(5) in order to enhance heat transfer, what ways can be employed? Solution:
（1） enthalpy balance q?m1cp1(t2?t1)?m2cp2(T1?T2) m1?4.187?（55-15）=500?3.35?（90-40） m1=500.8kg/h
(2) overall coefficient based on outside surface of tube:
Uo?1d01?hidih0?11801?1000?160299?224W/m2.k
(3) t1?15℃???t2?55℃
T2?40℃???T1?90℃
?t1?25℃ ?t2?35℃
?tm?35?25?29.7℃ 35ln25energy balance q?m1cp1(t2?t1)?UOAo?tm
500.8?4.187?103?(55?15)?224???0.18L?29.7 3600 L=4.64m (4) when t1?20℃ energy balance
500.8?4.187?（t′2-20）=500?3.35?（90-T′2） t′2=92-0.8 T′2 (1)
??20)UA?tm?q?m2cp2(t2?? qm2cp2(55?15)UA?tmsimplifying the equation above
???20?tm?t?q?t2???m (2) q55?15?tm29.7???tm??(T2??20)90?t2 (3) ?90?t2lnT2??20combining equations 12 and 3
ln0.8T2??214.86?0.15T2?? （4）
T2??2072?0.8T2?solving for outlet temperature of warm fluid by trial-error T′2=50℃
Substituting this temperature into equation 1 gives t′2=52℃
4.22 There are two same shell-tube exchangers (1-1 pass) in stock. Each one consists of 64 tubes with dimension ?27?3.5 mm and heat transfer area 20 m2. The saturated vapor with condensation latent heat 2054 kJ/kg at 170 oC goes through the shell and condenses to saturated liquid. Air at 30 oC passes fully turbulently through the tubes with mass flow rate 2.5 kg/s.
(1)If two exchangers are installed parallelly, mass flow rate of air (cp= 1 kJ/kg?K) is 1.25kg/s for each exchanger and heat transfer coefficient of air is 38 W/m2?K. If the flow pattern of air is fully turbulent, what are outlet temperature of air and vapor flow rate?
(2)If two exchangers work in series with air mass flow rate 2.5kg/s, what are outlet temperature of air and vapor flow rate now? The heat resistances of pipe wall and vapor and the heat loss are ignored.
(answer: 93.6oC, 0.077kg/s; 121.4oC, 0.11kg /s)
Solution :
(1)Write energy balance equation
mcp(t2?t1)?UoAo?tm?UoAot2?t1
T?t1lnT?t2so
lnT?t1UoAo?
T?t2mcpset Uo=hi because the thermal resistance from saturated vapor to wall of tube and resistance of wall are very small and negligible
ln170?3038?20??0.608
170?t21.25?1000170?3038?20??1.837
170?t21.25?1000t2=93.8 oC
the rate of condensate for one condenser
mh1?mcp(t2?t1)??1.25?1000?93.8?30??0.0388kg/s
2054?1000sum of condensate for two condensers in parallel mh=2mh1=2×0.0388=0.0776kg/s
(2) two condensers operate in series
heat transfer coefficient between the air and wall of tubes
??hi???u??Uo??????u?Uo?h?i???0.8?20.8?1.74
U′38=66.12 W/m2?K. o=1.74Uo=1.74×
lnso
??2AoT?t1Uo? ?T?t2mcpln170?3066.12?40??1.058 ?170?t22.5?1000170?30?2.88 ?170?t2 o
t′2=121.4C
mh???t1)m?cp(t2??2.5?1000?121.4?30??0.111kg/s
2054?1000