D
Tfb
X
X
q
Kf
Saturated
Saturated
L
Vapor, Tsat
L
Vapor, Tsat
Kf
g
g
δ
q
δ(L)
Figure 4. Pin fin in upward
Tfb
D
and downward vertical ori-
entations.
(a) (U)pUparardPoiinttiingg
a w w d Po n n
(b) (D)oDonwward Pointiting
b w wn ard P oinng
Selecting a number of values for D, the corresponding values of L can be found. The re-
sults are summarized below:
D (mm)
L (mm)
5
8.18
7.5
10.54
10
12.60
12.5
14.51
15
16.26
Vertical cylindrical (pin) fin
Figure 4 shows a cylindrical fin in two vertical orientations--upward and downward.
For the upward pointing fin, the distance x is measured from the tip, while for the
downward pointing fin, the same is measured from the base. The essential difference
between the horizontal and vertical fins is that for the former, the surface was isothermal
along the direction (circumferential) of condensate flow, while in the latter, the tempera-
ture decreases for upward configuration or increases for downward configuration along
the condensate flow direction. Thus the original Nusselt's theory, which assumes isother-
mal conditions along the condensate flow direction, is not directly applicable for the
vertical fins of Figure 4. However, Lienhard and Dhir (1974) have shown that the Nus-
selt's theory, if appropriately modified to account for a nonisothermal surface, gives
results that are close to the predictions of the full boundary layer equations. For a noniso-
thermal flat vertical surface, the modified Nusselt's theory gives the following expression
for the value of (circumferential average) at any location x from the leading edge:
1/ 4
gρ (ρ - ρ ) k 3h
h = 0.7071
v l fg
.
(7)
ll
l ∫0 (Tsat - Tf ) dx
x
Equation 7 applies to a cylindrical surface if the curvature effects are small, that is,
δ (L) << 1 2 D . Using the definitions of θ and X from Horizontal Cylindrical Fin, eq 7 can be
5
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