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Incropera & DeWitt
L3
Lecture 3 Heat Exchangers J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.1
Heat Exchangers •Transfer heat from one fluid to another. •Want to minimise necessary hardware.
Examples: boilers, condensors, car radiator, air-conditioning coils, human body.
Types: eg.
LIQUID-LIQUID
LIQUID-GAS
GAS-GAS
Shell and tube
Air-conditioning
Furnace superheater
J. H. Kent
1
Heat Exchangers
Incropera & DeWitt 11.1
J. H. Kent
Incropera & DeWitt 11.1
J. H. Kent
2
Incropera & DeWitt
Heat Exchangers
11.1
Configurations FLUID B FLUID A
FLUID B FLUID A
COUNTERFLOW
PARALLEL FLOW
FLUID A
FLUID B
(unmixed)
ONE-SHELL, FOUR TUBE PASSES
CROSSFLOW
(mixed) J. H. Kent
Heat Exchangers
Incropera & DeWitt 11.2 Table 11.1, 11.2
Overall Heat Transfer Coefficient U Internal and external thermal resistances in series.
1 1 1 = + UA (UA)c (UA)h R′′ R′′ 1 1 1 = + f ,c + Rw + + f ,c (hηo A)h (ηo A)h UA (hηo A)c (ηo A)c
Rw
wall A is wall total surface area hot or cold side.
fin
Fouling factor R"f (m2 K/W) for seawater, fuel oil etc.
ηo overall surface efficiency (if finned) J. H. Kent
3
Incropera & DeWitt
Heat Exchangers
11.3
Heat Exchanger Analysis Want a relationship Q& = UA ∆Tm where ∆Tm is some mean ∆T between hot and cold fluid. Th1
Th1
hot fluid
∆T1
dTh
Tc1
dQ cold fluid
Th2 Th2
∆T1
∆T2
∆T2
dTc
Tc2
Tc2
Tc1
end 1
end 2 Counterflow Note Th,out can be < Tc,out
end 1
Parallel Flow T’s cannot cross
end 2
J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.3
Energy Balance (counterflow)
Th1
on element shown.
dQ& = − m& h ch dTh = − m& c cc dTc
(1)
Tc1
m& mass flow rate of fluid c specific heat
end 1
Rate Equation dQ& = UdA(Th − Tc ) Now from (1)
dTh =
dTc =
dQ dTc Tc
Th2 Tc2 end 2
(dT in direction 1 → 2)
(2)
− dQ& m& h ch
Th dTh
− dQ& m& c cc
1 1 ∴ d (Th − Tc ) = dQ& − m& c cc m& h ch J. H. Kent
4
Incropera & DeWitt
Heat Exchangers
11.3
& from (2), Sub. dQ 1 d (Th − Tc ) 1 dA = U − (Th − Tc ) m& c cc m& h ch Integrate 1 → 2
T −T 1 1 ln h 2 c 2 = UA − Th1 − Tc1 m& c cc m& h ch
Th1 Tc1
Total heat transfer rate
Th2 Tc
Q& = m& h ch (Th1 − Th 2 )
and
Q& = m& c cc (Tc1 − Tc 2 ) J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.3
Sub for m& c and put
∆T1 = Th1 − Tc1
END 1
∆T2 = Th 2 − Tc 2
END 2
∆T2 − ∆T1 Q& = UA ln (∆T2 ∆T1 )
∆T1 ∆T2 end 1
end 2
Q& = UA(LMTD) LOG MEAN TEMPERATURE DIFFERENCE • Remember - 1 and 2 are ends, not fluids • Same formula for parallel flow (but ∆T’s are different) • Counterflow has highest LMTD, for given T’s therefore smallest area for Q.
J. H. Kent
5
Incropera & DeWitt
Heat Exchangers
11.3
∆T1 ∆T2
end 1
end 2
∆T1 ∆T2 end 1
Condenser
end 2 Evaporator
J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.3
Crossflow and Multipass Q& = F UA(LMTD )counterflow where F = f(Th1, Th2, Tc1, Tc2, configuration) is correction factor relative to counterflow (ideal) configuration. • F
L3
Lecture 3 Heat Exchangers J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.1
Heat Exchangers •Transfer heat from one fluid to another. •Want to minimise necessary hardware.
