Skip to main content
SpringerLink
Log in

Effect of horizontal spacing between inner circular cylinders on three-dimensional natural convection in rectangular channel

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Three-dimensional numerical simulations were conducted for natural convection phenomena around a horizontal array of hot inner circular cylinders positioned in a cold rectangular channel in the range of 104 ≤ Ra ≤ 106 at the Prandtl number of Pr = 0.7. The immersed boundary method (IBM) was used to capture the virtual wall boundary of the inner cylinders based on the finite volume method (FVM). This study investigated the thermal and flow regimes with various patterns at different Rayleigh numbers and horizontal spacing between the inner cylinders. Detailed effects of the spacing (1 L ≤ S ≤ 4 L) were analyzed by visualization of three-dimensional isothermals and vortical structures. The three-dimensionality and heat transfer characteristics resulting from flow and thermal structure changes were also investigated.

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

Similar content being viewed by others

Abbreviations

A :

Surface area of cylinder and walls of enclosure.

f i :

Momentum forcing

g :

Gravitational acceleration

H :

Vertical length of enclosure

h :

Heat source or sink

n :

Direction normal to the wall

Nu :

Local Nusselt number

<Nu> :

Surface-averaged Nusselt number

\( \overline{\left\langle Nu\right\rangle } \) :

Time and surface-averaged Nusselt number

L :

Characteristic length

P :

Dimensionless pressure

Pr :

Prandtl number

q :

Mass source or sink

R :

Radius of circular cylinder

Ra :

Rayleigh number

S :

Distance between inner cylinders

T :

Temperature

t :

Dimensionless time

u i :

Dimensionless velocity vector

V :

Volume of fluid

x i :

Cartesian coordinates system

α :

Thermal diffusivity

β :

Thermal expansion coefficient

δ j2 :

Kronecker delta

θ :

Dimensionless temperature

λ 2 :

Lamda-2 criteria for vortical structure

ν :

Kinematic viscosity

ξ :

Volume averaged orthogonal enstrophy

\( \overline{\xi_{x,y}} \) :

Time and volume-averaged orthogonal enstrophy

ρ :

Density

τ p :

Period of the fluctuation of thermal and flow fields

φ :

Angle (degrees)

ω :

Vorticity

B :

Bottom wall

c:

Cold

C :

Cylinder

EN :

Enclosure

h :

Hot

i, j :

Tensor notation

T :

Top wall

*:

Dimensional variable

References

  1. Kitamura K, Mitsuishi A, Suzuki T, Kimura F (2016) Fluid flow and heat transfer of natural convection induced around a vertical row of heated horizontal cylinders. Int J Heat Mass Transf 92:414–429

    Article  Google Scholar 

  2. Ashjaee M, Yousefi T, Farahmand S, Chavoshi E (2009) Enhancement of free convection heat transfer from a vertical array of isothermal cylinders by flow diverters. Heat Transfer Eng 30:197–206

    Article  Google Scholar 

  3. Farouk B, Guceri SI (1983) Natural convection from horizontal cylinders in interacting flow fields. Int J Heat Mass Transf 26:231–243

    Article  MATH  Google Scholar 

  4. Corcione M (2005) Correlating equations for free convection heat transfer from horizontal isothermal cylinders set in a vertical array. Int J Heat Mass Transf 48:3660–3673

    Article  MATH  Google Scholar 

  5. Dash SM, Lee TS, Huang H (2014) Natural convection from an eccentric square cylinder using a novel flexible forcing IB-LBM method. Numer Heat Transfer, Part A 65:531–555

    Article  Google Scholar 

  6. Angeli D, Levoni P, Barozzi GS (2008) Numerical predictions for stable buyant regimes within a square cavity containing a heated horizontal cylinder. Int J Heat Mass Transf 51:553–565

    Article  MATH  Google Scholar 

  7. Park YG, Ha MY, Choi C, Park J (2014) Natural convection in a square enclosure with two inner circular cylinders positioned at different vertical locations. Int J Heat Mass Transf 77:501–518

    Article  Google Scholar 

  8. Karimi F, Xu HT, Wang Z, Yang M, Zhang Y (2014) Numerical simulation of unsteady natural convection from heated horizontal circular cylinders in a square enclosure. Numer Heat Transfer, Part A 65:715–731

    Article  Google Scholar 

  9. Nada SA (2007) Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate. Int J Heat Mass Transf 50:667–679

    Article  MATH  Google Scholar 

  10. Lee JR, Ha MY, Balachandar S, Yoon HS, Lee SS (2004) Natural convection in a horizontal layer of fluid with a periodic array of square cylinders in the interior. Phys Fluids 16:1097–1117

