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A semi-analytical approach for temperature distribution in Dean flow

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Abstract

Numerical simulations of the flow field and heat transfer require the conjugate solution of the Navier–Stokes and energy equations, a highly compute-intensive process. Here a semi-analytical approach is proposed to solve the energy equation in curved pipes. It requires the flow velocity field, the wall temperature, and the temperature at only one point of the flow cross-section to provide the entire temperature field.

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Abbreviations

a :

Duct radius, m

d :

Pipe diameter, m

D :

Thermal diffusivity, m2 s

r :

Radial coordinate in the pipe cross section \( \sqrt {x^{2} + y^{2} } \)

R :

Bend curvature radius, m

T :

Temperature, K

u, v :

Radial velocities in the pipe cross section, m s−1

W :

Mean axial velocity, m s−1

x, y :

Cartesian coordinates

z :

Curvilinear coordinate

ε :

Relative error between exact and approximate solution

θ :

Curvature angle in the bend plane, rad

μ :

Dynamic viscosity, Pa s

υ :

Kinematic viscosity, m2 s−1

ρ :

Density, kg m−3

app :

Solution obtained from the present approach

ext :

Exact solution

c :

Mixer centerline

i, j, k :

Iteration number

w :

Wall

0:

Constant values

′:

First-degree partial derivative

″:

Second-degree partial derivative

De :

Dean number = (W 2 a 3)/(Rυ 2)

Re :

Reynolds number = Wd/υ

References

  1. Mori Y, Nakayama W (1965) Study on forced convective heat transfer in curved pipes. Int J Heat Mass Transf 8:67–82

    Article  MATH  Google Scholar 

  2. David AN, Smith KA, Merrill EW, Brian PLT (1971) Effect of secondary fluid motion on laminar heat transfer in helically coiled tubes. AIChE J 17:1114–1122

    Article  Google Scholar 

  3. Acharya N, Sen M, Cheng HC (1992) Heat transfer enhancement in coiled tubes by chaotic advection. Int J Heat Mass Transf 35:2475–2489

    Article  Google Scholar 

  4. Duchene C, Peerhossaini H, Michard PJ (1995) On the velocity-field and tracer patterns in a twisted duct flow. Phys Fluids 7:1307–1317

    Article  Google Scholar 

  5. Mokrani A, Castelain C, Peerhossaini H (1997) The effects of chaotic advection on heat transfer. Int J Heat Mass Transf 40:3089–3104

    Article  Google Scholar 

  6. Lemenand T, Peerhossaini H (2002) A thermal model for prediction of the Nusselt number in a pipe with chaotic flow. Appl Therm Eng 22:1717–1730

    Article  Google Scholar 

  7. Naphon P, Wongwises S (2006) A review of flow and heat transfer characteristics in curved tubes. Renew Sustain Energy Rev 10:463–490

    Article  Google Scholar 

  8. Dean WR (1927) Note on the motion of fluid in curved pipe. Philos Mag 4:208–227

    MATH  Google Scholar 

  9. Dean WR (1928) The streamline motion of fluid in curved pipe. Philos Mag 5:673–695

    Google Scholar 

  10. Jones SW, Thomas OM, Aref H (1989) Chaotic advection by laminar flow in a twisted pipe. J Fluid Mech 209:335–357

    Article  MathSciNet  Google Scholar 

  11. Habchi C, Lemenand T, Della Valle D, Peerhossaini H (2009) Liquid-liquid dispersion in a chaotic advection flow. Int J Multiph Flow 35:485–497

    Article  Google Scholar 

  12. Habchi C, Ouarets S, Lemenand T, Della Valle D, Bellettre J, Peerhossaini H (2009) Influence of viscosity ratio on droplets formation in a chaotic advection flow. Int J Chem React Eng 7:A50

    Google Scholar 

  13. Cain GL, Meyer GH (2006) Separation of variables for partial differential equations: an eigenfunction. CRC Press, Boca Raton, FL, pp 1–281

    Google Scholar 

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Author information

Authors and Affiliations

  1. Energy and Thermo-Fluids Group ETF, School of Engineering, Lebanese International University LIU, P.O. Box 146404, Mazraa, Beirut, Lebanon

    Charbel Habchi & Mahmoud Khaled

  2. Thermofluid Complex Flows and Energy Research Group, Laboratoire de Thermocinétique de Nantes, CNRS UMR 6607, LUNAM Université, 44306, Nantes, France

    Thierry Lemenand, Dominique Della Valle & Hassan Peerhossaini

  3. ONIRIS, 44322, Nantes, France

    Dominique Della Valle

  4. School of Computing and Technology, University of Sunderland, Sunderland, SR6 0DD, UK

    Ahmed Elmarakbi

  5. Institut des Energies de Demain (IED), Univ Paris Diderot, Sorbonne Paris Cité, 75013, Paris, France

    Hassan Peerhossaini

Authors
  1. Charbel Habchi
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  2. Mahmoud Khaled
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  3. Thierry Lemenand
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  4. Dominique Della Valle
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  5. Ahmed Elmarakbi
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  6. Hassan Peerhossaini
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Corresponding author

Correspondence to Hassan Peerhossaini.

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Habchi, C., Khaled, M., Lemenand, T. et al. A semi-analytical approach for temperature distribution in Dean flow. Heat Mass Transfer 50, 23–30 (2014). https://doi.org/10.1007/s00231-013-1222-z

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  • DOI: https://doi.org/10.1007/s00231-013-1222-z

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