In cars, the coolant cools down the engine and prevents overheating. By absorbing heat from the engine, the coolant becomes heated. The coolant is then cooled down by the radiator. A primitive car radiator can be considered an unmixed crossflow heat exchanger where cold air from the outside serves as cold fluid that cools down the hot coolant. Assume the average specific heat of air and the coolant are, respectively, 1007 J/kg-K and 3300 J/kg.K. The coolant enters the radiator at 120°C and exits at 50°C. The mass flow rate of the coolant is 0.4 kg/s. The air intake temperature is 20°C and you measured the outlet temperature of the air to be 40°C. What is the effectiveness of this radiator? What is the UA of this radiator?
In cars, the coolant cools down the engine and prevents overheating. By absorbing heat from the engine, the coolant becomes heated. The coolant is then cooled down by the radiator. A primitive car radiator can be considered an unmixed crossflow heat exchanger where cold air from the outside serves as cold fluid that cools down the hot coolant. Assume the average specific heat of air and the coolant are, respectively, 1007 J/kg-K and 3300 J/kg.K. The coolant enters the radiator at 120°C and exits at 50°C. The mass flow rate of the coolant is 0.4 kg/s. The air intake temperature is 20°C and you measured the outlet temperature of the air to be 40°C. What is the effectiveness of this radiator? What is the UA of this radiator?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Heat Exchangers
Heat exchangers are the types of equipment that are primarily employed to transfer the thermal energy from one fluid to another, provided that one of the fluids should be at a higher thermal energy content than the other fluid.
Heat Exchanger
The heat exchanger is a combination of two words ''Heat'' and ''Exchanger''. It is a mechanical device that is used to exchange heat energy between two fluids.
Question
Transcribed Image Text:In cars, the coolant cools down the engine and prevents overheating. By absorbing heat from the engine,
the coolant becomes heated. The coolant is then cooled down by the radiator. A primitive car radiator
can be considered an unmixed crossflow heat exchanger where cold air from the outside serves as cold
fluid that cools down the hot coolant. Assume the average specific heat of air and the coolant are,
respectively, 1007 J/kg-K and 3300 J/kg.K. The coolant enters the radiator at 120°C and exits at 50°C.
The mass flow rate of the coolant is 0.4 kg/s. The air intake temperature is 20°C and you measured
the outlet temperature of the air to be 40°C. What is the effectiveness of this radiator? What is the
UA of this radiator?
![Effectiveness and NTU relationships for common heat exchangers
Effectiveness as a function of NTU and Cr:
Parallel flow:
Counter flow:
One shell and 2, 4, ... tube passes":
n shells and 2n, 4n, ... tube passes*:
Cross-flow both unmixed:
Cross-flow* Cmar on mixed side:
Cross-flow* Cmin on mixed side:
All heat exchangers with C, = 0:
NTU as a function of e and Cr:
Parallel flow:
Counter flow:
One shell and 2, 4, ... tube passest:
n shells and 2n, 4n, ... tube passes¹:
Cross-flow both unmixed:
Cross-flow" Cmaz on mixed side:
Cross-flow* Cmin on mixed side:
€ =
All heat exchangers with Cr = 0:
€ =
=
1 - exp[-NTU (1 + Cr)]
1+ Cr
1- exp[-NTU (1 - Cr)]
1 - C, exp[-NTU (1 — Cr)]'
NTU
1+ NTU'
when C₂ = 1
€1 = 21+ C₂ + (1+C²) ¹1/²
€ =
1
€ =
= [(²₁₁ ²¹+ )" - ¹] [(²¹²¹)" - c]'
1-
€1
€1
Use ₁ and NTU₁ from Eqn. 4
€ = 1- exp
F
NTU=
(1 - exp{-C, [1 - exp(-NTU)]})
NTU=
€ = 1 - exp[-C₂¹ (1 - exp[-CrNTU])]
€ = 1- exp(- NTU)
=
[(+)₁ NTU0.22 [exp(-C, NTU0.78) - :
1+ exp-NTU₁ (1+ -C²) ¹/2
1- exp -NTU₁ (1+C²) ¹/2]
C₂²-1¹n (6--11),
In
Cr
In [1 - € (1 + Cr)]
1+ Cr
1 when C₁ = 1
€
NTU₁ = (1 + C²)-¹/2 In
€1 =
when Cr < 1
F-1
F-Cr
Solve Eqn. 6 numerically
NTU - In
NTU=-
NTU = nx NTU₁, use NTU₁ is from Eqn. 13 with €₁ as
1/n
= (Cr-1) ¹/
F =
1
Cr
ln (1-ɛ)
when Cr < 1
(E = 1).
