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• Catherine Masoud

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CHE 350: Chemical Engineering Transport Phenomena Lab I Jacketed Vessel Heat Exchanger Date of Experiment: 23/11/2015 Date of Report Submittal: 30/11/2015 Lab Instructor: Dr. Ahmed Aidan Section 1, Group 3 Name

ID

Catherine Masoud

55020

Haya Nassrullah

55344

Fares Hesham

52268

Marah Ali

53450

Ahmed Radwan

49969

1

Abstract In this experiment, we have been observing the effect of varying the hot water flow rates and the stirrer speeds on the overall heat transfer coefficient of the jacket (U). Five different hot water flowrates, which range from 1.3 L/min to 2.39 L/min, were examined at stirring speeds of 0%, 50% and 100%. At a stirring speed of 0%, it was observed that the overall heat transfer coefficient increased from 172.56 W/m 2 K at 1.3 L/min to 366.229 W/m2 K at 2.39 L /min. A positive trend was observed to confirm the relationship between the hot water flowrate and the overall heat transfer coefficient at a particular stirring speed. The results show that overall heat transfer coefficient fluctuates as the hot water flowrate increases probably due to software errors, but the overall trend observed was positive. At a stirring speed of 0%, U increased from 172.56 W/m2 K at 1.3 L/min to 571 W/m2 K at 2 L/min. Then, a large drop in the overall heat transfer coefficient is observed as the hot water flow rate increases to 2.1 L/min, with U= 45.8 W/m2 K. As the hot water flowrate increases to 2.39 L/min, the overall heat transfer coefficient increases again to a value of 366.229 W/m 2 K. These fluctuations are due to heat losses to the surroundings, although the apparatus is designed to be adiabatic. In addition, the cold water was assumed to be constant at a value of 1 L/min. However, the data recorded shows variations in the cold water flowrate. Last but not least, each tested hot water flowrate was not constant throughout the run, which could have affected the overall heat transfer coefficient calculated. To observe a clear 2

trend, the experiment should be repeated ensuring that all variables other than the hot water flowrate remain constant.

Table of Contents Cover Page..................................................................................................1 Abstract.......................................................................................................2 List of Tables................................................................................................4 List of Figures..............................................................................................5 Data, Results and Sample Calculations.......................................................6 Catherine Masoud.....................................................................................6 Haya Nassrullah......................................................................................10 Marah Ali................................................................................................13 Ahmed Ahmed........................................................................................17 Fares Hesham.........................................................................................19 Discussion.................................................................................................22 Conclusion.................................................................................................25 References.................................................................................................26

3

List of Tables Table 1: Data at Hot Water Flowrate = 2.39L/min ....................................................................................................................6 Table 2: Constant Properties........................................................................6 Table 3: Results for Tank at Hot Water Flowrate = 2.39L/min .....................6 Table 4: Results for Jacket at Hot Water Flowrate = 2.39L/min....................7 Table 5: Overall Results at Hot Water Flowrate = 2.39L/min ......................7 Table 6: Data at Hot Water Flowrate = 2.1L/min.......................................10 Table 7: Constant Properties......................................................................10 Table 8: Results for Tank at Hot Water Flowrate = 2.1L/min......................10 Table 9: Results for Jacket at Hot Water Flowrate = 2.1L/min....................11 Table 10: Overall Results at Hot Water Flowrate = 2.1L/min.....................11 Table 11: Data at Hot Water Flowrate = 2.05L/min...................................13 Table 12: Raw data from the jacketed vessel............................................17 Table 13: Processed Results.......................................................................17 Table 14: Data for Hot Water Flowrate= 1.3 L/min....................................19 Table 15: Constants...................................................................................19 Table 16: Processed Data for the Jacket at Various Stirrer Speeds............19 Table 17: Processed Data for the Tank at Various Stirrer Speeds ..............19 4

Table 18: Overall Heat Transfer Coefficient of Jacket.................................20 Table 18: Overall Heat Transfer Coefficient at different flowrates.............22

