Page 212 - Mechanical Engineers' Handbook (Volume 4)

4 Boiling and Condensation Heat Transfer 201

Table 24 Values of C and n for Simplified Relations for Boiling in Water
Surface q (kW/m ) C n
2
Horizontal q 16 1042 1/3
16 q 240 5.56 3
Vertical q 3 5.7 1/7
3 q 63 7.96 3

4.2 Condensation
Depending on the surface conditions, the condensation may be a film condensation or a
dropwise condensation. Film condensation usually occurs when a vapor, relatively free of
impurities, is allowed to condense on a clean, uncontaminated surface. Dropwise conden-
sation occurs on highly polished surfaces or on surfaces coated with substances that inhibit
wetting. The condensate provides a resistance to heat transfer between the vapor and the
surface. Therefore, it is desirable to use short vertical surfaces or horizontal cylinders to
prevent the condensate from growing too thick. The heat-transfer rate for dropwise conden-
sation is usually an order of magnitude larger than that for film condensation under similar
conditions. Silicones, Teflon, and certain fatty acids can be used to coat the surfaces to
promote dropwise condensation. However, such coatings may lose their effectiveness owing
to oxidation or outright removal. Thus, except under carefully controlled conditions, film
condensation may be expected to occur in most instances, and the condenser design calcu-
lations are often based on the assumption of film condensation.
For condensation on surface at temperature T the total heat-transfer rate to the surface
s
is given by q hA (T sat T ), where T sat is the saturation temperature of the vapor. The
s
L
mass flow rate is determined by ˙m q/h ; h is the latent heat of vaporization of the fluid
ƒg
ƒg
(see Table 25 for saturated water). Correlations are based on the evaluation of liquid prop-
erties at T (T T )/2, except h , which is to be taken at T .
sat
ƒ
s
sat
ƒg
Film Condensation on a Vertical Plate
The Reynolds number for condensate flow is defined by Re V D / , where and
l
l
h

l
m
are the density and viscosity of the liquid, V is the average velocity of condensate, and
l
m
D is the hydraulic diameter defined by D 4 condensate film cross-sectional area/
h
h
wetted perimeter. For the condensation on a vertical plate Re 4 / , where is the mass
l

flow rate of condensate per unit width evaluated at the lowest point on the condensing
surface. The condensate flow is generally considered to be laminar for Re 1800, and

turbulent for Re 1800. The average Nusselt number is given by 22

Nu 1.13 g ( )hL 3 0.25 for Re 1800
fg
v
l
l

L
T )
k (T
sat
ll
s
Nu 0.0077 g ( )L 3 1/3 0.4
l
l
v
L

2 Re for Re 1800
l
Film Condensation on the Outside of Horizontal Tubes and Tube Banks
Nu 0.725 g ( )hD 3 0.25
v
l
l
fg
D
N k (T sat T )
s
l l
where N is the number of horizontal tubes placed one above the other; N l for a single
tube. 23