- In [1 + / - In (1 - eCr)]
E =
2 − (1+Cr)
(1+C2) ¹1/2
In [Cr In (1 e) + 1]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(16)
NTU=
(17)
1: If it is only a one-shell heat exchanger, € = ₁ and NTU = NTU₁. If there are n shells, use the ₁ and NTU₁ calculated based on one
shell formulation and calculate final and NTU for the entire heat exchanger. Also note, number of tubes does not directly feature in these
equations, they come in via the total area calculation.
*: Single pass crossflow heat exchangers
(13)
(14)
(15)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20000a63-5a8a-4b5e-adbd-85ecbf6c298b%2F7a3664ed-5f27-417f-9977-9fdf8e39da6f%2Fuwcekui_processed.png&w=3840&q=75)
Transcribed Image Text:Effectiveness and NTU relationships for common heat exchangers
Effectiveness as a function of NTU and Cr:
Parallel flow:
Counter flow:
One shell and 2, 4, ... tube passes":
n shells and 2n, 4n, ... tube passes*:
Cross-flow both unmixed:
Cross-flow* Cmar on mixed side:
Cross-flow* Cmin on mixed side:
All heat exchangers with C, = 0:
NTU as a function of e and Cr:
Parallel flow:
Counter flow:
One shell and 2, 4, ... tube passest:
n shells and 2n, 4n, ... tube passes¹:
Cross-flow both unmixed:
Cross-flow" Cmaz on mixed side:
Cross-flow* Cmin on mixed side:
€ =
All heat exchangers with Cr = 0:
€ =
=
1 - exp[-NTU (1 + Cr)]
1+ Cr
1- exp[-NTU (1 - Cr)]
1 - C, exp[-NTU (1 — Cr)]'
NTU
1+ NTU'
when C₂ = 1
€1 = 21+ C₂ + (1+C²) ¹1/²
€ =
1
€ =
= [(²₁₁ ²¹+ )" - ¹] [(²¹²¹)" - c]'
1-
€1
€1
Use ₁ and NTU₁ from Eqn. 4
€ = 1- exp
F
NTU=
(1 - exp{-C, [1 - exp(-NTU)]})
NTU=
€ = 1 - exp[-C₂¹ (1 - exp[-CrNTU])]
€ = 1- exp(- NTU)
=
[(+)₁ NTU0.22 [exp(-C, NTU0.78) - :
1+ exp-NTU₁ (1+ -C²) ¹/2
1- exp -NTU₁ (1+C²) ¹/2]
C₂²-1¹n (6--11),
In
Cr
In [1 - € (1 + Cr)]
1+ Cr
1 when C₁ = 1
€
NTU₁ = (1 + C²)-¹/2 In
€1 =
when Cr < 1
F-1
F-Cr
Solve Eqn. 6 numerically
NTU - In
NTU=-
NTU = nx NTU₁, use NTU₁ is from Eqn. 13 with €₁ as
1/n
= (Cr-1) ¹/
F =
1
Cr
ln (1-ɛ)
when Cr < 1
(E = 1).
- In [1 + / - In (1 - eCr)]
E =
2 − (1+Cr)
(1+C2) ¹1/2
In [Cr In (1 e) + 1]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(16)
NTU=
(17)
1: If it is only a one-shell heat exchanger, € = ₁ and NTU = NTU₁. If there are n shells, use the ₁ and NTU₁ calculated based on one
shell formulation and calculate final and NTU for the entire heat exchanger. Also note, number of tubes does not directly feature in these
equations, they come in via the total area calculation.
*: Single pass crossflow heat exchangers
(13)
(14)
(15)
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