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Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2049-2062. doi: 10.3934/mbe.2019100
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Renormalization group analysis of heat transfer in the presence of endothermic and exothermic chemical reactions

  • 1.
    Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, 2a, Zhelyabov Str., Kiev, 03057, Ukraine
  • 2.
    Institute of General Mechanical Engineering, TH Köln–University of Applied Sciences, 51643 Gummersbach, Germany
  • Received: 30 November 2018 Accepted: 19 February 2019 Published: 11 March 2019

  • In the present paper, renormalization group methods are used to develop a macroscopic turbulence model for thermal diffusivity in turbulent fluid flow under conditions of endothermic and exothermic chemical reactions in flow. The temperature field is divided into slow (large-scale) and fast (small-scale) modes. With the help of the renormalization procedure, energy equations for the large-scale modes and relations for effective turbulent thermal diffusivity were obtained. It was shown how the type of the chemical reaction affects turbulent thermal diffusivity. In addition, the conditions were identified where effective thermal diffusivity undergoes a sharp growth.

    Citation: Andriy A. Avramenko, Igor V. Shevchuk. Renormalization group analysis of heat transfer in the presence of endothermic and exothermic chemical reactions[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2049-2062. doi: 10.3934/mbe.2019100

    Related Papers:

  • In the present paper, renormalization group methods are used to develop a macroscopic turbulence model for thermal diffusivity in turbulent fluid flow under conditions of endothermic and exothermic chemical reactions in flow. The temperature field is divided into slow (large-scale) and fast (small-scale) modes. With the help of the renormalization procedure, energy equations for the large-scale modes and relations for effective turbulent thermal diffusivity were obtained. It was shown how the type of the chemical reaction affects turbulent thermal diffusivity. In addition, the conditions were identified where effective thermal diffusivity undergoes a sharp growth.


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    [1] M. Gell-Mann and F. Low, Quantum electrodynamics at small distances, Phys. Rev., 95 (1954), 1300–1312.
    [2] K. G. Wilson, Renormalization group and critical phenomena and the Kondo problem, Phys. Rev. B., 4 (1971), 3174–3187.
    [3] R. H. Kraichnan, The structure of isotropic turbulence at very high Reynolds number, J. Fluid Mech., 5 (1959), 497–543.
    [4] D. Forster, D. R. Nelson and M. J. Stephen, Large-distance and longtime properties of a randomly stirred fluid, Phys. Rev. А., 16 (1977), 732–749.
    [5] C. De Dominicis and P. C. Martin, Energy spectra of certain randomly-stirred fluids, Phys. Rev. А., 19 (1979), 419–422.
    [6] J. D. Fournier and U. Frisch, Remarks on the renormalization group in statistical fluid dynamics. Phys. Rev. 28 (1983), 1000–1002.
    [7] V. Yakhot and S. A. Orszag, Renormalization group analysis of turbulence. I. Basic theory, J. Sci. Соmp. 1 (1986), 3–51.
    [8] R. H. Kraichnan, An interpretation of the Yakhot–Orszag turbulence theory, Phys. Fluids, 30 (1987), 2400–2405.
    [9] L. M. Smith and W. С. Reynolds, On the Yakhot–Orszag renormalization group method for deriving turbulence statistics and models, Phys. Fluids A., 4 (1992), 364–390.
    [10] V. Yakhot, S. A. Orszag, S. Thangam, et al., Development of turbulence models for shear flows by double expansion technique, Phys. Fluids A., 4 (1992), 1510–1520.
    [11] R. Rubinstein and J. M. Barton, Nonlinear Reynolds stress models and the renormalization group, Phys. Fluids A., 2 (1990), 1472–1485.
    [12] С. G. Speziale, T. B. Gatski and N. Fitzmaurice, An analysis of RNG based turbulence models for homogeneous shear flow, Phys. Fluids A., 3 (1991), 2278–2281.
    [13] G. L. Eyink, Renormalization group and operator-product expansion in turbulence: shell models, Phys. Rev. E., 48 (1993), 1823–1837.
    [14] G. L. Eyink, The renormalization group method in statistical hydrodynamics, Phys. Fluids., 6 (1994), 3063–3078.
    [15] V. Yakhot and L.M. Smith, The renormalization group, the e-expansion and derivation of turbulence models, J. Sci. Comput., 7 (1992), 35–52.
    [16] A. A. Avramenko and A. V. Kuznetsov, Renormalization group model of large-scale turbulence in porous media, Transport Porous Med., 63 (2006), 175–193.
    [17] A. A. Avramenko, N. P. Dmitrenko and A. I. Tyrinov, Renormalization group analysis of the stability of turbulent flows in porous media, J. Eng. Phys. Thermophys., 89 (2016), 592–605.
    [18] A. A. Avramenko, I. V. Shevchuk, A. V. Kravchuk, et al., Application of renormalization group analysis to two-phase turbulent flows with solid dust particles, J. Math. Physics, 59 (2018), 073101.
    [19] M. P. Martίn and G. V. Candler, Effect of chemical reactions on decaying isotropic turbulence, Phys. Fluids, 10 (1998), 1715–1724.
    [20] S. Subramanian and V. Balakotaiah, Convective instabilities induced by exothermic reactions occurring in a porous medium, Phys. Fluids, 6 (1994), 2907–2922.
    [21] K. A. Maleque, Effects of exothermic/endothermic chemical reactions with Arrhenius activation energy on MHD free convection and mass transfer flow in presence of thermal radiation, J. Thermodynamics, (2013).
    [22] D. T. Conroy and S. G. L. Smith, Endothermic and exothermic chemically reacting plumes, J. Fluid Mech., 612 (2008), 291–310.
    [23] A. A. Avramenko, S. G. Kobzar, I. V. Shevchuk, et al., Symmetry of turbulent boundary layer flows: investigation of different eddy viscosity models, Acta Mechanica, 151 (2001), 1–14.
    [24] A. A. Avramenko, D. G. Blinov, I. V. Shevchuk, et al., Symmetry analysis and self-similar forms of fluid flow and heat-mass transfer in turbulent boundary layer flow of a nanofluid, Phys. Fluids, 24 (2012), 092003.
    [25] A. A. Avramenko, I. V. Shevchuk, S. Abdallah, et al., Symmetry analysis for film boiling of nanofluids on a vertical plate using a nonlinear approach, J. Molecular Liquids, 223 (2016) 156–164.
    [26] W. D. McComb, The Physics of Fluid Turbulence, (1990) Clarendon Press, Oxford.
    [27] J. C. Collins, Renormalization. An introduction to renormalization, the renormalization group and the operator-product expansion, Cambridge university press, (1984), 380.
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