Effect of Rayleigh Number on Internal Eccentricity in a Heated Horizontal Elliptical Cylinder to its Coaxial Square Enclosure

Abdelkrim Bouras 1 , Djedid Taloub 2 ,  and Zied Driss 3
  • 1 Department of Physics, Faculty of Sciences, University Mohamed Boudiaf of M’sila, Laboratory of Energetic Physics, University Frères Mentouri Constantine 1, M’sila, Algeria
  • 2 Department of Physics, Faculty of Sciences, University Mohamed Boudiaf of M’sila, Laboratory of Renewable Energy and Sustainable Development (LRESD), University Frères Mentouri Constantine1, M’sila, Algeria
  • 3 Laboratory of Electromechanical Systems (LASEM), National School of Engineers of Sfax (ENIS), University of Sfax, Sfax, Tunisia

Abstract

This paper deals with numerical investigation of a natural convective flow in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder with a Newtonian fluid. Uniform temperatures are imposed along walls of the enclosure. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The effects of Geometry Ratio GR and Rayleigh numbers on fluid flow and heat transfer performance are investigated. The Rayleigh number is varied from 103 to 106. Throughout the study the relevant results are presented in terms of isotherms, and streamlines. From the results, we found that the increase in the Geometry Ratio B leads to an increase of the heat transfer coefficient. The heat transfer rate in the annulus is translated in terms of the average Nusselt numbers along the enclosure’s sides. Tecplot 7 program was used to plot the curves which cleared these relations and isotherms and streamlines which illustrate the behavior of air through the channel and its variation with other parameters. The results for the streamlines, isotherms, local and average Nusselt numbers average Nusselt numbers are compared with previous works and show good agreement.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Kuehn T.H. and Goldstein R.J. (1978): An experimental study of natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli. – J. Heat Transfer, vol.100. No.4, pp.635-640.

  • [2] Kuehn T.H. and Goldstein R.J. (1980): A parametric study of prandtl number and diameter ratio effects on natural convection heat transfer in horizontal cylindrical annuli. – J. Heat Transfer, vol.102, pp.768-770.

  • [3] Manal H. Al-HafidhRaed G. Saihood (2008): Parametric study of mixed convective radiative heat transfer in an inclined annulus. –Al-Khwarizmi Engineering Journal, vol.4, No.4, pp.45-56.

  • [4] Lacroix M. and Joyeux A. (1996): Coupling of wall conduction with natural convection from heated cylinders in a rectangular enclosure. – International Communication of Heat and Mass Transfer, vol.23, pp.143-151.

  • [5] Mohammed Abed W., Shareef A.J. and Najeeb A.A. (2010): Annulus between outer cylinder and inner flat tube. – Anbar Journal for Engineering Sciences, AJES, vol.3, No.2.

  • [6] Lee J.H., Back Y.R., Lee S.R. and Faghri M. (1992): Natural convection in enclosures with an irregular wall. – In: Reizes, J.A. (Ed.), Transport Phenomena in Heat and Mass Transfer. Elsevier, pp.112-123.

  • [7] Cheng C.H. and Chao C.C. (1996): Numerical prediction of the buoyancy-driven flow in the annulus between horizontal eccentric elliptical cylinders. – Numerical Heat Transfer Part A 30, pp.283-303.

  • [8] Bouras A., Djezzar M., Naji H. and Ghernoug C. (2014): Numerical computation of double-diffusive natural convective flow within an elliptic-shape enclosure. – International Communications in Heat and Mass Transfer, vol.57, pp.183-192.

  • [9] Bouras A., Djezzar M. and Ghernoug C. (2013): Numerical simulation of natural convection between two elliptical cylinders: Influence of Rayleigh number and Prandtl number. – Energy Procedia, vol.36, pp.788–797.

  • [10] Li H. and Tong S. (2016): Natural convective heat transfer in the inclined rectangular cavities with low widthtoheight ratios. – International Journal of Heat and Mass Transfer, vol.93, pp.398-407.

  • [11] Awasarmol U.V. and Pise A.T. (2015): An experimental investigation of natural convection heat transfer enhancement from perforated rectangular fins array at different inclinations. – Experimental Thermal and Fluid Science, vol.68, pp.145-154.

  • [12] El Shamy M.M., Ozisik M.N. and Coulter J.P. (1990): Correlation for laminar natural convection between confocal horizontal elliptical cylinders. – Numer. Heat Transfer, Part A 18, pp.95-112.

  • [13] Bouras A., Taloub D., Djezza M. and Driss Z. (2018): Natural convective heat transfer from a heated horizontal elliptical cylinder to its coaxial square enclosure. – Mathematical Modelling of Engineering Problems, vol.5, No.4, pp.379-385.

  • [14] Zhang K., Yang M. and Zhang Y. (2011): Numerical analysis of natural convection in a cylindrical envelope with an internal concentric cylinder with slots, number. – Heat Transfer A, vol.59, No.10, pp.739-754.

  • [15] Yu Z.T., Hu Y.C., Fan L.W. and Cen K.F. (2010): A parametric study of prandtl number effects on laminar natural convection heat transfer from a horizontal circular cylinder to its coaxial triangular enclosure, number. – Heat Transfer A vol.58, No.7, pp.564-580.

  • [16] Farooq Hassan Ali Alinnawi Ali Safa Nouri Alsaegh Najlaa Ali Hussein (2013): Laminar natural convection in square enclosure containing different cross sections of inner pipes with internal heat generation. – Journal of Babylon University/Engineering Sciences / No.2. vol.21.

  • [17] Mehrizi A.A., Sedighi K., Farhadi M. and Sheikholeslami M. (2013): Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus. – International Communications in Heat and Mass Transfer, vol.48, pp.164-177.

  • [18] Xing Y., Fatemeh T. and Kambiz V. (2015): Analysis of natural convection in horizontal concentric annuli of varying inner shape numerical heat transfer. – Part A, vol.68, pp.1155-1174.

OPEN ACCESS

Journal + Issues

Search