A vertical rectangular water duct 1-m-high and 0.1-m-deep shown in the sketch is placed in an environment of saturated steam at atmospheric pressure. If the outer surface of the duct is about 50°C, estimate the rate of steam condensation per unit length.
GIVEN
? Water-cooled rectangular duct, 1-m-high, 0.1-m-deep
? Duct surface is 50°C
? Steam environment
FIND
(a) Rate of steam condensation per unit length of the duct
ASSUMPTIONS
? The steam is at 1 atmosphere pressure
? Condensation from the horizontal duct surfaces can be neglected
? Laminar film condensation on the vertical surfaces (must be checked)
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 13, the properties of saturated liquid at the mean temperature of 75°C are
From Appendix 2, Table 35, the properties of the saturated vapor at the saturation temperature of 100°C are
The mean flow of condensate per unit duct length is from Equation (9.14)
and the film thickness can be found from Equation (9.17)
where
Calculating the condensate film thickness at the bottom edge of the duct, we have
Now, we can calculate the film flow per unit duct length
Doubling this to account for both sides of the duct, we have 0.171 kg/m s for the rate of condensate flow, per unit duct length.
To confirm that the Reynolds number for the condensate film flow is laminar
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