Skip to main content
SpringerLink
Log in

Prediction of Free Convection from Vertical and Inclined Rows of Horizontal Isothermal Cylinders Using ANFIS

  • Research Article - Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The current study is conducted to predict the laminar free convection from horizontal isothermal cylinder sets in vertical and inclined rows, using an adaptive neuro-fuzzy inference system (ANFIS). The effects of the Rayleigh number, vertical and horizontal separation distances on average heat transfer from the rows are considered via this prediction. The training data for optimizing the ANFIS structure is based on available experimental data. A hybrid learning algorithm consisting of the gradient descends method and least-squares method is used for ANFIS training. In the view of the physics of the problem, it was observed that in the vertical row, by increasing the vertical separation spacing heat transfer increases. Moreover, the heat transfer increases by increasing the horizontal spacing ratio. In addition, according to good consistency obtained between the experimental and predicted results, it can be concluded that ANFIS can be used to predict the experimental results accurately.

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

Similar content being viewed by others

Abbreviations

d :

Diameter of the cylinders (m)

g :

Gravitational acceleration (m/s2)

l :

Length of cylinder (m)

N :

Number of cylinders in the row (N = 5)

N i :

Ordinal number of the ith cylinder in the row

\({\overline {Nu}_a}\) :

Average Nusselt number of the rows

\({\overline {Nu}_{ai}}\) :

Average Nusselt number for all the cylinders in the inclined row

\({\overline {Nu}_{av}}\) :

Average Nusselt number for all the cylinders in the vertical row

\({\overline {Nu}_{ii}}\) :

Average Nusselt number of the ith cylinder in the inclined row

\({\overline {Nu}_{iv}}\) :

Average Nusselt number of the ith cylinder in the vertical row

p :

Pressure (pa)

P x :

Horizontal center-to-center separation distance (m)

P y :

Vertical center-to-center separation distance (m)

Ra :

Rayleigh number based on the cylinder diameter (Ra = gβ (T w − T ∞)d 3/να)

T :

Temperature (K)

α :

Thermal diffusivity of air (m2/s)

β :

Coefficient of volumetric thermal expansion of air (1/K)

ε :

Fringe shift

λ :

Laser wave length =  632.8 nm

v :

Kinematic viscosity of air (m2/s)

φ :

Angle of flow diverter =  45°

w :

Referred to undisturbed air

∞:

Referred to the cylinder surface

ref:

Referred to a fringe shift= 0

References

  1. Kuehn, T.H.; Goldstein, R.J.: Numerical solution to the Navier-Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder. Int. J. Heat Mass Tran. 23, 971–979 (1980)

    Article  MATH  Google Scholar 

  2. Wang, P.; Kahawita, R.; Nguyen,T.H.: Numerical computation of the natural convection flow about a horizontal cylinder using splines. Numer. Heat Tran. 17, 191–215 (1990)

    Article  MATH  Google Scholar 

  3. Saitoh, T.; Sajiki, T.;Maruhara, K.: Bench mark solutions to natural convection heat transfer problem around a horizontal circular cylinder. Int. J. Heat Mass Tran. 36, 1251–1259 (1993)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  5. Eckert, E.R.G.; Soehngen, E.E.: Studies on heat transfer in laminar free convection with the Zehnder–Mach interferometer. AF Technical Report, USAF Air Material Command, Wright–Paterson Air Force Base, Ohio, USA (1984)

  6. Ozoe, H.; Shibata, T.; Churchill, W.: Natural convection in an inclined circular cylindrical annulus heated and cooled on its end plates. Int. J. Heat Mass Tran. 24, 721–737 (1981)

    Google Scholar 

  7. Farouk, B.; Guceri, S.I.: Natural convection from horizontal cylinders in interacting flow fields. Int. J. Heat Mass Tran. 26, 231–243 (1983)

    Article  MATH  Google Scholar 

  8. D’Orazio, A.; Fontana, L.: Experimental study of free convection from a pair of vertical arrays of horizontal cylinders at very low Rayleigh numbers. Int. J. Heat Mass Tran. 53, 3131–3142 (2010)

    Article  Google Scholar 

  9. Rezvantalab, H.; Ghazian, O.; Yousefi, T.; Ashjaee, M.: Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders. Exp. Therm. Fluid Sci. 35, 1398–1408 (2011)

    Google Scholar 

  10. Chouikh, R.; Guizani, A.; Maalej, M.; Belghith, A.: Numerical study of the laminar natural convection flow around an array of two horizontal isothermal cylinders. Int.Commun.Heat Mass 26, 329–338 (1999)

    Google Scholar 

  11. Ashjaee, M.; Yousefi, T.: Experimental study of free convection heat transfer from horizontal isothermal cylinders arranged in vertical and inclined arrays. J. Heat Tran. Eng. 28, 460–471 (2007)

