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Answer - Ert 216 Midterm2

The document contains a mid-term test with three questions on heat exchangers: 1. It defines the fouling factor equation and describes phenomena like deposits and biological growth that contribute to fouling of heat exchangers. It discusses adding chemical inhibitors to minimize these problems. 2. It describes cross-flow and shell-and-tube heat exchangers, sketching their designs. It then calculates heat transfer rates and exit temperatures for a problem involving hot oil and water in a counterflow shell-and-tube exchanger. 3. It solves for the area required for a heat exchanger problem involving cooling oil with water, calculating temperatures, heat transfer rates, and the exit temperature of the

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2K views5 pages

Answer - Ert 216 Midterm2

The document contains a mid-term test with three questions on heat exchangers: 1. It defines the fouling factor equation and describes phenomena like deposits and biological growth that contribute to fouling of heat exchangers. It discusses adding chemical inhibitors to minimize these problems. 2. It describes cross-flow and shell-and-tube heat exchangers, sketching their designs. It then calculates heat transfer rates and exit temperatures for a problem involving hot oil and water in a counterflow shell-and-tube exchanger. 3. It solves for the area required for a heat exchanger problem involving cooling oil with water, calculating temperatures, heat transfer rates, and the exit temperature of the

Uploaded by

norsiah
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MID-TERM TEST 2 ERT216

Question 1

a) Define fouling factors by equation.


[10 Marks]
The fouling factor, Rf is define as: 1 1
Rf  
U dirty U clean

b) Describe phenomena that contribute to fouling factors of heat exchanger and discuss on
how to avoid or lessen these fouling problems.
[20 Marks]

• After a period of operation, the heat transfer surface for a heat exchanger may become
coated with various deposits present in the flow system, dirt, soot or the surface may
become corroded as a result of the interaction between the fluids and the material used
for construction of the heat exchanger.
• Biological growth such as algae can occur with cooling water in the biological
industries.
• These deposits offer additional resistance to the flow of heat and reduce the overall heat
transfer coefficient U.
• To avoid or lessen these fouling problems, chemical inhibitors are often added to
minimize corrosion, salt deposition and algae growth.
• It is necessary to oversize an exchanger to allow for the reduction in performance during
operation.

c) Oil flowing at the rate of 5.04 kg/s (c pm=2.09 kJ/kg K) is cooled in a 1-2 heat exchanger
from 366.5 K to 344.3 K by 2.02 kg/s of water entering at 283.2 K. The overall heat-
transfer coefficient Uo is 340 W/m2 K. Calculate the area required.
[20 Marks]
T’2=366.5K
T’1=344.3K
∆T2

∆T1 T2

T1=283.2K

Oil heat balance


moil  5.04kg / s
c pm  2.09kJ / kg.K
q  m  c pm  T ' 2  T '1    5.04 2.09 366.5  344.3  233.85kJ / kg.K

Water heat balance


2
mH 2O  2.02kg / s
c pm  4.185kJ / kg.K
q  233.95 10 3   2.02  4.185 10 3  T 2283.2 
T2  310.9 K

T2  366.5  310.9  55.6 K


T1  344.3  283.2  61.4 K

Equation 4.9.1

T1  T2 61.4  55.6


Tlm    58.31K
 T1  ln 61.4 / 55.6 
ln 
 T2 
Thi  T ' 2  366.5 K Tho  T '1  344.3K
Tci  T1  283.2 K Tco  T2  310.9 K

Figure 4.9.4a

Thi  Tho 366.5  344.3


Z   0.801
Tco  Tci 310.9  283.2

Tco  Tci 310.9  283.2


Y    0.333
Thi  Tci 366.5  283.2
FT  0.97

Equation 4.9.6
Tm  FT Tlm   0.97  58.31 K

Equation 4.9.5

q  U o Ao Tm
233.85   340 Ao  0.97  5831
Ao  12.16m 2

Question 2
3
a) In the process industries, the transfer of two fluids is generally done by heat exchanger.
Discuss the characteristics and functions of cross-flow exchanger AND shell and tube
exchanger. Sketch the diagrams of the respective heat exchangers.
[30 Marks]
1. Cross-flow exchanger
• A common device used to heat or cool a gas such as air
• One of the fluids, which is a liquid, flows inside through the tubes, and the exterior gas
flows across the tube bundle by forced or sometimes natural convection.
• The fluid inside the tubes is considered to be unmixed, since it is confined and cannot mix
with any other stream.
• The gas flow outside the tubes is mixed, since it can move about freely between the
tubes, and there will be a tendency for the gas temperature to equalize in the direction
normal to the flow.
• For the unmixed fluid inside the tubes, there will be a temperature gradient both parallel
and normal to the direction of flow.
• A second type of cross-flow heat exchanger shown in Fig. 1.7(b) is typically used in air-
conditioning and space-heating applications.
• In this type the gas flows across a finned-tube bundle and is unmixed, since it is confined
in separate flow channels between the fins as it passes over the tubes. The fluid in the
tubes is unmixed.

Cross-flow heat exchangers: (a) one fluid mixed (gas) and one fluid unmixed; (b)
both fluids unmixed.

2. Shell and Tube Exchanger


• The most important type of exchanger in use in oil refineries and larger chemical
processes and is suited for higher-pressure applications.
• Useful for larger flow rates as compared to double pipe heat exchanger.
• The simplest configuration: 1-1 counterflow exchanger (one shell pass and one tube
pass) – refer to Figure 1.2.
• consists of a shell (a large pressure vessel) with a bundle of tubes inside it.
4
• One fluid runs through the tubes, and another fluid flows over the tubes (through the
shell) to transfer heat between the two fluids.
• The cold fluid enters and flow inside through all the tubes in parallel in one pass
• The hot fluid enters at the other end and flow counterflow across the outside of the tubes.
• Cross-baffles – increase the shell side heat transfer coefficient

Shell and tube heat exchanger (1 shell pass and 1 tube passes (1-1 exchanger)

b) Hot oil at a flow rate of 3.00 kg/s (cp=1.92 kJ/kg K) enters an existing counterflow
exchanger at 400 K and is cooled by water entering at 325 K (under pressure) and flowing
at a rate of 0.70 kg/s. The overall heat transfer coefficient, U=350 W/m 2 K and area,
A=12.9 m2. Calculate the heat-transfer rate and the exit oil temperature.
[20 Marks]

m oil   3.00kg / s THi=400K


H=oil
m H 2 O   0.70kg / s
c p  oil   1.92kJ / kg.K
Tco THo
U  350W / m 2
A  12.9m 2 C=H2O

Tci=325K
Assume water outlet Tco=374K

374  325
Tav   349 K , Refer A.2 for H2O at 349K
2

c p  4.196kJ / kg .K

Oil
mc p  H
 c H   3.00  1.02  103   5760W / K
5
H2O
mc p  c
 cc   0.7  1.92 103   2.937W / K  C min

Equation 4.9.19

NTU  UA / C min  3.512.9 / 2937  1.537

Figure 4.10-7a, ɛ=0.70

Equation 4.9-10

q  C min  THi  Tci   0.70 2937  400  325  154190W

Equation 4.9-7

q  154190   mc p  c  Tco  Tci   2936 Tco  325


Tco  377.5 K
(Close enough to assumed value 374K)

q  154190  mc p  H  Tco  Tci   5760 400  THO 


THO  373.2 K

Check on the above


Tlm 
 373.2  325   400  377.5  33.74
ln  373.2  325 /  400  377.5 
q  UATlm  35012.9 33.74  152320W

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