Skip to main content
SpringerLink
Log in

Effect of opposed eccentricity on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations

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

Abstract

This paper presents an experimental investigation for the effect of opposed lateral and vertical eccentricities on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations. Three test specimens of elliptical cylinders having an equal radius ratio and an equal length were prepared. The surface area of the inner cylinder is the same for each specimen as well as the area of the outer cylinder. Different elliptical ratios of 0.662, 0.866 and 0.968 were investigated. Experimental tests were done by maintaining constant heat flux on the inner cylinder and the outer one was exposed to approximately constant temperature of the closed laboratory. Both annuals ends of the annular elliptical cylinders were closed by cork to form the annular enclosure space. The experimental tests monitored Rayleigh number (1.642 × 103 ≤ Ra* ≤ 3.849 × 106). The effects of both opposed vertical and lateral eccentricities for both blunt and slender orientations were investigated. The experimental results were fitted by correlations. Considerable agreement was found in the comparison among the results of present and previous works. Opposed eccentricity enhances free convective heat transfer by about 40 % from concentric. Slender orientation results in more enhancements in free convection than blunt one.

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

Similar content being viewed by others

Abbreviations

A:

Surface area (m2)

a:

Semi-major axis (m)

b:

Semi-minor axis (m)

Gr:

Grashof of number

g:

Gravity acceleration (m/s2)

h:

Heat transfer coefficient (W/(m2 K))

I:

Electric current (Ampere)

k:

Thermal conductivity (W/(m K))

L:

Cylinder length (m)

Nu:

Local Nusselt number

Pr:

Prandtl number

Q′:

Heat transfer rate (W)

q″:

Heat flux (W/m2)

r:

Radius (m)

Ra:

Rayleigh number

Ra*:

Modified Rayleigh number

T:

Temperature (K)

t:

Cylinder wall thickness (m)

V:

Voltage (Volt)

β:

Volume coefficient of expansion (K)

δ:

Eccentricity (m)

ε:

Surface emissivity

ϕ:

Angle of attack (degree)

λ:

Vertical gap width (m)

λ = b0 − bi for blunt, and

λ = a0 − ai for slender

ϑ:

Kinematical viscosity (m2/s)

σ:

Stefan-Boltzmann constant (W/m2K4)

ω:

Horizontal gap width (m)

ω = a0−ai for blunt, and

ω = b0−bi for slender

\(\xi\) :

Elliptical ratio \(\xi = \sqrt {1 - (b^{2} /a^{2} )}\)

a:

Air

avg:

Average

cond:

Conduction regime

conv:

Convection regime

e:

End-section

f:

Film

i:

Inner cylinder

l:

Lateral

m:

Mid-section

o:

Outer cylinder

rad:

Radiation regime

s:

Solid

t:

Total

v:

Vertical

References

  1. Eid EI (2011) Experimental study of free convection in an elliptical annular enclosure in blunt and slender orientations. Heat Mass Transf 47:81–91

    Article  Google Scholar 

  2. Projahn U, Beer H (1985) Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli. Warme-und Stofftibertragung 19:249–254

    Article  Google Scholar 

  3. Yousefi T, Ashjaee M (2007) Experimental study of natural convection heat transfer from vertical array of isothermal horizontal elliptic cylinders. Exp Therm Fluid Sci 32:240–248

    Article  Google Scholar 

  4. Suofang W (1995) An experimental and numerical study of natural convection heat transfer in horizontal annuli between eccentric cylinders. J Therm Sci 4(1):38–43

    Article  Google Scholar 

  5. Li HZ, Li W, Tao WQ (1995) Experimental study of natural convection heat transfer between an outer horizontal cylindrical envelope and an inner concentric heated square cylinder with two slots. Heat Mass Transf 30:455–459

    Article  Google Scholar 

  6. Elsayed AO, Ibrahim EZ, Elsayed SA (2003) Free convection from a constant heat flux elliptic tube. Energy Convers Manag 44:2445–2453

    Article  Google Scholar 

  7. Berkengetm AA (1973) A study of natural convection in horizontal cylindrical gaps. Sergo Ordzhonikidze Institute of Aviation, Moscow, Translated from Inzhenerno-Ftzicheskii Zhurnal 25(4):676–680

  8. Cheng CY (2007) A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model. Int Commun Heat Mass Transf 34:613–622

    Article  Google Scholar 

  9. Sakr RY, Berbish NS, Abd-Alziz AA, Hanafi AS (2008) Experimental and numerical investigation of natural convection heat transfer in horizontal elliptic annuli. J Appl Sci Res 4(2):138–155

    Google Scholar 

  10. Ho CJ, Lin YH, Chen TC (1989) A numerical study of natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions. Int J Heat Fluid Flow 10(1):40–47

    Article  Google Scholar 

  11. Zhu YD, Shu C, Qiu J, Tani J (2004) Numerical simulation of natural convection between two elliptical cylinders using DQ method. Int J Heat Mass Transf 47:797–808

    Article  MATH  Google Scholar 

  12. Habeeb LJ, Mohammed AA (2012) Natural convection heat transfer in horizontal annuli with inner elliptic and circular cylinder. In: Proceedings of International Conference on Engineering and Information Technology “ICEIT2012”, Toronto, Canada, 17–18 Sep 2012

  13. D’Alessio SJD, Finlay LA, Pascal JP (2008) Free convection from elliptic cylinders at small Grashof numbers. Int J Heat Mass Transf 51:1379–1392

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Suez University, Suez, Egypt

    E. I. Eid, M. Abdel-Halim & A. S. Easa

Authors
  1. E. I. Eid
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Abdel-Halim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Easa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. I. Eid.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eid, E.I., Abdel-Halim, M. & Easa, A.S. Effect of opposed eccentricity on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations. Heat Mass Transfer 51, 239–250 (2015). https://doi.org/10.1007/s00231-014-1408-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-014-1408-z

Keywords

Search

Navigation