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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

Special Issues: Inverse problems in the natural and social sciences

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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