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Thermodynamic’s Second Law Analysis for Laminar Non-Newtonian Fluid Flow

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Abstract

In this paper, the entropy generation of a non-Newtonian fluid such as Tho2 inside a circular channel with constant surface temperature has been investigated. The pressure gradient along the pipe line, the difference between the dimensionless inlet wall temperature and fluid temperature and modified Stanton number are the key elements to calculate the entropy generation for three different non-Newtonian fluids. Also the variation of the dimensionless entropy generation and the pumping power to heat transfer rate ratio is calculated for two different cases, the first case involves fixed pipe length and variable inlet temperature and the second case considers fixed fluid inlet temperature and variable pipe length.

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Abbreviations

C p :

specific heat capacity (J/kg K)

R :

pipe radius (m)

Ec :

Eckert number [ \(\bar{U}^2/[C_{p} (T_{\rm w} -T_0 )\)]]

f :

friction factor

\(\bar {h}\) :

average heat transfer coefficient (W/m2 K)

\(\bar{h}_{\rm c.p}\) :

constant property average heat transfer coefficient (W/m2 K)

k :

thermal conductivity (W/m K)

l :

length of the pipe (m)

\(\dot{m}\) :

mass flow rate (kg/s)

P :

pressure (N/m2)

τ0 :

yield

μ0 :

viscosity yield shear stress (Ns/m2)

τ R :

shear stress in R radius (N/m2)

T 0 :

inlet fluid temperature (K)

R p :

ratio of the plug radius to pipe radius =  \(({r_{\rm p}}/{R})\)

Q :

flow flux m3/s

Re :

Reynolds number \(\rho \bar {U}D/\mu]\)

s :

entropy (J/kg K)

\(\dot{S}_{\rm gen}\) :

entropy generation (W/K)

St :

Stanton number \([\bar{h}/(\rho \bar {U}(C_{p} )]\)

T :

temperature (K)

T ref :

reference temperature (=293 K)

T w :

wall temperature the pipe (K)

\(\bar {U}\) :

fluid bulk velocity (m/s)

P r :

pumping power to heat transfer rate ratio

Ψ:

dimensionless entropy generation [ \(\dot {S}_{\rm gen}/[\dot{Q}/ (T_{\rm w} -T_0)\)]

D :

Pipe diameter (m)

λ:

dimensionless axial distance [l/D]

Π1 :

modified Stanton number [St λ]

Π2 :

dimensionless group [Ec/(St Re)]

ρ:

density (kg/m3)

τ:

dimensionless inlet wall-to-fluid

μb :

viscosity of fluid at bulk temperature (N s/ m2)

x :

axial distance (m)

ΔT :

increase of fluid temperature (K)

μ:

viscosity (N s/ m2)

r 0 :

plug radius for Bingham fluid (m)

r p :

plug radius for Casson model (m)

V z :

velocity along the pipe for Bingham model (m/s)

n :

the degree of non-Newtonian fluid for power-law model

References

  1. Bejan A. (1979) ASME, J. Heat Transfer 101:718–725

    Google Scholar 

  2. Bejan A. (1980) Energy 5:721–732

    Article  Google Scholar 

  3. Bejan A. (1982) Adv. Heat Transfer 15:1–58

    Google Scholar 

  4. Bejan A. (1988) Advanced Engineering Thermodynamics. John Wiley & Sons Inc., New York, pp. 594–602

    Google Scholar 

  5. Carrington C. G., Sun Z. F. (1992) Int. J. Heat Fluid Flow 13:65–70

    Article  Google Scholar 

  6. Gbadebo A. S., Yilbas B. S., Boron K. (1999) Int. J. Energy Res. 23:1101–1110

    Article  Google Scholar 

  7. Kays W. M., London A. L. (1958) Compact Heat Exchangers. Mc Graw-Hill, New-York, p. 49

    Google Scholar 

  8. Knudsen M. (1934) the Kinetic Theory of Gases. Methuen, London

    MATH  Google Scholar 

  9. Kennard E. H. (1938) Kinetic Theory of Gases. Mc Graw-Hill, New-York

    Google Scholar 

  10. J. A. Lane, MacPherson and F. Masalan, Transport phenomena (Addison-Wesley, Reading, Mass., 1958), Contributed by Thomas, D.G.

  11. H. G. Langeroudi and C. Aghanajafi, Int. J. Fusion Energy, 25, (this issue) (2006)

  12. Metzner A. B. (1956) Advanced in Chemical Engineering, VolI. Academic Press, New York, p. 103

    Google Scholar 

  13. Patterson G. N. (1956) Molecular Flow of Gases. Wiley, New York

    MATH  Google Scholar 

  14. Perry J. H. (1950) Chemical Engineers Hand Book. Mc Graw-Hill, New York, Third Edition, pp. 388–389

    Google Scholar 

  15. M. Reiner, In F. R. Eirich (Ed.), Phenomenological Macrorheology, Chapter 2 in Rheology, Vol. 1 (Academic Press, New York, 1956), p. 45

  16. Reiner M. (1960) Deformation, Strain, and flow. Interscience, New York

    Google Scholar 

  17. Sahin A. Z. (1998) Int. J. Heat Mass Transfer 120:76–83

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanical Engineering, K.N.T. University of Technology, Tehran, Iran

    H. G. Langeroudi & C. Aghanajafi

Authors
  1. H. G. Langeroudi
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  2. C. Aghanajafi
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Correspondence to H. G. Langeroudi.

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Langeroudi, H.G., Aghanajafi, C. Thermodynamic’s Second Law Analysis for Laminar Non-Newtonian Fluid Flow. J Fusion Energ 25, 165–173 (2006). https://doi.org/10.1007/s10894-006-9014-9

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