Hardy–Littlewood maximal function: Difference between revisions
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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. | |||
The complete Reynolds analogy* is: | |||
<math> \frac{f}{2} = \frac{h}{C_p\times G} = \frac{k'_c}{V_{av}} </math> | |||
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/> | |||
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 | |||
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/> | |||
==See also== | |||
* [[Reynolds number]] | |||
* [[Chilton and Colburn J-factor analogy]] | |||
==References== | |||
<references/> | |||
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[[Category:Chemical engineering]] | |||
[[Category:Analogy]] | |||
Revision as of 18:07, 20 January 2014
Reynolds analogy is popularly known to relate turbulent momentum and heat transfer.[1] 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.
The complete Reynolds analogy* is:
Experimental data for gas streams agree approximately with above equation if the Schmidt and 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.[1]
In 2008, the qualitative form of validity of Reynolds' analogy was re-visited for laminar flow of incompressible fluid with variable dynamic viscosity (μ).[2] It was shown that the inverse dependence of Reynolds number (Re) and skin friction coefficient(cf) 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•Pr2/3 increasing with increasing cf is qualitatively valid whenever the Reynolds’ analogy is valid. Further, the validity of the Reynolds’ analogy is linked to the applicability of Prigogine's Theorem of Minimum Entropy Production.[3] 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.[2]
See also
References
- ↑ 1.0 1.1 Geankoplis, C.J. Transport processes and separation process principles (2003), Fourth Edition, p. 475.
- ↑ 2.0 2.1 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.
- ↑ Prigogine, I. Introduction to Thermodynamics of Irreversible Processes (1961), Interscience Publishers, New York.