Chilton and Colburn J-factor analogy

1. Chilton and Colburn J-factor analogy Recall: The equation for heat transfer in the turbulent regime Sieder-Tate Equation (for forced convection/ turbulent, Re > 10000 & 0.5 < Pr < 100) If we divide this by

2. Dimensionless Groups

3. Chilton and Colburn J-factor analogy This can be rearranged as For the turbulent flow region, an empirical equation relating f and Re

4. Chilton and Colburn J-factor analogy This is called as the J-factor for heat transfer

5. Chilton and Colburn J-factor analogy In a similar manner, we can relate the mass transfer and momentum transfer using the equation for mass transfer of all liquids and gases If we divide this by

6. Chilton and Colburn J-factor analogy T

7. Chilton and Colburn J-factor analogy This is called as the J-factor for mass transfer

8. Chilton and Colburn J-factor analogy Extends the Reynolds analogy to liquids

9. Chilton and Colburn J-factor analogy If we let Applies to the following ranges: For heat transfer:10,000 < Re < 300,000 0.6 < Pr < 100 For mass transfer: 2,000 < Re < 300,000 0.6 < Sc < 2,500

10. Martinelli Analogy Reynolds Analogy  demonstrates similarity of mechanism (the gradients are assumed equal)  Pr = 1 and Sc = 1 Chilton-Colburn J-factor Analogy  demonstrates numerical similarity (implies that the correlation equations are not faithful statements of the mechanism, but useful in predicting numerical values of coefficients  wider range of Pr and Sc

11. Martinelli Analogy Martinelli Analogy (heat and momentum transfer)  applicable to the entire range of Pr number Assumptions: The T driving forces between the wall and the fluid is small enough so that μ/μ1 = 1 Well-developed turbulent flow exists within the test section Heat flux across the tube wall is constant along the test section Both stress and heat flux are zero at the center of the tube and increases linearly with radius to a maximum at the wall At any point εq = ετ

12. Martinelli Analogy Assumptions: 6. The velocity profile distribution given by Figure 12.5 is valid

13. Martinelli Analogy Both equal to zero; For cylindrical geometry

14. Martinelli Analogy Integrated and expressed as function of position Converted in the form Both equal to zero; For cylindrical geometry

15. Martinelli Analogy

16. Martinelli Analogy Martinelli Analogy (heat and momentum transfer)  applicable to the entire range of Pr number  predicts Nu for liquid metals  contributes to understanding of the mechanism of heat and momentum transfer

17. Martinelli Analogy Martinelli Analogy (heat and momentum transfer)  applicable to the entire range of Pr number  predicts Nu for liquid metals  contributes to understanding of the mechanism of heat and momentum transfer

18. Analogies EXAMPLE Compare the value of the Nusselt number, given by the appropriate empirical equation, to that predicted by the Reynolds, Colburn and Martinelli analogies for each of the following substances at Re= 100,000 and f = 0.0046. Consider all substances at 1000F, subject to heating with the tube wall at 1500F.

19. Example Sample Calculation For air,

20. Example Sample Calculation For air, by Reynolds analogy

21. Example Sample Calculation For air, by Colburn analogy

22. Example Sample Calculation For air, by Martinelli analogy

23. FIN