List of Figures Figure 1: Properties of stream at T=32.45 ....................................................................................................................7 Figure 2: Graph of Ujacket vs Stirrer Speed for Hot Flowrate=2.39 L/min...9 Figure 3: Graph of Ujacket vs Stirrer Speed for Hot Flowrate=2.10 L/min.12 Figure 4: Graph of Ujacket vs Stirrer Speed for Hot Flowrate=2.05 L/min.16 Figure 5: Overall heat transfer coefficient vs. Stirrer spee ..................................................................................................................17 Figure 6: Overall Heat Transfer Coefficient of the Jacket ..........................20 Figure 7: ΔT(hot) vs. Hot Water Flow Rate................................................22 Figure 8: ΔT(cold) vs. Hot Water Flow RateY.............................................23 Figure 9: Qjacket vs. Hot Water Flow Rate.....................................................23 Figure 10: U

jacket

vs. Hot Water Flow Rate..................................................24

5

Hot Water Flowrate qvh (L/min)

Cold Water Flowrate qvc (L/min)

Stirrer Speed (%)

T1 (°C)

T2 (°C)

T3 (°C)

T6 (°C)

2.39

0.21

0.00

42.1

46.8

46.3

22.8

2.39

0.21

50.00

39.7

45.8

45.2

22.4

2.39

0.21

100.00

42.5

47.6

46.9

22.5

Data, Results and Sample Calculation Hot Stream Flowrate: 2.39 L/min (Catherine Masoud, @55020) Table 1: Data at Hot Water Flowrate = 2.39L/min

Table 2: Constant Properties di (m)

0.1524

do (m)

0.1542

davg (m)

0.1533

l (m)

0.0800

A (m2)

0.03853

6

Table 3: Results for Tank at Hot Water Flowrate = 2.39L/min Stirrer Speed (%)

Ttank,avg (°C)

ρtank (kg/m3)

Cptank (kJ/gK)

mtank (kg/s)

Qtank (W)

0.00

32.5

994.87

4.1783

0.003482 0

280.796

50.00

31.1

995.31

4.1784

0.003483 5

251.815

100.00

32.5

994.87

4.1783

0.003482 0

290.980

Table 4: Results for Jacket at Hot Water Flowrate = 2.39L/min Stirrer Speed (%)

Tjacket,avg (°C)

ρjacket (kg/m3)

Cpjacket (kJ/gK)

mjacket(kg/ s)

Qjacket (W)

0.00

46.53

989.57

4.1797

0.039418

-82.377

50.00

45.70

989.92

4.1797

0.039432

-98.888

100.00

47.31

989.23

4.1799

0.039404

-115.294

Table 5: Overall Results at Hot Water Flowrate = 2.39L/min Stirrer Speed (%)

HL (W)

∆ T lm

Uj (W/m2K)

0.00

363.174

4.4453

480.976

50.00

350.703

5.7948

442.915

100.00

406.275

4.7414

631.132

Sample Calculations: 7

Properties of hot and cold water streams such as heat capacity and density values were obtained from an empirical data calculator found at: http://antoine.frostburg.edu/chem/senese/javascript/water-properties.html. A screenshot of data obtained at Ttank,avg = 32.45C is shown below. [1]

Figure 1: Properties of stream at T=32.45C

For data obtained at stirring speed = 0.00%: 1. Tank/Vessel Calculations: T 1+T 6 (42.1+22.8)℃ T tank ,avg= = =32.45 ℃  2 2



994.87 kg ∗0.21 L m3 ∗1 L Min ∗1 Min 1000 m3 0.003482 kg Tank Mass Flowrate :mtank = ρtank∗qvc = = 60 s s

 0.003482kg ∗4.1783∗1000 J s J Qtank=mtank∗C ptank∗( T 1−T 6 )= ∗( 42.1−22.8 ) ℃=280.79 W ¿ kgK s

( )

2. Jacket Calculations: T 2+T 3 (46.8+ 46.3)℃ T jacket , avg= = =46.55 ℃  2 2

8



989.57 kg ∗2.39 L m3 ∗1 L Min ∗1 Min 1000 m3 0.03942 kg Jac ket Mass Flowrate: m jacket =ρ jacket∗qvh= = 60 s s

 0.03942 kg ∗4.1797∗1000 J s J Q jacket =m jacket∗C p jacket∗( T 3−T 2 ) = ∗( 46.3−46.8 ) ℃=−82.377 W ¿ kgK s

( )

