Heat transfer from laminar flow in ducts with elliptic cross-section |
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Authors: | J Schenk and Bong Swy Han |
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Institution: | (1) Laboratorium voor Technische Natuurkunde der Technische Hogeschool, Delft, Nederland |
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Abstract: | Summary The cooling of a hot fluid in laminar Newtonian flow through cooled elliptic tubes has been calculated theoretically. Numerical data have been computed for the two values 1.25 and 4 of the axial ratio of the elliptic cross-section . For =1.25 the influence of non-zero thermal resistance between outmost fluid layer and isothermal surroundings has also been investigated. Special attention has been given to the distribution of heat flux around the perimeter; when increases the flux varies more with the position at the circumference. This positional dependence becomes less pronounced, however, as the (position-independent) thermal resistance of the wall increases.Flattening of the conduit, while maintaining its cross-sectional area constant, improves the cooling. Comparison with rectangular pipes shows that this improvement is not as marked with elliptic as with rectangular pipes.Nomenclature
A
k
=A
m, n
coefficients of expansion (6)
-
a, b
half-axes of ellipse, b<a
-
a
p
=a
r, s
coefficients of representation (V)
-
D
hydraulic diameter, = 4S/P; S = cross-sectional area, P = perimeter
-
D
e
equivalent diameter, according to (13)
-
n
coordinate (outward) normal to the tube wall
-
T
temperature of fluid
-
T
i
temperature of fluid at the inlet
-
T
s
temperature of surroundings
-
v
0
mean velocity of fluid
-
v
z
longitudinal velocity of fluid
-
x, y
carthesian coordinates coinciding with axes of ellipse
-
z
coordinate in flow direction
-
,
dimensionless half-axes of ellipse, =a/D and =b/D
-
t
heat transfer coefficient from fluid at bulk temperature to surroundings; equation (11)
-
w
heat transfer coefficient at the wall; equation (3)
-
axial ratio of ellipse, = a/b = /
-
, , ,
dimensionless coordinates; =x/D, =y/D, =z/D, =n/D
-
dimensionless temperature, = (T–T
s)/(T
i–T
s)
-
0
cup-mixing mean value of ; equation (10)
-
thermal conductivity of fluid
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m,n
=
k
eigenvalue
-
c
volumetric heat capacity of fluid
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m, n
=
k
=
k
eigenfunction; equations (6) and (I)
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Nu
total Nusselt number, =
t
D/
-
Nusselt number at large distance from the inlet
-
Nu
w
wall Nusselt number, =
w
D/ , based on
w
-
Pé
Péclet number, =
0
D c/![lambda](/content/h525j4x06287543m/xxlarge955.gif) |
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Keywords: | |
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