A model has been developed to numerically study the developing laminar free convection in vertical open-ended eccentric annuli with isothermal boundary conditions. For a fluid of Prandtl number 0.7 in an annulus of radius ratio 0.5, the developing velocity profiles in addition to the development of the pressure along the annulus are presented. The channel heights required to naturally induce different flow rates have also been obtained for three values of the dimensionless eccentricity, namely, 0.1, 0.5, and 0.7. Variations of the total heat absorbed by the fluid with the channel height are provided for the three values of dimensionless eccentricity.

1.
Al-Arabi
M.
,
El-Shaarawi
M. A. I.
, and
Khamis
M.
,
1987
, “
Natural Convection in Uniformly Heated Vertical Annuli
,”
Int. J. Heat Mass Transfer
, Vol.
30
, No.
7
, pp.
1381
1389
.
2.
Bodoia
J. R.
, and
Osterle
J. F.
,
1962
, “
The Development of Free Convection Between Heated Vertical Plates
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
84
, pp.
40
44
.
3.
Carnahan, B., Luther, H. A., and Wilkes, D., 1969, Applied Numerical Methods, John Wiley and Sons, New York, pp. 298-301, 450.
4.
Cheng
K. C.
, and
Hwang
G. J.
,
1968
, “
Laminar Forced Convection in Eccentric Annuli
,”
A. I. Ch. E. Journal
, Vol.
14
, No.
3
, pp.
510
512
.
5.
Coney
J. E. R.
, and
El-Shaarawi
M. A. I.
,
1975
, “
Finite Difference Analysis for Laminar Flow Heat Transfer in Concentric Annuli with Simultaneously Developing Hydrodynamic and Thermal Boundary Layers
,”
Int. J. Numr. Methods Engr.
, Vol.
9
, pp.
17
38
.
6.
El-Saden
M. R.
,
1961
, “
Heat Conduction in an Eccentrically Hollow, Infinitely Long Cylinder with Internal Heat Generation
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
83
, pp.
510
511
.
7.
El-Shaarawi, M. A. I., 1974, “Heat Transfer and Hydrodynamics in the Entrance Region of Concentric Annuli with Stationary and Rotating Inner Walls,” Ph.D. Dissertation, The University of Leeds, England.
8.
El-Shaarawi
M. A. I.
,
1990
, “
Derivation of Boundary Layer Equations for Cases with Curved Boundaries
,”
Int. J. Engineering Fluid Mechanics
, Vol.
3
, No.
2
, pp.
113
128
.
9.
El-Shaarawi
M. A. I.
, and
El-Nimr
M. A.
,
1990
, “
Fully Developed Laminar Natural Convection in Open-ended Vertical Concentric Annuli
,”
Int. J. Heat Mass Transfer
, Vol.
33
, pp.
1873
1884
.
10.
El-Shaarawi
M. A. I.
, and
Mokheimer
E.
,
1995
, “
Transient Conduction in Eccentrically Hollow Cylinders
,”
Int. J. Heat Mass Transfer
, Vol.
38
, No.
11
, pp.
2001
2010
.
11.
El-Shaarawi
M. A. I.
, and
Sarhan
A.
,
1980
, “
Free Convection Effects on the Developing Laminar Flow in Vertical Concentric Annuli
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
102
, pp.
617
622
.
12.
El-Shaarawi
M. A. I.
, and
Sarhan
A.
,
1981
, “
Developing Laminar Free Convection in an Open Ended Vertical Annulus with a Rotating Inner Cylinder
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
103
, pp.
552
558
.
13.
El-Shaarawi
M. A. I.
,
Abualhamayel
H. I.
, and
Mokheimer
E. M. A.
,
1997
, “
Developing Laminar Flow in Eccentric Annuli
,”
ASME Journal of Fluids Engineering
, Vol.
119
, pp.
724
728
.
14.
Feldman
E. E.
,
Hornbeck
R. W.
, and
Osterle
J. F.
,
1982
a, “
A Numerical Solution of Laminar Developing Flow in Eccentric Annular Ducts
,”
Int. J. Heat Mass Transfer
, Vol.
25
, No.
2
, pp.
231
241
.
15.
Feldman
E. E.
,
Hornbeck
R. W.
, and
Osterle
J. F.
,
1982
b, “
A Numerical Solution of Developing Temperature for Laminar Developing Flow in Eccentric Annular Ducts
,”
Int. J. Heat Mass Transfer
, Vol.
25
, No.
2
, pp.
243
253
.
16.
Heaton
H. S.
,
Reynolds
W. C.
, and
Kays
W. M.
,
1964
, “
Heat Transfer in Annular Passages. Simultaneous Development of Velocity and Temperature Fields in Laminar Flow
,”
Int. J. Heat Mass Transfer
, Vol.
5
, pp.
763
781
.
17.
Heyda
J. F.
,
1959
, “
A Green’s Function Solution for the Case of Laminar Incompressible Flow Between Non-Concentric Cylinders
,”
J. Franklin Inst.
, Vol.
267
, pp.
25
34
.
18.
Hughes, W. F., and Gaylord, E. W., 1964, Basic Equations of Engineering Science (Schaum’s Outline Series), McGraw-Hill, New York, pp. 1-11, 151.
19.
Moon, P., and Spencer, D. E., 1971, Field Theory Handbook, 2nd Ed., Springer-Verlag, Berlin, pp. 1–5.
20.
Redberger
P. J.
, and
Charles
M. E.
,
1962
, “
Axial Laminar Flow in a Circular Pipe Containing a Fixed Eccentric Core
,”
The Canadian Journal of Chemical Engineering
, Vol.
40
, pp.
148
151
.
21.
Reynolds
W. C.
,
Lundberg
R. E.
, and
McCuen
P. A.
,
1963
, “
Heat Transfer in Annular Passages. General Formulation of the Problem for Arbitrarily Prescribed Wall Temperatures or Heat Fluxes
,”
Int. J. Heat Mass Transfer
, Vol.
6
, pp.
483
493
.
22.
Schlichting, H., 1987, Boundary Layer Theory, 7th Ed., McGraw-Hill, New York, pp. 127–149.
23.
Snyder
W. T.
,
1963
, “
An Analysis of Slug Flow Heat Transfer in an Eccentric Annulus
,”
A. I. Ch. E. Journal
, Vol.
9
, No.
4
, pp.
503
506
.
24.
Snyder
W. T.
, and
Goldstein
G. A.
,
1965
, “
An Analysis of a Fully Developed Laminar Flow in an Eccentric Annulus
,”
A. I. Ch. E. Journal
, Vol.
11
, No.
3
, pp.
462
469
.
25.
Sparrow
E. M.
, and
Lin
S. H.
,
1964
, “
The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts
,”
J. Basic Engineering
, Vol.
86
, pp.
827
834
.
26.
Suzuki
K.
,
Szmyd
J. S.
, and
Ohtsuka
H.
,
1990
, “
Laminar Forced Convection Heat Transfer in Eccentric Annuli
,”
Heat Transfer-Japanese Research
, Vol.
20
, pp.
169
183
.
27.
Trombetta
M. L.
,
1972
, “
Laminar Forced Convection in Eccentric Annuli
,”
Int. J. Heat Mass Transfer
, Vol.
14
, pp.
1161
1172
.
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