3. Overall Calculations Heat Loss : HL=Q tank −¿ Q jacket ∨¿ ( 280.79−|−82.377|) W =363.173 W    

∆ T lm=

( T 2−T 1 )−(T 3−T 1) ( 46.8−42.1 ) ℃−( 46.3−42.1) ℃ = =4.445℃∨K T 2−T 1 46.8−42.1 ln ⁡( ) ln T 3−T 1 46.3−42.1

(

)

A jacket=πDL=π∗0.1533m∗0.0800 m=¿ 0.03853 m2 ¿ Q jacket ∨

|−82.377 W | 366.229 W ¿ = = A jacket∗∆ T lm 0.03853 m2∗4.445 K m2 K Overall Heat Transfer Coefficient :U =¿

Graph of Ujacket versus Stirrer Speed 700.000 600.000

f(x) = 1.5x + 443.26

500.000 400.000

Ujacket (W/m2.K) 300.000 200.000 100.000 0.000

0

20

40

60

80

100

120

Stirrer Speed (%)

Figure 2: Graph of Ujacket vs Stirrer Speed for Hot Water Flowrate = 2.39 L/min 9

Hot Water Flowrate qvh (L/min)

Cold Water Flowrate qvc (L/min)

Stirrer Speed (%)

T1 (°C)

T2 (°C)

T3 (°C)

T6 (°C)

2.1

0.80

0.00

31.0

47.5

47.3

22.2

2.1

0.73

50.00

33.0

49.6

47.0

21.5

2.1

0.69

100.00

33.4

50.3

46.6

22.2

Hot Stream Flowrate: 2.1 L/min (Haya Nassrullah, @55344)

Table 6: Data at Hot Water Flowrate = 2.1L/min

Table 7: Constant Properties 10

di (m)

0.1524

do (m)

0.1542

davg (m)

0.1533

l (m)

0.0800

A (m2)

0.03853

Table 8: Results for Tank at Hot Water Flowrate = 2.1L/min Stirrer Speed (%)

Ttank,avg (°C)

ρtank (kg/m3)

Cptank (kJ/gK)

mtank (kg/s)

Qtank (W)

0.00

26.6

995.3

4.178

0.01327

487.89

50.00

27.25

994.7

4.178

0.01210

581.37

100.00

27.8

994.6

4.178

0.01144

535.32

Table 9: Results for Jacket at Hot Water Flowrate = 2.1L/min Stirrer Speed (%)

Tjacket,avg (°C)

ρjacket (kg/m3)

Cpjacket (kJ/gK)

mjacket(kg/ s)

Qjacket (W)

0.00

47.4

989.2

4.180

0.03462

-28.94

50.00

48.3

988.8

4.180

0.03461

-376.14

100.00

48.45

988.7

4.180

0.03460

-535.12

Table 10: Overall Results at Hot Water Flowrate = 2.1L/min

11

Stirrer Speed (%)

HL (W)

∆ T lm

Uj (W/m2K)

0.00

458.95

16.40

45.80

50.00

205.23

15.26

639.73

100.00

0.2

14.97

927.75

Sample Calculations: For data obtained at stirring speed = 0.00%: 1. Tank/Vessel Calculations: T 1+T 6 (31+22.2)℃ = =26.6 ℃ 2 2



T tank ,avg=



995.3 kg ∗0.8 L 3 m ∗1m3 Min ∗1 Min 1000 L 0.01327 kg Tank Mass Flowrate :mtank = ρtank∗qvc = = 60 s s

 0.01327 kg ∗4.178∗1000 J s J Qtank=mtank∗C ptank ∗( T 1−T 6 )= ∗( 31−22.2 ) ℃=487.89 W kgK s

()

2. Jacket Calculations: T 2+T 3 (47.5+ 47.3)℃ = =47.4 ℃ 2 2



T jacket , avg=



989.2 kg ∗2.1 L 3 m ∗1 m3 Min ∗1 Min 1000 L 0.03462 kg Jacket Mass Flowrate :m jacket =ρ jacket∗qvh= = 60 s s

12

 0.03462 kg ∗4.180∗1000 J s J Q jacket =m jacket∗C p jacket∗( T 3−T 2 ) = ∗( 47.3−47.5 ) ℃=−28.94 W kgK s

()