    Article  MATH  Google Scholar 

  11. Arquis E, Rady M (2005) Study of natural convection heat transfer in a finned horizontal fluid layer. Int J Therm Sci 44:43–52

    Article  Google Scholar 

  12. El Alami M, Najam M, Semma E, Oubarra A, Penot F (2005) Electronic components cooling by natural convection in horizontal channel with slots. Energy Convers Manag 46:2762–2772

    Article  Google Scholar 

  13. Bakkas M, Hasnaoui M, Amahmid A (2010) Natural convective flows in a horizontal channel provided with heating isothermal blocks: effect of the inter blocks spacing. Energy Convers Manag 51:296–304

    Article  Google Scholar 

  14. Bakkas M, Amahmid A, Hasnaoui M (2008) Numerical study of natural convection heat transfer in a horizontal channel provided with rectangular blocks releasing uniform heat flux and mounted on its lower wall. Energy Convers Manag 49:2757–2766

    Article  Google Scholar 

  15. Najam M, Amahmid A, Hasnaoui M, El Alami M (2003) Unsteady mixed convection in a horizontal channel with rectangular blocks periodically distributed on its lower wall. Int J Heat Fluid Flow 24:726–735

    Article  Google Scholar 

  16. Trias FX, Soria M, Oliva A, Perez-Segarra CD (2007) Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4. J Fluid Mech 586:259–293

    Article  MATH  Google Scholar 

  17. Shu C, Liu N, Chew YT (2007) A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder. J Comput Phys 226:1607–1622

    Article  MATH  Google Scholar 

  18. Silva ALE, Neto AS, Damasceno JJR (2003) Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method. J Comput Phys 189:351–370

    Article  MATH  Google Scholar 

  19. Chan AMC, Banerjee S (1979) A numerical study of three-dimensional roll cells within rigid boundaries. J Heat Transf 101:233–243

    Article  Google Scholar 

  20. Uhlmann M (2005) An immersed boundary method with direct forcing for the simulation of particulate flow. J Comput Phys 209:448–476

    Article  MathSciNet  MATH  Google Scholar 

  21. Kim J, Kim D, Choi H (2001) An immersed-boundary finite-volume method for simulations of flow in complex geometries. J Comput Phys 171:132–150

    Article  MathSciNet  MATH  Google Scholar 

  22. Kim J, Choi H (2004) An immersed-boundary finite-volume method for simulations of heat transfer in complex geometries. KSME Int J 18:1026–1035

    Article  Google Scholar 

  23. Choi H, Moin P (1994) Effect of the computational time step on numerical solutions of turbulent flow. J Comput Phys 113:1–4

    Article  MATH  Google Scholar 

  24. Fiscaletti D, Angeli D, Tarozzi L, Barozzi GS (2013) Buoyancy-induced transitional flows around an enclosed horizontal cylinder: an experiment. Int J Heat Mass Transf 58:619–631

    Article  Google Scholar 

  25. Seo YM, Doo JH, Ha MY (2016) Three-dimensional flow instability of natural convection induced by variation in radius of inner circular cylinder inside cubic enclosure. Int J Heat Mass Transf 95:566–578

    Article  Google Scholar 

  26. Poncet P (2002) Vanishing of mode B in the wake behind a rotationally oscillating circular cylinder. Phys Fluids 14:2021–2023

    Article  MATH  Google Scholar 

  27. Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology(NRF-2017R1A2B3004883 and NRF-2017R1C1B2007296).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan, 609-735, Republic of Korea

    Young Min Seo, Jeong Min Lee & Man Yeong Ha

  2. Rolls-Royce and Pusan National University Technology Centre in Thermal Management, Jang Jeon 2-Dong, Geum Jeong Gu, Busan, 609-735, Republic of Korea

    Yong Gap Park

Authors
  1. Young Min Seo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeong Min Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Gap Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Man Yeong Ha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yong Gap Park or Man Yeong Ha.

Additional information

Highlights

• Three-dimensional numerical simulations were conducted for natural convection.

• The Immersed Boundary Method was used, based on the Finite Volume Method.

• The effect of horizontal spacing between inner circular cylinders were analyzed.

• Three-dimensional isothermals and vortical structures were investigated.

• Three-dimensionality and heat transfer characteristics were also investigated.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seo, Y.M., Lee, J.M., Park, Y.G. et al. Effect of horizontal spacing between inner circular cylinders on three-dimensional natural convection in rectangular channel. Heat Mass Transfer 54, 537–551 (2018). https://doi.org/10.1007/s00231-017-2160-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-017-2160-y

Search

Navigation