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Entropy generation analysis for microscale forced convection with radiation in thermal entrance region

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Abstract

In this paper the effects of radiation and dissipation in the entropy generation in microtube is evaluated. Governing equations are solved with analytically solution. Fluid flow in the entrance area is laminar and independent of time, and radiation is also a fluid property. Results in this paper extracted with dimensionless numbers Knudsen (k n ), Brinkman (Br) and Prandtl (Pr) that compared with the case without radiation. It is shown that entropy generation decreases with increasing Knudsen number. It can be observed that increasing Br augments the entropy generation.

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Abbreviations

Br :

Brinkman number (μu 2 m /qw 0)

D :

Tube diameter (m)

x :

Distance along tube (m)

x*:

Dimensionless distance along tube

k f :

Thermal conductivity (w/m k)

k n :

Knudsen number (λ/D)

k′:

Constant

k″:

Constant

N s :

Dimensionless entropy generation

N H :

Dimensionless entropy generation through heat transfer

Q :

Heat flux (w/m2)

r :

Radius (m)

r*:

Dimensionless radius

r 0 :

Channel radius (m)

Re:

Reynolds number (ρu m D/μ)

T :

Temperature (K)

u :

Velocity in x direction (m/s)

u*:

Dimensionless velocity (u/um)

\(\dot{S}_{gen}^{\prime \prime \prime }\) :

Entropy generation rate (w/m 3 k)

α :

Thermal diffusivity (k/ρc)

T*:

Dimensionless temperature [(T − T 0)k/q w r 0]

λ :

Mean free path; eigenvalue (m)

μ :

Dynamic viscosity (kg/ms)

ρ :

Density (kg/m3)

Ω :

Dimensionless heat flux

References

  1. Viskanta R (1963) Interaction of heat transfer by conduction, convection, and radiation in a radiating fluid. J Heat Mass Transf 85:318–328

    Google Scholar 

  2. Jeng DR, Lee EJ, and Dewitt KJ (1974) Simultaneous sonductive and radiative heat transfer for laminar flow in circular tubes with constant wall temperature, Int Heat Transf Conf, 118–122

  3. Jeng DR, Lee EJ, Dewitt KJ (1976) A study of two limiting cases in convective and radiative heat transfer with nongray gases. J Heat Mass Transf 19:589–596

    Article  Google Scholar 

  4. Desoto S, Edwards DK (1965) Radiative emission and absorption in non-isothermal nongray gases in tube. Heat Transf Fluid Mech Inst 22:358–372

    Google Scholar 

  5. Mahmud S (2003) The second law analysis in fundamental convective heat transfer problems. Int J Therm Sci 42:177–186

    Article  Google Scholar 

  6. Sahin AZ (1998) Irreversibilities in various duct geometries with constant wall heat flux and laminar flow. J Energy 23:465–473

    Article  Google Scholar 

  7. Ratts EB, Rauts AG (2004) Entropy generation minimization of fully developed internal flow with constant heat flux. J Heat Transf 126:656–659

    Article  Google Scholar 

  8. Mahmud S, Fraser RA (2006) Second law analysis of forced convection in a circular duct for non-newtonian fluids. Int J Energy Res 31:2226–2244

    Article  Google Scholar 

  9. Chen K (2005) Second law analysis and optimization of microchannel flows subject to different boundary conditions. Int J Energy Res 29:249–263

    Article  Google Scholar 

  10. Avci M, Aydin O (2007) Second-law analysis of heat and fluid flow in microscale geometries. Int J Exergy 4:286–301

    Article  Google Scholar 

  11. Haddad O, Abuzaid M, Al-Nimr M (2004) Entropy generation due to laminar incompressible forced convection flow through parallel-plates microchannel. J Entropy 6:413–426

    Article  MATH  Google Scholar 

  12. Hooman K (2007) Entropy generation for microscaleforced convection: effect of different thermal boundary conditions velocity slip, temperature jump, viscous dissipation, and duct geometry. Int Commun Heat Mass Transf 34:945–957

    Article  Google Scholar 

  13. Hung YM (2008) Viscous dissipation effect on entropy generation for non-newtonian fluid in microchannels. Int Commun Heat Mass Transf 35:1125–1129

    Article  Google Scholar 

  14. Graetz L (1883) Uber die WarmeleitungsfahighevonvonFlussingkeiten. Annalen der PhysikundChemie 18:79–94

    Google Scholar 

  15. Graetz L (1885) Uber die WarmeleitungsfahighevonvonFlussingkeiten. Annalen der Physikund Chemie 25:337–357

    Article  Google Scholar 

  16. Cetin B, Yazicioglu A, Kakac S (2009) Slip-flow heat transfer in microtubes with axial conduction and viscous dissipation an extended graetz problem. Int J Therm Sci 48:1673–1678

    Article  Google Scholar 

  17. Bejan A (1982) Entropy generation through heat and fluid flow. Wiley, New York

    Google Scholar 

  18. Vandadi V, Aghanajafi C, Vandadi A, Niazmand H (2012) Entropy generation analysis for micro scale forced convection in thermal entrance region. J Mech 28:71–76

    Article  Google Scholar 

  19. Siegel Howell (1980) Thermal radiation heat transfer. Hemisphere Publishing Corporation, London

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanical Engineering, K.N. Toosi University, P.O Box: 19395-1999, Tehran, Iran

    Cyrus Aghanajafi, Maziar Alasvand Bakhtiarpoor, Mehran Taghipour & Farid Mohamadi

Authors
  1. Cyrus Aghanajafi
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  2. Maziar Alasvand Bakhtiarpoor
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  3. Mehran Taghipour
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  4. Farid Mohamadi
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Correspondence to Maziar Alasvand Bakhtiarpoor.

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Aghanajafi, C., Bakhtiarpoor, M.A., Taghipour, M. et al. Entropy generation analysis for microscale forced convection with radiation in thermal entrance region. Heat Mass Transfer 51, 307–312 (2015). https://doi.org/10.1007/s00231-014-1398-x

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  • DOI: https://doi.org/10.1007/s00231-014-1398-x

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