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| '''Reynolds analogy''' is popularly known to relate turbulent momentum and heat transfer.<ref name=Gean>Geankoplis, C.J. ''Transport processes and separation process principles'' (2003), Fourth Edition, p. 475.</ref> The main assumption is that heat flux q/A in a turbulent system is analogous to momentum flux τ, which suggests that the ratio τ/(q/A) must be constant for all radial positions.
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| The complete Reynolds analogy* is:
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| <math> \frac{f}{2} = \frac{h}{C_p\times G} = \frac{k'_c}{V_{av}} </math>
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| Experimental data for gas streams agree approximately with above equation if the [[Schmidt number|Schmidt]] and [[Prandtl number|Prandtl]] numbers are near 1.0 and only [[skin friction]] is present in flow past a flat plate or inside a pipe. When liquids are present and/or [[form drag]] is present, the analogy is conventionally known to be invalid.<ref name=Gean/>
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| In 2008, the qualitative form of validity of Reynolds' analogy was re-visited for laminar flow of incompressible fluid with variable dynamic viscosity (μ).<ref name=Mah>Mahulikar, S.P., & Herwig, H., 'Fluid friction in incompressible laminar convection: Reynolds' analogy revisited for variable fluid properties,' ''European Physical Journal B: Condensed Matter & Complex Systems'', '''62(1)''', (2008), pp. 77-86.</ref> It was shown that the inverse dependence of Reynolds number (''Re'') and skin friction coefficient(''c''<sub>f</sub>) is the basis for validity of the Reynolds’ analogy, in laminar convective flows with constant & variable μ. For μ = const. it reduces to the popular form of Stanton number (''St'') increasing with increasing ''Re'', whereas for variable μ it reduces to ''St'' increasing with decreasing ''Re''. Consequently, the Chilton-Colburn analogy of ''St''•''Pr''<sup>2/3</sup> increasing with increasing ''c''<sub>f</sub> is qualitatively valid whenever the
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| Reynolds’ analogy is valid. Further, the validity of the Reynolds’ analogy is linked to the applicability of Prigogine's Theorem of Minimum Entropy Production.<ref>Prigogine, I. ''Introduction to Thermodynamics of Irreversible Processes'' (1961), Interscience Publishers, New York.</ref> Thus, Reynolds' analogy is valid for flows that are close to developed, for whom, changes in the gradients of field variables (velocity & temperature) along the flow are small.<ref name=Mah/>
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| ==See also==
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| * [[Reynolds number]]
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| * [[Chilton and Colburn J-factor analogy]]
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| ==References==
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| <references/>
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| <!-- Categories -->
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| [[Category:Chemical engineering]]
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| [[Category:Analogy]]
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