3. Overall Calculations  



Heat Loss : HL=Q tank −¿ Q jacket ∨¿ ( 487.89−|−28.94|) W =458.95 W ∆ T lm =

( T 2−T 1 )−(T 3−T 1) ( 47.5−31 ) ℃−(47.3−31) ℃ = =16.4 ℃∨K T 2−T 1 47.5−31 ln ⁡( ) ln T 3−T 1 47.3−31

(

)

|−28.94 W | 45.80 W ¿ = = A jacket∗∆ T lm 0.03853 m2∗16.4 K m2 K Overall Heat Transfer Coefficient :U =¿

¿ Q jacket ∨

Ujacket vs. stirrer speed 1000 800 600 Ujacket (W/m^2.K)

400 200 0 0

20

40

60

80

100

120

stirrer speed %

Figure 3: Graph of Ujacket vs Stirrer Speed for Hot Water Flowrate = 2.1 L/min

13

Hot Stream Flowrate~ 2.05 L/min (Marah Ali, @53450) Table 11: Data at Hot Water Flowrate = 2.05L/min Stirr er Spee d

Hot Water Flowrat e average

0% 50% 100%

[l/min] 2.02 2.07 2.03

Cold Water Flowrat e averag e [l/min] 0.63 0.53 0.49

Cold Water Outlet Temp T1

Hot Water Inlet Temp T2

Hot Water Outlet Temp T3

Cold Water Inlet Temp T6

[°C] 33.3 34.8 37.0

[°C] 50.0 49.6 47.7

[°C] 46.8 45.8 44.8

[°C] 23.0 23.8 23.8

Constant Properties and Sample Calculations for all Stirrer Speeds: Specific heat capacity of water (Cp) = 4.179 kJ/kg.K Density of hot water (ρh) = 989.5 kg/m3 Density of cold water (ρc) = 994.2 kg/m3 Vessel wall inner diameter (Dvessel i) = 0.1524 m Vessel wall outer diameter (Dvessel o) = 0.1542 m Heating jacket shell inner diameter (Dshell) = 0.175 m Heat transfer length = 0.08 m Jacketed Heat Transfer Area: A vessel =π × Dvessel × L=π ×

0.1524+ 0.1542 m× 0.08 m=0.0385 m2 2

A jacket=π × D jacket × L=π × 0.175 m×0.08 m=0.040 m2

14

Stirrer Speed: 0% Mass Flow Rate: 3 ´ hot =V´ hot × ρ hot =2.02 L ×989.5 kg3 × 1 m × 1 min =0.0333 kg m min s m 1000 L 60 s 3 ´ cold=V´ cold × ρcold =0.63 L × 994.2 kg3 × 1 m × 1min =0.0104 kg m min s m 1000 L 60 s

Heat Transfer Rate: Qvessel =m ´ cold × C p × ( T 1−T 6 )=0.0104

kg kJ kJ ×4.179 × ( 33.3−23 ) ℃=0.448 s kg K s

Q jacket =m ´ hot ×C p × ( T 2−T 3 )=0.0333

kg kJ kJ × 4.179 × ( 50−46.8 ) ℃=0.445 s kg K s

Log Mean Temperature Difference: ∆ t 1=T 3−T 1=46.8−33.3=13.5 ℃ ∆ t 2=T 2−T 6=50−23=27 ℃ ∆ T lm=

∆ t 2−∆ t 1 ln

∆ t2 ∆ t1

=

27−13.5 =19.48℃ 27 ln 13.5

( ) ( )

Overall Heat Transfer Coefficient: U vessel =

Q vessel 0.448 kJ = =0.597 A vessel × ∆T lm 0.0385 ×19.48 s . m2 . ℃

U jacket =

Q jacket 0.445 kJ = =0.571 2 A jacket × ∆T lm 0.040 × 19.48 s . m .℃

Stirrer Speed: 50% Mass Flow Rate: 3 ´ hot =V´ hot × ρ hot =2.07 L × 989.5 kg3 × 1 m × 1min =0.0341 kg m min s m 1000 L 60 s

15

3 ´ cold=V´ cold × ρcold=0.53 L × 994.2 kg3 × 1 m × 1min =0.00878 kg m min s m 1000 L 60 s

