Skip to main content
SpringerLink
Log in

Entropy generation analysis of radiative heat transfer effects on channel flow of two immiscible couple stress fluids

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

An analysis is presented to investigate the effects of radiative heat transfer on entropy generation in flow of two immiscible non-Newtonian fluids between two horizontal parallel plates. Both the plates are maintained at constant temperatures higher than that of the fluid. The Stokes’ couple stress flow model is employed. The flow region consists of two zones with the flow of the heavier fluid taking place in the lower zone. The classical “no-slip” condition is prescribed at the plates and continuity of velocity, vorticity, shear stress, couple stress, temperature and heat flux are imposed at the interface. The original partial differential Navier–Stokes equations are converted to ordinary differential equations by assuming velocity and temperature are functions of vertical distance and solved mathematically by usual classical methods. The derived velocity and temperature profiles are used to compute the expressions for the entropy generation number and Bejan number. The effects of relevant parameters on velocity, temperature, entropy generation number and Bejan number are investigated. The computations show that the entropy production decreases with thermal radiation, whereas it increases with viscous dissipation. The effect of viscous dissipation is justified since it significantly affects heat transfer and entropy generation characteristics and therefore should not be ignored.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

Be :

Bejan number

Br :

Brinkman number

(Br/Ω):

Viscous dissipation parameter

E :

Specific internal energy

Ek :

Eckert number

\( \overline{f} \) :

Body forces per unit mass

2h :

Height of the free channel

\( {\bar{\mathbf{h}}} \) :

Heat flux

k 1, k 2 :

Thermal conductivity of the fluid in zone-I, II

\( \overline{\ell } \) :

Body couple per unit mass

n η :

Couple stress coefficients ratio

n k :

Thermal conductivity ratio

n μ :

Viscosity ratio

n ρ :

Density ratio

\( Nf_{i} \) :

Entropy generation due to viscous dissipation

\( Ns_{i} \) :

Dimensionless total entropy generation number

\( Ny_{i} \) :

Entropy generation due to transverse conduction

\( Nu \) :

Nusselt number

q r :

Radiation heat flux

Pr :

Prandtl number

\( \bar{q} \) :

Velocity vector

N R :

Radiation parameter

P :

Pressure

Re :

Reynolds number

s 1, s 2 :

Couple stress parameters

\( \left( {S_{i} } \right)_{\text{G}} \) :

Entropy generation rate

\( \left( {S_{1} } \right)_{{{\text{G}},{\text{C}}}} \) :

Characteristic entropy transfer rate

T 1, T 2 :

Non-dimensional temperatures

u :

Non-dimensional velocity in X-direction

x, y :

Non-dimensional space coordinates

X, Y :

Space co-ordinates

μ 1, μ 2 :

Viscosity coefficients

η, η′:

Couple stress viscosity coefficients

\( \bar{\omega } \) :

Rotation of the fluid particle

Ω :

Dimensionless temperature difference

Φ :

Dissipation function

ϕ :

Irreversibility distribution ratio

ρ :

Density

θ :

Non-dimensional temperature

1:

Fluid in zone I

2:

Fluid in zone II

References

  1. Arpaci VS (1986) Radiative entropy production. AIAA J 24(11):1859–1860

    Article  MATH  Google Scholar 

  2. Arpaci VS (1987) Radiative entropy production—lost heat into entropy. Int J Heat Mass Transf 30:2115–2123

    Article  Google Scholar 

  3. Arpaci VS (1991) Radiative entropy production—heat lost to entropy. Adv Heat Transf 21:239–276

    Article  Google Scholar 

  4. Arpaci VS, Selamet A (1986) Radiative entropy production. In: Tien CL, Carey VP, Ferrell JK (eds) Proceedings of 8th international heat transfer conference, San Francisco, California, vol 2, pp 729–734

  5. Selamet A, Arpaci VS (1990) Entropy production in boundary layers. AIAA J Thermophys Heat Transf 4:404–407

    Article  Google Scholar 

  6. Chen Chao-Kuang, Yang Yue-Tzu, Chang Kuei-Hao (2011) Entropy generation of radiation effect on laminar-mixed convection along a wavy surface. Heat Mass Transf 47:385–395

    Article  Google Scholar 

  7. Bataller RC (2008) Radiation effects in the Blasius flow. Appl Math Comput 198:333–338

    MathSciNet  MATH  Google Scholar 

  8. Bejan A (1979) A study of entropy generation in fundamental convective heat transfer. ASME J Heat Transf 101:718–725

    Article  Google Scholar 

  9. Bejan A (1980) Second law analysis in heat transfer. Energy 5:721–732

    Article  Google Scholar 

  10. Hooman K (2005) Second law analysis of thermally developing forced convection in a porous medium. Heat Transf Res 36(6):437–448

    Article  Google Scholar 

  11. Hacen D, Slimi K, Nasrallah SB (2008) Entropy generation for pulsating flow in a composite fluid/porous system. J Porous Media 11(6):557–574

