meccanica (2007, in press)

  29. Bég, O.A., Zueco, J., Takhar, H.S., Sajid, A.: Transient Couette flow in a rotating non-Darcian porous medium parallel-plate configuration—network simulation method solutions. Acta Mech. (accepted)

  30. Siegel R., Howell J.R.: Thermal Radiation Heat Transfer, International Student Edition. MacGraw-Hill, New York (1972)

    Google Scholar 

  31. Hossain M.A., Takhar H.S.: Radiation effects on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transf. J. 31, 243–248 (1996)

    Article  Google Scholar 

  32. Hossain M.A., Alim M.A., Takhar H.S.: Effects of radiation on mixed convection boundary layer flow along a vertical cylinder. Int. J. Appl. Mech. Eng. 3, 393–404 (1998)

    MATH  Google Scholar 

  33. Chamkha A.J., Takhar H.S., Beg O.A.: Radiative free convective non-Newtonian fluid flow past a wedge embedded in a porous medium. Int. J. Fluid Mech. Res. 31, 101–115 (2004)

    Article  Google Scholar 

  34. Domenico P.A., Schwartz F.W.: Physical and Chemical Hydrogeology. Wiley, New York (1990)

    Google Scholar 

  35. Bear J.: Dynamics of Fluids in Porous Media. Dover, New York (1988)

    Google Scholar 

  36. Bég, O.A., Zueco, J., Takhar, H.S., Bég, T.A., Sajid, A.: Transient non-linear optically-thick radiative–convective double-diffusive boundary layers in Darcian media adjacent to an impulsively started surface: network simulation. Int. J. Nonlinear Mech. (submitted)

  37. Raptis A.: Radiation and free convection flow through a porous medium. Int. Commun. Heat Mass Transf. 25, 289–295 (1998)

    Article  Google Scholar 

  38. Prasad V.R., Reddy N.B., Muthucumaraswamy R.: Radiation and mass transfer effects on two-dimensional flow past an impulsively started infinite vertical plate. Int. J. Thermal Sci. 46(12), 1251–1258 (2007)

    Article  Google Scholar 

  39. Zueco J.: Network method to study the transient heat transfer problem in a vertical channel with viscous dissipation. Int. Commun. Heat Mass Transf. 33, 1079–1087 (2006)

    Article  Google Scholar 

  40. Pspice 6.0. Microsim Corporation. Irvine, California 92718 (1994)

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Author notes

  1. O. A. Bég

    Present address: Civil Engineering Program, R-Block, Castle College, Granville Road, Sheffield, S22RL, UK

Authors and Affiliations

  1. Aerodynamics Group, Aerosciences Program, Academic Wing, BAE Systems, Riyadh, 11441, Kingdom of Saudi Arabia

    O. A. Bég

  2. Departamento de Ingeniería Térmica y Fluidos, ETS Ingenieros Industriales, Universidad Politécnica de Cartagena, Campus Muralla del Mar, Cartagena, Murcia, 30203, Spain

    J. Zueco

  3. Engineering Mechanics and Seismic Dynamics Research, 18 Milton Grove, Manchester, M16 OBP, UK

    T. A. Bég

  4. Engineering Department, Manchester Metropolitan University, Manchester, M15GD, UK

    H. S. Takhar

  5. Hydrology, Water Resources and Hydraulics Program, Civil Engineering Department, Istanbul Technical University, Ayazaga, Istanbul, 34469, Turkey

    E. Kahya

Authors
  1. O. A. Bég
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  2. J. Zueco
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  4. H. S. Takhar
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Correspondence to O. A. Bég.

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Bég, O.A., Zueco, J., Bég, T.A. et al. NSM analysis of time-dependent nonlinear buoyancy-driven double-diffusive radiative convection flow in non-Darcy geological porous media. Acta Mech 202, 181–204 (2009). https://doi.org/10.1007/s00707-008-0018-6

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  • DOI: https://doi.org/10.1007/s00707-008-0018-6

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