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Temperature profiles of local thermal nonequilibrium for thermal developing forced convection in porous medium parallel plate channel

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Abstract

Based on the two-energy equation model, taking into account viscous dissipation due to the interaction between solid skeleton and pore fluid flow, temperature expressions of the solid skeleton and pore fluid flow are obtained analytically for the thermally developing forced convection in a saturated porous medium parallel plate channel, with walls being at constant temperature. It is proved that the temperatures of the two phases for the local thermal nonequilibrium approach to the temperature derived from the one-energy equation model for the local thermal equilibrium when the heat exchange coefficient goes to infinite. The temperature profiles are shown in figures for different dimensionless parameters and the effects of the parameters on the local thermal nonequilibrium are revealed by parameter study.

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References

  1. de Boer R. Theory of Porous Media: Highlights in the Historical Development and Current State[M]. Springer-Verlag, Berlin, Heidelberg, 2000.

    Google Scholar 

  2. Voller V R, Peng S. An algorithm for analysis of polymer filling of molds[J]. Poly Eng Science, 1995, 35(22):1758–1765.

    Article  Google Scholar 

  3. Schrefler B A, Pesavento F. Multiphase flow in deforming porous material[J]. Computer and Geotechnics, 2004, 31(3):237–250.

    Article  Google Scholar 

  4. Spiga G, Spiga M. A rigorous solution to a heat transfer two-phase model in porous media and packed beds[J]. Heat Mass Transfer, 1981, 24(2):355–364.

    Article  MATH  MathSciNet  Google Scholar 

  5. Schrefler B A. Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions[J]. Appl Mech Rev, 2002, 55(4):351–388.

    Article  Google Scholar 

  6. Nield D A, Bejan A. Convection in Porous Media[M]. Second Ed. Spring-Verlag, New York, 1999.

    Google Scholar 

  7. Haji-Sheikh A, Vafai K. Analysis of flow and heat transfer in porous media imbedded inside various-shaped ducts[J]. Heat Mass Transfer, 2004, 47(8/9):1889–1905.

    MATH  Google Scholar 

  8. Simacek P, Advani S G. An analytic solution for the temperature distribution in flow through porous media in narrow gaps: I—linear injection[J]. Heat Mass Transfer, 2001, 38(1/2):25–33.

    Article  Google Scholar 

  9. Kuznetsov A V, Ming Xiong, Nield D A. Thermally developing forced convection in a porous medium: circular duct with walls at constant temperature, with longitudinal conduction and viscous dissipation effects[J]. Transport in Porous Media, 2003, 53(3):331–345.

    Article  MathSciNet  Google Scholar 

  10. Nield D A, Kuznetsov A V. Thermally developing forced convection in a channel occupied by a porous medium saturated by a non-Newtonian fluid[J]. Heat Mass Transfer, 2005, 48(6):1214–1218.

    Article  Google Scholar 

  11. Nield D A. Effects of local thermal nonequilibrium in steady convection processes in a saturated porous medium: forced convection in a channel[J]. Porous Media, 1998, 1(2):181–186.

    MATH  Google Scholar 

  12. Nield D A, Kuznetsov A V. Local thermal nonequilibrium effects in forced convection in a porous medium channel: a conjugate problem[J]. Heat Mass Transfer, 1999, 42(17):3245–3252.

    Article  MATH  Google Scholar 

  13. Ming Xiong, Nield D A, Kuznetsov A V. Effect of local non-equilibrium on thermally developing forced convection in a porous medium[J]. Heat Mass Transfer, 2002, 45(25):4949–4955.

    Article  Google Scholar 

  14. Quintard M, Whitaker S. Two-medium treatment of heat transfer in porous media: numerical results for effective properties[J]. Adv Water Resour, 1997, 20(2/3):77–94.

    Article  Google Scholar 

  15. Zhang H Y, Huang X Y. A two-equation analysis of convection heat transfer in porous media[J]. Transport in Porous Media, 2001, 44(2):305–324.

    Article  Google Scholar 

  16. Yang Xiao. Gurtin-type variational principles for dynamics of a non-local thermal equilibrium saturated porous medium[J]. Acta Mechanica Solida Sinica, 2005, 18(1):37–45.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanics, Shanghai University, Shanghai, 200444, P. R. China

    Yang Xiao  (杨骁) (Professor) & Liu Xue-mei  (刘雪梅)

  2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P. R. China

    Yang Xiao  (杨骁) (Professor) & Liu Xue-mei  (刘雪梅)

Authors
  1. Yang Xiao  (杨骁)
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  2. Liu Xue-mei  (刘雪梅)
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Corresponding author

Correspondence to Yang Xiao  (杨骁).

Additional information

Communicated by CHENG Chang-jun

Project supported by the National Natural Science Foundation of China (No. 10272070) and the Shanghai Leading Academic Discipline Project (No. Y0103)

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Yang, X., Liu, Xm. Temperature profiles of local thermal nonequilibrium for thermal developing forced convection in porous medium parallel plate channel. Appl Math Mech 27, 1123–1131 (2006). https://doi.org/10.1007/s10483-006-0813-z

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  • DOI: https://doi.org/10.1007/s10483-006-0813-z

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Chinese Library Classification

2000 Mathematics Subject Classification

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