Question 3 A commercial air-conditioning system unit in a motel rejects heat ordinarily to the atmosphere. It is proposed that a heat exchanger be installed in which water from the swimming pool will...

Question 1:
Solution:
The schematic representation of the system is shown below,
By using the given data the computation are performed,
Using ? − ??? method, the capacity rates are found,
?ℎ = ?ℎ̇ ??,ℎ = (?????)ℎ?. ??,ℎ
?ℎ =
1
1.0850 ∗ 10−3
?3
??

∗
?
4
(10.2 ∗ 10−3 ?)2 ∗ 0.5
?
?
∗ 32 ∗ 4297
?
??. ?
= 5178
?
?

?? = ????,? = (??)?̇ ??,? = 1.2407
??
?3
∗ 1
?3
?
∗ 1007
?
??. ?
= 1249
?
?

The heat transfer co-efficient is computed as below by considering cold fluid as the minimum
fluid,
???? = [
1
ℎ???
+
1
ℎ???
]
−1

The Reynolds number is computed for estimating internal flow co
ections,
??? =
?????
?
=
(
1
1.0850 ∗ 10−3 ?3??
) ∗ 0.5
?
? ∗
(10.2 ∗ 10−3 ?)
188 ∗ 10−6
?. ?
?2
= 25,002
Hence the flow us tu
ulent,
?
??
=
0.6?
10.2 ∗ 10−3 ?
= 59
The Dittus-Boelter co
elation is used with assumption of n=0.3 we get,
??? =
ℎ???
?
= 0.023???
0.8Pr0.3 = 0.023(25,002)0.8(1.18)0.3 = 79.7
ℎ? =
?
??
??? =
0.688
?
?. ?
10.2 ∗ 10−3?
∗ 79.7 = 5376
?
?2. ?

Substituting for heat transfer co-efficient we get,
?? = [(
12.5??
10.2??
)
1
5376
?
?2. ?
+
1
400
?
?2. ?
]
−1
= 366.6
?
?2. ?

??? =
????
????
=
366.6
?
?2. ?
∗ (32 ∗ ? ∗ 12.5 ∗ 10−3? ∗ 0.6 ?)
1249
?
?2. ?
= 0.22
Therefore the ratio of mixed to the unmixed condition is,
??????
????????
=
????
????
=
??
?ℎ
=
1249
?
?
5178
?
?
= 0.24
Hence,
? =
?
????
=
??(??,? − ??,?)
????(?ℎ,? − ??,?)

??,? = ??,? + ?(?ℎ,? − ??,?) = 10
?? + 0.19(150 − 10)?? = 36.6??
By equating energy balance we get,
??(??,? − ??,?) = ?ℎ(?ℎ,? − ?ℎ,?)
?ℎ,? = ?ℎ,? −
??
?ℎ
(??,? − ??,?)
?ℎ,? = 150
?? −
1249
?
?
5178
?
?
(36.6 − 10)?? = 143.5??
Hence the outlet temperature of air is 36.6??
Question 2:
Solution:
From the questionnaire it has been given as 3
?
?2?
as convection heat transfer co-efficient by
assuming it for ventilation system the heat transfer are expressed and the sche,matic
epresentation of the system is,
Thermal simulation of the building in flow-sheet is,
The performance estimate are expressed below,
Conduction:
The rate of heat conduction through elements such as roof, wall or floor are,
????? = ??∆? = ??(??? − ???)
Where ? =
1
??

The total thermal resistance is computed using the below expression,
?? =
1
ℎ?
+ (∑
??
??
?
?=1
) +
1
ℎ?

The heat flow rate in the building envelope is,
?? = ∑ ????∆??
??
?=1

Where, i  building element and Nc  number of components
Ventilation:
The heat flow rate between interior of the building and the exterior is determined using the
computation of ventilation,
?? = ????∆?
Where,
? → ??????? ?? ??? (
??
?3
)
?? → ??????????? ???? (
?3
?
)
? → ???????? ℎ??? ?? ??? (
?
??
− ? )
∆? → ??????????? ?????????? (??? − ???) ?
Once the number of air changes known the above expression will be expressed as,
?? =
??
3600

Where,
? → ?????? ?? ??? ?ℎ????? ??? ℎ???
? → ?????? ?? ?ℎ? ???? (??) ????? (?3)
?? = ??
??
3600
∆?
Hence by following the above method helps in computation of heat transfer by ventilation
system.
Question 3:
Solution:
Part (A) Fin Efficiency
???? =
�̇�???
�̇�???,???
=
√ℎ???? (?? − ?∞)
ℎ????(?? − ?∞)
→ ??. (1)
???? = 2. ?. [?
2 + (
?
2
)
2
]
1
2
= 2 ∗ 30 ∗ 10−2 [7.86 ∗ 10−3 + (
12 ∗ 10−3
2
)
2
]
1
2
= 0.05332 ?2
? = ?? = ? ∗ 30 ∗ 10−2 = 0.9425 ?
? = 14.4
?
??

ℎ = 2400
?
?2?

?? = ? ∗ ? = 7.86 ∗ 10
−3 ∗ 12 ∗ 10−3 = 94.32 ∗ 10−6 ?2
???? =
√2400 ∗ 0.9425 ∗ 14.4 ∗ 94.32 ∗ 10−5 ∗ ((88 + 273) −...