Heat Transfer Rate: kg kJ kJ × 4.179 × ( 34.8−23.8 ) ℃=0.404 s kg K s

Qvessel =m ´ cold × C p × ( T 1−T 6 )=0.00878

Q jacket =m ´ hot ×C p × ( T 2−T 3 )=0.0341

kg kJ kJ × 4.179 × ( 49.6−45.8 ) ℃=0.542 s kg K s

Log Mean Temperature Difference ∆ t 1=T 3−T 1=45.8−34.8=11 ℃ ∆ t 2=T 2−T 6=49.6−23.8=25.8 ℃ ∆ T lm=

∆ t 2−∆ t 1 ln

∆ t2 ∆ t1

=

25.8−11 =17.36 ℃ 25.8 ln 11

( ) ( )

Overall Heat Transfer Coefficient: U vessel =

Q vessel 0.404 kJ = =0.604 A vessel × ∆T lm 0.0385 ×17.36 s . m2 . ℃

U jacket =

Q jacket 0.542 kJ = =0.781 A jacket × ∆T lm 0.040 × 17.36 s . m2 . ℃

Stirrer Speed: 100% Mass Flow Rate: 3 ´ hot =V´ hot × ρ hot =2.03 L ×989.5 kg3 × 1 m × 1 mi n =0.0335 kg m min s m 1000 L 60 s 3

´ cold=V´ cold × ρcold=0.49 L × 994.2 kg3 × 1 m × 1min =0.00812 kg m min s m 1000 L 60 s Heat Transfer Rate: Qvessel =m ´ cold × C p × ( T 1−T 6 )=0.00812

kg kJ kJ × 4.179 × ( 37−23.8 ) ℃=0.449 s kg K s 16

Q jacket =m ´ hot ×C p × ( T 2−T 3 )=0.0335

kg kJ kJ × 4.179 × ( 47.7−44.8 ) ℃=0.406 s kg K s

Log Mean Temperature Difference ∆ t 1=T 3−T 1=44.8−37=7.8 ℃ ∆ t 2=T 2−T 6=47.7−23.8=23.9 ℃ ∆ T lm=

∆ t 2−∆ t 1 ln

∆ t2 ∆ t1

=

23.9−7.8 =14.37 ℃ 23.9 ln 7.8

( ) ( )

Overall Heat Transfer Coefficient: U vessel =

Q vessel 0.449 kJ = =0.812 A vessel × ∆T lm 0.0385 ×14.37 s . m2 .℃

U jacket =

Q jacket 0.403 kJ = =0.701 A jacket × ∆T lm 0.040 × 14.37 s . m2 . ℃

U jacket vs. Stirrer Speed 900 800 700 600

U jacket (J/(m^2 s ˚C))

500 Ujacket (J/m^2 s ˚C))

Linear (U jacket (J/(m^2 s ˚C)))

400 300 200 100 0 0

0.5

1

1.5

Stirrer Speed%

Figure 3: Graph of Ujacket vs Stirrer Speed for Hot Water Flowrate ~ 2.05 L/min

17

Stirrer speed [%]

Q jacketed [kw]

Q vessel [kw]

Area of the jacket[m^ 2]

Log mean – temperat ure [K]

0 50 100

0.1211 0.096 0.497

0.323 0.308 0.328

0.0385 0.0385 0.0385

13.85 9.79 11.93

Over all heat transfer coefficient [kw/m^2* k] 0.227 0.252 1.081

Hot Stream Flowrate: 1.70L/min (Ahmed H.S. Ahmed, @49969)

Table 12: Raw data from the jacketed vessel Stirring speed [%]

Mass flowrate h [kg/s]

0 50 100

0.029 0.029 0.029

Mass T1 [ flow Co ] rate c [kg/s] 0.006 37.4 0.006 37.2 0.006 38.0

T2 [ T3 [ T6 [ CPh [kj/kg. Co¿ Co¿ Co¿ K]

CPc [kj/kg. K]