    Article  Google Scholar 

  12. Karami, A.; Rezaei, E.; Shahhosseni, M.; Aghakhani, M.: Fuzzy logic to predict the heat transfer in an air cooler equipped with different tube inserts. Int. J. Thermal Sci. 53, 141–147 (2012)

    Article  Google Scholar 

  13. Mehrabi, M.; Pesteei, S.M.; Pashaee, T.: Modeling of heat transfer and fluid flow characteristics of helicoidally double-pipe heat exchangers using adaptive neuro-fuzzy inference system (ANFIS). Int.Commun. Heat Mass 38, 525–532 (2011)

    Google Scholar 

  14. Rezaei, E.; Karami, A.; Yousefi, T.; Mahmoudinezhad, S.: Modeling the free convection heat transfer in a partitioned cavity using ANFIS. Int. Commun. Heat Mass 39, 470–475 (2012)

    Article  Google Scholar 

  15. Karami, A.; Rezaei, E.; Rahimi, M.; Khani, S.: Modeling of heat transfer in an air cooler equipped with classic twisted tape inserts using adaptive neuro-fuzzy inference system. Manuscript acceptted, to be published in Chemical Engineering Communications

  16. Varol, Y.; Avci, E.; Koca, A.; Oztop, H.F.: Prediction of flow fields and temperature distributions due to natural convection in a triangular enclosure using adaptive-network-based fuzzy inference system (ANFIS) and artificial neural network (ANN). Int. Commun. Heat Mass 34, 887–896 (2007)

    Google Scholar 

  17. Karami, A.; Akbari, E.; Rezaei, E.; Ashjaee, M.: Modeling the free convection from a pair of vertical arrays of isothermal cylinders using ANFIS. Manuscript acceptted, to be published in the Journal of Thermophysics and Heat Transfer

  18. Ayata, T.; Çam, E.; Y\(\imath \)ld\(\imath \) z, O.: Adaptive neuro-fuzzy inference systems (ANFIS) application to investigate potential use of natural ventilation in new building designs in Turkey. Energ. Convers. Manag. 48, 1472–1479 (2007)

  19. Karami, A.; Rezaei, E.; Rahimi, M.; Zanjani, M.: Artificial neural modeling of the heat transfer in an air cooled heat exchanger equipped with butterfly inserts. Manuscript acceptted, to be published in International Energy Journal

  20. Ying, L.C.; Pan, M.C.: Using Adaptive network based fuzzy inference system to forecast regional electricity load. Energ. Convers. Manag. 49, 205–211 (2009)

    Article  Google Scholar 

  21. Yousefi, T.; Karami, A.; Rezaei, E.; Ebrahimi, S.: Fuzzy modeling of the forced convection heat transfer from a V-shaped plate exposed to an air impingement slot jet. Heat Transf. Asian Res. 41, 5 (2012)

    Google Scholar 

  22. Hauf, W.; Grigull, U.: Optical methods in heat transfer. In: Proceedings of Advances in Heat Transfer. vol. 6, pp. 133–366, Academic Press, New York (1970)

  23. Eckert, E.R.G.; Goldstein, R.J.: Measurements in Heat Transfer. 2nd ed., pp. 241–293, McGraw-Hill, New York (1972)

  24. JHT Editorial Board.: Journal of heat transfer policy on reporting uncertainties in experimental measurements and results. ASME J. Heat Transfer. 115, 5–6 (1993)

    Google Scholar 

  25. Jang, J.S.R.; Sun, C.T.: Neuro-fuzzy modeling and control. Special issue on fuzzy logic in engineering applications. Proc. IEEE 83, 378–406 (1995)

    Google Scholar 

  26. Jang, J.S.R.; Sun, C.T.; Mizutani, E.: Neuro-Fuzzy and Soft Computing. pp. 510–514, Prentice Hall, New York (1997)

  27. The MathWorks, Fuzzy Logic Toolbox User’s Guide Inc., pp. 1760–2098, 3 Apple Hill Drive, Natick (1995–2007)

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

    Alimohammad Karami

  2. Department of Mechanical Engineering, Razi University, Kermanshah, Iran

    Tooraj Yousefi

  3. Department of Mechanical Engineering, Harsin Branch, Islamic Azad University, Kermanshah, Iran

    Saeed Mohebbi

  4. Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Cyrus Aghanajafi

Authors
  1. Alimohammad Karami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tooraj Yousefi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saeed Mohebbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cyrus Aghanajafi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tooraj Yousefi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karami, A., Yousefi, T., Mohebbi, S. et al. Prediction of Free Convection from Vertical and Inclined Rows of Horizontal Isothermal Cylinders Using ANFIS. Arab J Sci Eng 39, 4201–4209 (2014). https://doi.org/10.1007/s13369-014-1094-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-014-1094-7

Keywords

Search

Navigation