As a thermo-fluid engineer working for an energy startup located at Greentown Labs, you are tasked to characterize the performance of a heat exchanger that will be used in the Arctic Region to heat cold water (Cp=4180 J/kg °C) with a wind-power-heated hot gas (cp=2100 J/kg-°C). Cold water enters the inner tube of a double-pipe parallel flow heat exchanger at 4°C at a rate of 1.2 kg/s. The mass flow rate and the inlet temperature of hot gas is 2.3 kg/s and 52°C, respectively. If the inner tube has a diameter of 5 cm with 8 m length and the overall heat transfer coefficient of the heat exchanger is 950 W/m2.°C, determine the outlet temperature of cold water in °C. If needed, use efficiency-NTU equations given below NOT the figures!!!

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Effectiveness relations for heat exchangers: NTU = UA/Cmin
and C = Cmin/Cmax = (mC,)min/(ṁCplmax
Heat exchanger
type
1 Double pipe:
NTU relations for heat exchangers NTU = UA/ Cmin
and C = Cmin/Cmax
Heat exchanger type
1 Double-pipe:
= (mCp)min/(mC,)max
Effectiveness relation
||
NTU relation
1- exp [-NTU(1 + C)]
1+ C
Parallel-flow
In[1- e(1 + C)]
1+ C
NTU = -
1- exp [-NTU(1 - C)]
1 - Cexp [-NTU(1 - C)]
Parallel-flow
Counter-flow
E =
1
-
2 Shell and tube:
Counter-flow
NTU
-In
One-shell pass
C- 1
€С - 1
-1
1+ exp [-NTUV1 + C®]
1 - Cexp [-NTUV1 + C]
2, 4, . . . tube
C+ V1 + C2.
2 Shell and tube:
passes
2/ɛ - 1-C- V1 + C2
One-shell pass
2, 4, . . . tube passes
1
|
Vnle - 1 – C + V1+ C²,
3 Cross-flow
NTU =
+ C?
2/8 -1-C+ V1 + C²,
(single-pass)
Both fluids
NTU0 22
3 Cross-flow (single-pass)
ɛ = 1- exp:
-[exp (-CNTUO.78) -
C
In(1 – ɛC)
Cmax mixed,
Cmin unmixed
unmixed
|
NTU = -In 1+
C
Cmax mixed,
Cmin unmixed
==(1 - exp(1-C[1 – exp (-NTU)]})
E
Cmin mixed,
Cmax unmixed
NTU = - InCIn(1 – ɛ) + 1]
C
|
Cmin mixed,
Cmax unmixed
e = 1- exp
exp (-CNTU)]
4 All heat exchangers
4 All heat
NTU = -In(1 - 8)
with C = 0
exchangers
with C = 0
e = 1- exp(-NTU)
Source: Kays and London, Ref. 7.
Source: Kays and London, Ref. 7.
Transcribed Image Text:Effectiveness relations for heat exchangers: NTU = UA/Cmin and C = Cmin/Cmax = (mC,)min/(ṁCplmax Heat exchanger type 1 Double pipe: NTU relations for heat exchangers NTU = UA/ Cmin and C = Cmin/Cmax Heat exchanger type 1 Double-pipe: = (mCp)min/(mC,)max Effectiveness relation || NTU relation 1- exp [-NTU(1 + C)] 1+ C Parallel-flow In[1- e(1 + C)] 1+ C NTU = - 1- exp [-NTU(1 - C)] 1 - Cexp [-NTU(1 - C)] Parallel-flow Counter-flow E = 1 - 2 Shell and tube: Counter-flow NTU -In One-shell pass C- 1 €С - 1 -1 1+ exp [-NTUV1 + C®] 1 - Cexp [-NTUV1 + C] 2, 4, . . . tube C+ V1 + C2. 2 Shell and tube: passes 2/ɛ - 1-C- V1 + C2 One-shell pass 2, 4, . . . tube passes 1 | Vnle - 1 – C + V1+ C², 3 Cross-flow NTU = + C? 2/8 -1-C+ V1 + C², (single-pass) Both fluids NTU0 22 3 Cross-flow (single-pass) ɛ = 1- exp: -[exp (-CNTUO.78) - C In(1 – ɛC) Cmax mixed, Cmin unmixed unmixed | NTU = -In 1+ C Cmax mixed, Cmin unmixed ==(1 - exp(1-C[1 – exp (-NTU)]}) E Cmin mixed, Cmax unmixed NTU = - InCIn(1 – ɛ) + 1] C | Cmin mixed, Cmax unmixed e = 1- exp exp (-CNTU)] 4 All heat exchangers 4 All heat NTU = -In(1 - 8) with C = 0 exchangers with C = 0 e = 1- exp(-NTU) Source: Kays and London, Ref. 7. Source: Kays and London, Ref. 7.
As a thermo-fluid engineer working for an energy startup located at Greentown Labs, you are tasked to
characterize the performance of a heat exchanger that will be used in the Arctic Region to heat cold water
(Cp=4180 J/kg °C) with a wvind-power-heated hot gas (c,=2100 J/kg·°C). Cold water enters the inner tube
of a double-pipe parallel flow heat exchanger at 4°C at a rate of 1.2 kg/s. The mass flow rate and the inlet
temperature of hot gas is 2.3 kg/s and 52°C, respectively. If the inner tube has a diameter of 5 cm with 8
m length and the overall heat transfer coefficient of the heat exchanger is 950 W/m2.°C, determine the
outlet temperature of cold water in °C. If needed, use efficiency-NTU equations given below NOT the
figures!!!
Transcribed Image Text:As a thermo-fluid engineer working for an energy startup located at Greentown Labs, you are tasked to characterize the performance of a heat exchanger that will be used in the Arctic Region to heat cold water (Cp=4180 J/kg °C) with a wvind-power-heated hot gas (c,=2100 J/kg·°C). Cold water enters the inner tube of a double-pipe parallel flow heat exchanger at 4°C at a rate of 1.2 kg/s. The mass flow rate and the inlet temperature of hot gas is 2.3 kg/s and 52°C, respectively. If the inner tube has a diameter of 5 cm with 8 m length and the overall heat transfer coefficient of the heat exchanger is 950 W/m2.°C, determine the outlet temperature of cold water in °C. If needed, use efficiency-NTU equations given below NOT the figures!!!
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