45.1 47.4 52.1

4.178 4.178 4.178

45.2 46.6 48.0

24.5 24.7 24.9

4.179 4.180 4.180

Table 13: Processed Results

18

Overall heat transfer coeficient vs. Stirrer speed 1.2 1 0.8 U [kw/m^2*k] 0.6

Column2

0.4 0.2 0 0

20

40

60

80 100 120

Stirrer speed %

Figure 5: Overall heat transfer coefficient vs. stirrer speed Sample calculations @ 0% stirring speed QJacket =m h C p ,h ( T 2−T 3 ) QJacket =0.029[kg/s]*4.179[kj/kg.k]*(318.1-318.2) K =0.1211 kW QTank =mc C p , c ( T 1−T 6 ) K QTank =0.006 [kg/ s]∗4.178 [kj /kg . k ]∗(310.4−297.5)¿ ]=0.323 kW d mean=

d o +d i 2

d mean=

0.1542+0.1524 =¿ 0.1533 m 2

A j=π . d mean . L A j=π . d mean .0.08 =0.0385 m^2

19

∆ T lm=

( T 2−T 1 )−( T 3−T 1 ) ln

∆ T lm=

(

T 2−T 1 T 3−T 1

)

( 318.1−310.4 )− (318.2−297.5 ) 318.1−310.4 =13.85 k ln 318.2−297.5

(

)

U j=

QJacket A j . ∆ T lm

U j=

0.1211 0.03885.13 .85 =0.227 kW/m^2*K

Where: Vessel wall inside diameter

di = 0.1524 m

Vessel wall outside diameter

do = 0.1542 m

Overflow height

L=0.08

Hot Stream Flowrate: 1.3 L/min (Fares Hesham, @52268) Data Fhot (L/min) 1.32 1.25 1.27

Fcold Speed (L/min) (%) T1 (°C) T2 (°C) T3 (°C) 0.33 0 41.0 45.2 44.9 0.33 50 36.5 45.6 44.7 0.32 100 36.8 46.1 45.2 Table 14: Data for Hot Water Flowrate= 1.3 L/min

T6 (°C) 24.8 24.9 24.1

20

Table 15: Constants Vessel wall inside diamet er, di(m) 0.1524

Vessel wall outsid e diamet er, do(m) 0.1542

Vessel Diameter, dmean (m)

Length, L (m)

0.1533

0.08

Results Table 16: Processed Data for the Jacket at Various Stirrer Speeds Spe ed (%) 0 50 100

Specific Heat of Hot Fluid, Cp,h(J/Kg K) 4179 4179 4179

Density of Hot Fluid(kg/m3)

m jacket (kg/s)

990.2 990.2 989.9

0.0217 0.0207 0.0209

Q jacke t (W) 26.61 75.93 85.35

Table 17: Processed Data for the Tank at Various Stirrer Speeds Spe ed (%) 0

Specific Heat of Cold Fluid, Cp,h(J/Kg K) 4178

Density of Cold Fluid(kg/m3)

mc (kg/s)

991.8

0.006

50

4178

993.5

0.005

100

4178

993.4

0.005

Q tank (W) 375.0 5 265.3 4 284.9 3

Table 18: Overall Heat Transfer Coefficient of the Jacket at Different Stirrer Speeds Spee d (%)

ΔT

LM

Area Jacket

U jacket (W/m2.K) 21

0 50 100

(m2) 0.039 0.039 0.039

4.00 8.59 8.83

172.56 229.51 250.90

Plot of Uj vs Stirrer Speeds 300.00 250.00 200.00 150.00 100.00 50.00 0.00

0

20

40

60

80

100

120

Figure 6: Relationship between Overall Heat Transfer Coefficient of the Jacket and Stirrer Speed for Hot Water Flowrate of 1.3 L/min Sample Calculations: For data obtained at stirring speed = 0.00%: 1. Tank



991.8 kg ∗0.33 L 3 m ∗1 L Min ∗1 Min 1000 m3 Cold Water Mass Flowrate:mc = ρc∗Fcold= =0.006 kg /s 60 s



0.006 kg ∗4178 J s Qtank=mtank∗C ptank ∗( T 1−T 6 )= ∗( 41−24.8 ) ℃=375.05 W kgK

2. Jacket Calculations:

22



990.2 kg ∗1.32 L 3 m ∗1 L Min ∗1 Min 1000 m3 0.0217 kg Hot Water Mass Flowrate: mh =ρh∗Fhot = = 60 s s



0.0217 kg ∗4179 J s Q jacket =mh∗C p h∗( T 2−T 3 ) = ∗( 45.2−44.9 ) ℃=26.61W kgK

3. Overall Calculations





∆ T lm=

d mean=

( T 2−T 1 )−(T 3−T 1) ( 45.2−41 ) ℃−(44.9−41) ℃ = =4.00 ℃ T 2−T 1 45.2−41 ln ⁡( ) ln T 3−T 1 44.9−41

