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.
Similar content being viewed by others
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
Viskanta R (1963) Interaction of heat transfer by conduction, convection, and radiation in a radiating fluid. J Heat Mass Transf 85:318–328
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
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
Desoto S, Edwards DK (1965) Radiative emission and absorption in non-isothermal nongray gases in tube. Heat Transf Fluid Mech Inst 22:358–372
Mahmud S (2003) The second law analysis in fundamental convective heat transfer problems. Int J Therm Sci 42:177–186
Sahin AZ (1998) Irreversibilities in various duct geometries with constant wall heat flux and laminar flow. J Energy 23:465–473
Ratts EB, Rauts AG (2004) Entropy generation minimization of fully developed internal flow with constant heat flux. J Heat Transf 126:656–659
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
Chen K (2005) Second law analysis and optimization of microchannel flows subject to different boundary conditions. Int J Energy Res 29:249–263
Avci M, Aydin O (2007) Second-law analysis of heat and fluid flow in microscale geometries. Int J Exergy 4:286–301
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
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
Hung YM (2008) Viscous dissipation effect on entropy generation for non-newtonian fluid in microchannels. Int Commun Heat Mass Transf 35:1125–1129
Graetz L (1883) Uber die WarmeleitungsfahighevonvonFlussingkeiten. Annalen der PhysikundChemie 18:79–94
Graetz L (1885) Uber die WarmeleitungsfahighevonvonFlussingkeiten. Annalen der Physikund Chemie 25:337–357
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
Bejan A (1982) Entropy generation through heat and fluid flow. Wiley, New York
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
Siegel Howell (1980) Thermal radiation heat transfer. Hemisphere Publishing Corporation, London
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-014-1398-x