    Article  Google Scholar 

  12. Khan WA, Gorla RSR (2010) Second law analysis for mixed convection in non-Newtonian fluids over a horizontal plate embedded in a porous medium. Spec Top Rev Porous Media 1(4):353–359

    Article  Google Scholar 

  13. Bird RB, Stewart WE, Lightfoot EN (1960) Transport phenomena. Wiley, New York

    Google Scholar 

  14. Kapur JN, Shukla JB (1964) On the unsteady flow of two incompressible immiscible fluids between two plates. J Appl Math Mech 44(6):268–269

    MathSciNet  MATH  Google Scholar 

  15. Bhattacharya RN (1968) The flow of immiscible fluids between rigid plates with a time dependent pressure gradient. Bull Calcutta Math Soc 1:129–137

    Google Scholar 

  16. Chaturani P, Samy RP (1985) A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases. Biorheology 22(6):521–531

    Google Scholar 

  17. Rao AR, Usha S (1995) Peristaltic transport of two immiscible viscous fluids in a circular tube. J Fluid Mech 298:271–285

    Article  MATH  Google Scholar 

  18. Bakhtiyarov SI, Siginer DA (1997) A note on the laminar core-annular flow of two immiscible fluids in a horizontal tube. In: International symposium on liquid–liquid two phase flow and transport phenomena, Santa Barbara, California, USA, pp 107–111

  19. Chamkha AJ (2004) Oscillatory flow and heat transfer in two immiscible viscous fluids. Int J Fluid Mech Res 31:13–36

    Article  Google Scholar 

  20. Kamisli F, Oztop HF (2008) Second law analysis of the 2D laminar flow of two-immiscible, incompressible viscous fluids in a channel. Heat Mass Transf 44:751–761

    Article  Google Scholar 

  21. Stokes VK (1966) Couple stresses in fluid. Phys Fluids 9(9):1709–1715

    Article  Google Scholar 

  22. Stokes VK (1984) Theories of fluids with microstructure. Springer, New York

    Book  Google Scholar 

  23. Naduvinamani NB, Hiremath PS, Gurubasavaraj G (2001) Squeeze film lubrication of a short porous journal bearing with couple stress fluids. Tribol Int J 34:739–747

    Article  Google Scholar 

  24. Naduvinamani NB, Hiremath PS, Gurubasavaraj G (2002) Surface roughness effects in a short porous journal bearing with couple stress fluid. Fluid Dyn Res 31:333–354

    Article  Google Scholar 

  25. Naduvinamani NB, Fathima ST, Hiremath PS (2003) Effects of surface roughness on characteristics of couple stress squeeze film between anisotropic porous rectangular plates. Fluid Dyn Res 32:217–231

    Article  MATH  Google Scholar 

  26. Brewster MQ (1992) Thermal radiative transfer and properties. Wiley, New York

    Google Scholar 

  27. Butt AS, Munawar S, Ali A, Mehmood A (2012) Entropy generation in the Blasius flow under thermal radiation. Phys Scr 85(3):035008

    Article  MATH  Google Scholar 

  28. Paoletti S, Rispoli F, Sciubba E (1989) Calculation exergetic loses in compact heat exchanger passages. ASME AES 10:21–29

    Google Scholar 

  29. Adesanya SO, Makinde OD (2015) Effects of couple stresses on entropy generation rate in a porous channel with convective heating. Comput Appl Math 34:293–307

    Article  MathSciNet  MATH  Google Scholar 

  30. Aïboud S, Saouli S (2010) Entropy analysis for viscoelastic magneto hydrodynamic flow over a stretching surface. Int J Non-Linear Mech 45(5):482–489

    Article  Google Scholar 

  31. Rashidi MM, Parsa AB, Bég OA, Shamekhi L, Sadri SM, Bég TA (2014) Parametric analysis of entropy generation in magneto-hemodynamic flow in a semi-porous channel with OHAM and DTM. Appl Bion Biomech 11:47–60

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Meghalaya, Shillong, Meghalaya, 793002, India

    J. Srinivas

  2. Department of Mathematics, National Institute of Technology Warangal, Hanamkonda, Telangana, 506004, India

    J. V. Ramana Murthy

  3. Fluid Mechanics, Aeronautical and Mechanical Engineering Department, School of Computing, Science and Engineering, University of Salford, Manchester, M54WT, UK

    O. Anwar Bég

Authors
  1. J. Srinivas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. V. Ramana Murthy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. Anwar Bég
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Anwar Bég.

Additional information

Technical Editor: Francis H. R. Franca.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Srinivas, J., Murthy, J.V.R. & Bég, O.A. Entropy generation analysis of radiative heat transfer effects on channel flow of two immiscible couple stress fluids. J Braz. Soc. Mech. Sci. Eng. 39, 2191–2202 (2017). https://doi.org/10.1007/s40430-017-0752-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-017-0752-6

Keywords

Search

Navigation