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Experimental study of free convection in an elliptical annular enclosure in blunt and slender orientations

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Abstract

In this paper, free convection heat transfer between two elliptical cylinders having different elliptical ratios in blunt and slender situations was studied experimentally. Three pairs of elliptical cylinders having the same radius ratio of 2.0, the same surface area and different elliptical ratios of 0.662, 0.866 and 0.968 were cut using the computed numerically controlled wire-cut machining. The tests were carried out by keeping a constant heat flux on the inner cylinder while cooling the outer one to be isothermal. The effects of vertical eccentricity, lateral eccentricity, angle of attack of the inner cylinder on natural convection for both blunt and slender situations of each pair were investigated. Empirical correlation was deduced within an acceptable uncertainty for the experimental results. Compatible and satisfactory to the conscience agreement was found in the comparison among the results of present and previous works. In the vision of the comparison, it was found that; the vertical eccentricity can enhance free convection by about 15% than the concentric case, the horizontal eccentricity can enhance natural convection by about 10% than concentric case and slender situation offers about 40% enhancement in free convection than the blunt situation for the same elliptical ratio.

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Abbreviations

A :

Surface area, m2

a :

Semi-major axis, m

b :

Semi-minor axis, m

CNC :

Computed numerically controlled

Gr :

Grash of number

g:

Gravity acceleration, m/s2

h:

Heat transfer coefficient, W/(m2 K)

h :

Average heat transfer coef., W/(m2 K)

i:

Electric current, Ampere

k :

Thermal conductivity, W/m K

L :

Cylinder length, m

Nu :

Local Nusselt number

Nu :

Average Nusselt number

Pr :

Prandtl number

Q :

Heat transfer rate, W

q″ :

Heat flux, W/m2

r :

Radius

Ra :

Rayleigh number

Ra*:

Modified Rayleigh number

T :

Temperature, K

T :

Film temperature, K

t :

Cylinder wall thickness, m

U :

Uncertainty

v:

Voltage, volt

β :

Volume coefficient of expansion, K−1

δ :

Eccentricity, m

ε :

Surface emissivity

ϕ :

Angle of attack, degree

λ:

Characteristic length (vertical gap width), m, λ = a 0−a i for slender; λ = b 0−b i for blunt

ϑ :

Kinematical viscosity, m2/s

σ :

Stefan-Boltzmann const., W/m2 K4

ω :

Horizontal gap width, m, ω = a 0−a i for blunt; ω = b 0−b i for slender

ξ :

Elliptical ratio

a:

Air

avg:

Average

c:

Mid-length section

cond:

Conduction regime

conv:

Convection regime

e:

End-section

h:

Horizontal

i:

Inner cylinder

o:

Outer cylinder

rad:

Radiation regime

s:

Solid

t:

Total

v:

Vertical

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Authors and Affiliations

  1. Mechanical Department, Faculty of Industrial Education, Suez Canal University, Suez, 43515, Egypt

    Eldesouki Ibrahim Eid

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  1. Eldesouki Ibrahim Eid
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Correspondence to Eldesouki Ibrahim Eid.

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Eid, E.I. Experimental study of free convection in an elliptical annular enclosure in blunt and slender orientations. Heat Mass Transfer 47, 81–91 (2011). https://doi.org/10.1007/s00231-010-0678-3

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  • DOI: https://doi.org/10.1007/s00231-010-0678-3

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