(

)

d i +d o 0.1524+0.1542 = =0.1533 m 2 2

 Heat Transfer Areaof Wall between jacket ∧vessel , Aj=π∗L ¿ d mean=π∗0.1533∗0.08=0.039 m2 

Overall Heat Transfer Coefficient : U=

Q jacket 26.61 W 172.56W = = A jacket∗∆ T lm 0.039 m2∗4.00 K m2 K

23

Discussion This experiment was designed in order to study the effect of stirrer speed on the overall heat transfer coefficient of a stirred vessel heated by an outer jacket using LMTD. It was found that as the stirring speed increases, the overall heat transfer coefficient also increases due to an increased heat transfer rate. The effect of flow rate is studied in the following graphs. The obtained results for 0% stirring speed are tabulated below. Hot ΔThot ΔTcold Qjacket Ujacket Water (J/s) (W/kg˚C Flow ) Rate 1.3 0.3 16.2 25.84 370.58 1.8 0.1 12.9 121.1 227 2.0 3.2 10.3 445 571 2.1 0.2 8.8 28.94 45.8 2.4 0.5 19.3 82.37 481 Table 19: Overall Heat Transfer Coefficient at different flow rates

In order to compare the data further, each of the four calculations is graphed against the hot water flow rate:

24

ΔT hot vs. Hot water Flow Rate 3.5 3 2.5 2 delta T hot ˚C 1.5 1 0.5 0 1.2

f(x) = 0.5x - 0.1 R² = 0.02 1.4

1.6

1.8

2

2.2

2.4

2.6

Hot Water Flow Rate L/min

Figure 7: ΔT(hot) vs. Hot Water Flow Rate

ΔT cold vs. Hot water Flow Rate 25 20 15 Delta T cold ˚C 10 5 0 1.2

f(x) = 0.12x + 13.27 R² = 0

1.4

1.6

1.8

2

2.2

2.4

2.6

Hot Water Flow Rate L/min

Figure 8: ΔT(cold) vs. Hot Water Flow Rate The graphs above shows a positive correlation between the flow rate and the temperature difference of the water within the jacket but a negative correlation between the flow rate and the temperature difference in the vessel. This implies that there is heat transfer taking place between the jacket and the vessel. However, the logical take is that the ΔT cold increases

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while the ΔThot decreases, and the discrepancy can be contributed to the experimental errors caused by the computerized data recording system.

Q jacket vs. How Water Flow Rate 500 400 300 Q jacket W 200 f(x) = 74.54x - 2.47 R² = 0.03

100 0 1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Hot Water Flow Rate L/min

Figure 9: Qjacket vs. Hot Water Flow Rate

U jacket vs. Hot Water Flow Rate 600 500 400 U jacket W/kg˚C

300

f(x) = 41.62x + 259.16 R² = 0.01

200 100 0 1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Hot Water Flow Rate L/min

Figure 10: U

jacket

vs. Hot Water Flow Rate

The graphs above show that as the hot water flow rate inside the jacket increases, the heat transfer rate and the overall heat transfer coefficient both increase. This implies that a higher flow rate results in a higher heat

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transfer rate, which is a sensible conclusion. However, there are several experimental outliers, as evident on the graph, which are due to experimental errors caused by the computerized data recording device.

Conclusion The objective of the experiment was to determine the effect of the stirring speed and flow rate on the overall heat transfer coefficient of a jacketed vessel, and this objective was achieved. According to the results, an increase in either the hot water flow rate or the stirring speed causes the overall heat transfer coefficient to increase, implying a positive correlation between the variables. However, as evident in the graphs, there were several outliers brought about by experimental errors. These errors include:

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

Not waiting for the apparatus to reach steady state before taking the

 

temperatures Heat losses to the surroundings Instrumental errors leading to inaccurate stirring speeds

References [1] “Properties of air-free water at 1 atm.” Available [Online]: http://antoine.frostburg.edu/chem/senese/javascript/water-properties.html Retrieved: November 29, 2015. [2] Aidan, A. 2015. Jacketed vessel with coil and stirrer heat exchanger. CHE 350 Lab Handout. AUS, Sharjah, UAE.

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