Examples: boilers, condensors, car radiator, air-conditioning coils, human body.
Types: eg.
LIQUID-LIQUID
LIQUID-GAS
GAS-GAS
Shell and tube
Air-conditioning
Furnace superheater
J. H. Kent
1
Heat Exchangers
Incropera & DeWitt 11.1
J. H. Kent
Incropera & DeWitt 11.1
J. H. Kent
2
Incropera & DeWitt
Heat Exchangers
11.1
Configurations FLUID B FLUID A
FLUID B FLUID A
COUNTERFLOW
PARALLEL FLOW
FLUID A
FLUID B
(unmixed)
ONE-SHELL, FOUR TUBE PASSES
CROSSFLOW
(mixed) J. H. Kent
Heat Exchangers
Incropera & DeWitt 11.2 Table 11.1, 11.2
Overall Heat Transfer Coefficient U Internal and external thermal resistances in series.
1 1 1 = + UA (UA)c (UA)h R′′ R′′ 1 1 1 = + f ,c + Rw + + f ,c (hηo A)h (ηo A)h UA (hηo A)c (ηo A)c
Rw
wall A is wall total surface area hot or cold side.
fin
Fouling factor R"f (m2 K/W) for seawater, fuel oil etc.
ηo overall surface efficiency (if finned) J. H. Kent
3
Incropera & DeWitt
Heat Exchangers
11.3
Heat Exchanger Analysis Want a relationship Q& = UA ∆Tm where ∆Tm is some mean ∆T between hot and cold fluid. Th1
Th1
hot fluid
∆T1
dTh
Tc1
dQ cold fluid
Th2 Th2
∆T1
∆T2
∆T2
dTc
Tc2
Tc2
Tc1
end 1
end 2 Counterflow Note Th,out can be < Tc,out
end 1
Parallel Flow T’s cannot cross
end 2
J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.3
Energy Balance (counterflow)
Th1
on element shown.
dQ& = − m& h ch dTh = − m& c cc dTc
(1)
Tc1
m& mass flow rate of fluid c specific heat
end 1
Rate Equation dQ& = UdA(Th − Tc ) Now from (1)
dTh =
dTc =
dQ dTc Tc
Th2 Tc2 end 2
(dT in direction 1 → 2)
(2)
− dQ& m& h ch
Th dTh
− dQ& m& c cc
1 1 ∴ d (Th − Tc ) = dQ& − m& c cc m& h ch J. H. Kent
4
Incropera & DeWitt
Heat Exchangers
11.3
& from (2), Sub. dQ 1 d (Th − Tc ) 1 dA = U − (Th − Tc ) m& c cc m& h ch Integrate 1 → 2
T −T 1 1 ln h 2 c 2 = UA − Th1 − Tc1 m& c cc m& h ch
Th1 Tc1
Total heat transfer rate
Th2 Tc
Q& = m& h ch (Th1 − Th 2 )
and
Q& = m& c cc (Tc1 − Tc 2 ) J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.3
Sub for m& c and put
∆T1 = Th1 − Tc1
END 1
∆T2 = Th 2 − Tc 2
END 2
∆T2 − ∆T1 Q& = UA ln (∆T2 ∆T1 )
∆T1 ∆T2 end 1
end 2
Q& = UA(LMTD) LOG MEAN TEMPERATURE DIFFERENCE • Remember - 1 and 2 are ends, not fluids • Same formula for parallel flow (but ∆T’s are different) • Counterflow has highest LMTD, for given T’s therefore smallest area for Q.
J. H. Kent
5
Incropera & DeWitt
Heat Exchangers
11.3
∆T1 ∆T2
end 1
end 2
∆T1 ∆T2 end 1
Condenser
end 2 Evaporator
J. H. Kent
Incropera & DeWitt
Heat Exchangers
11.3
Crossflow and Multipass Q& = F UA(LMTD )counterflow where F = f(Th1, Th2, Tc1, Tc2, configuration) is correction factor relative to counterflow (ideal) configuration. • F
