Effect of Tube Thickness for Shell and Tube Heat Exchanger in Portable Solar Water Distiller

DOI : 10.17577/IJERTV4IS110084

Download Full-Text PDF Cite this Publication

Text Only Version

Effect of Tube Thickness for Shell and Tube Heat Exchanger in Portable Solar Water Distiller

Ali Jaber Alkhakani , Hanaa Kadhim Alsabahi

M. Sc. Student,

Department of Mechanical Engineering, University Putra

Malaysia

Dr. Abdul Aziz Hairuddin

Lecturer,

Dr. Nor Mariah Adam

Associate Professor, Department of Mechanical Engineering,

University Putra Malaysia

Department of Mechanical Engineering, University Putra

Malaysia

AbstractDistillation is the process of water purification that utilized a source of heat to vaporize water and separate it from pollutants and other impurities. Then guide the vapor into a condenser to convert it to the liquid form. This process achieved by a simple device which uses solar energy as a heat source and called solar distiller. This study present experimental comparison and mathematical approach for pressure drop between four separate heat exchanger H.Es (A, B, C, and D) as a condenser in a portable solar water distiller. The heat exchangers were fabricating from stainless steel material with same physical specifications and different in thickness or length of tube. The H.Es able to be assembled and dismantled without tools. The experimental test show that all H.Es produce the same amount of distilled water as 22.8 liter/day. The experimental and mathematical results proved that the optimum design is heat exchanger D which has lower tube thickness and length. Further, reducing thickness of tube will increase pressure drop in shell and tube sides. While reducing length of tubes will lead to reduction of pressure drop in tube side and increasing in shell side with same number of baffles. However, the effect of reducing length of tube on reduction in tube side and increase in shell side is more than the effect of thickness reductions. However, the results proved that the systems able to dispensing on pumping power, because of lower value of . In addition, reducing thickness or length of tube will lead to reduce fabrication cost.

KeywordsHeat Exchanger; Solar Distiller; Shell And Tube; Pressure Drope; Tube Thickness

  1. INTRODUCTION

    Several countries are suffered from lower drinkable water supply especially in flooded areas. Growth in agriculture, industrial, and increase the water source pollution by industry wastes will lead to increase required of fresh water in future [15]. Therefore, countries tended to use solar distiller to overcome this problem.

    Solar distiller is the equipment convert fresh water to drinking water by using solar energy as a heat source [6,7]. The distilled process including two stages, evaporating water by using solar radiation and condensing the pure vapor by using Heat exchanger device.

    Heat exchangers are the device use to transfer heat from one streaming fluid to another through solid partition separating these fluids [813]. It is important to reduce weight of H.E in order to investigate the condition of portable water distiller, with pay attention to pressure drop which should be small value, in order dispensing on pumping power. The system consist of the vapor source and stainless steel heat exchanger as a condenser with separate tank for accumulation production water. The Heat exchangers able to be assembled and dismantled without tools and will be easy cleaning [14].

    The aims of this study is to achieve economic heat exchanger with higher heat efficiency by considering change in some dimensions. Another goal, is to study effect of the reduce thickness, length, or both to gather on pressure drop in both side shell and tube.

  2. MATERIAL AND METHOD

    1. Device Description

      The study presented four (E type) shell and tube heat exchangers with, one pass parallel flow [15,16] and two 25 mm inside diameter tubes. The tubes was arrangement on a square pitch with pitch ratio (PR) 1.25. In each heat exchangers the vapor enters the tube side with 4 liter/hour as a volume flow rate. while 130 liter /hour as volume flow rate of coolant water flow in shell side which has 100 mm inside diameter with four segment baffles to guide the water flow cross the tube for enhancing heat transfer, as well as, supporting the tube bundle to prevent vibration [14,17,18]. Segmental baffle and H.E manufacture stages are shown in fig. 1.

      The four heat exchangers which is used in this study are different with each other in thickness and length of tube with same produce distilled water. The heat exchangers (A) has two tubes with length and outside diameter as 0.4 m and 31 mm respectively. The heat exchangers (B) modified to 28 mm tubes outside diameter with 0.4 m tube length. The heat exchangers (C) fabricated with 31 mm and 0.3 m as tube outside diameter and length of tube respectively. The heat exchangers (D) was built with 28 mm outside tube diameter

      and 0.3 m as a tube length. The big inside tube diameter will help to ease cleaning and increase in surface area which will lead to increase heat transfer coefficient.

      Where:

      =

      (7)

    2. Select of Material

      Several limitation such as hardness, yield stress, tensile stress, corrosion resistance, healthy, and cost, as well as, material properties like thermal conductivity k, should be considered to select type of material. Therefore, Stainless Steel (304) with (k= 14.9 W/m. K) [19] as thermal conductivity was used to fabricate heat exchangers as a healthy [20], corrosion resistance material, strong, and economic material [21,22].

    3. Experimental set up

    When the flow velocity in the nozzle of shell side exceeds a limit, the vibration happen in the tubes, specially, after reducing tubes thickness, the size of nozzle should be considered to solve this problem. Therefor Saunders (1990),

    : Reynolds number

    : Equivalent diameter (m) for square pitch layout

    : Fluid dynamic viscosity in shell side (kg/m².s)

    : Outside tube diameter (m)

    : Tube pitch (m)

    : Shell diameter (mm)

    : Clearance between tubes (constant numbers)

    : Baffle space (m)

    The pressure drop in shell side of H.E depends on number of baffles, number of tubes inside shell, and length of tube. Therefore, the shell side pressure drop can be calculation based on Kern method by following expression [15][23]

    calculated the minimum inside nozzle diameter of shell by [23]:

    (2( + 1). )

    =

    (2)

    (8)

    =

    (1)

    Where the relation between Reynolds number Re and friction factor for laminar region is

    (4)

    2250

    Where:

    = (0.5760.19.()) (9)

    =

    (2)

    = (

    0.14

    )

    (10)

    Where:

    Where: is number of baffles and ( + 1) is number

    : Minimum inside nozzle diameter in shell side (mm)

    : Mass flow rate in shell side (kg/sec)

    : Fluid density in shell side (kg/m³)

    of times the shell fluid pass the tube bundle; is the dynamic viscosity at average wall temperature (()) (K) [15].

    +

    2

    : Nozzle flow velocity (m/sec)

    () = , ,

    (11)

    Reynolds number is the criteria of flow, whether it is laminar or turbulent, and this will lead to select suitable equation for friction factor and pressure drop, the Reynolds number in shell side was expressed as [15,2326]:

    ( . )

    Where , and , is the hot and cold fluid balance temperature respectively

    The number of baffles can be calculatd as [23,27]

    Where:

    =

    2

    (3)

    = 1 (12)

    = 4

    (2

    4 )

    (4)

    Where is length of tubes in (m), and the baffle space

    is recommended between 0.4 – 0.6 of the shell diameter, the

    ()

    range can be increased more than 0.6, however it is not prefer to be less than 0.4 of shell diameter [15].

    = (5)

    = ()

    (6)

    The tube side Reynolds number can be calculation by the expression [15,24,25]:

    . .

    change in fluid properties. By using the equation (1) and (2), the nozzle size of coolant water for each heat exchangers is

    12.5 mm.

    Where:

    =

    (13)

    In the beginning the forth heat exchangers are connected separately with vapor source. The vapor entered the heat exchanger with volume flow rate of 4 liter/hour at 96 °C as

    =

    .

    4

    2

    (14)

    average inlet temperature. The heat exchanger convert the vapor to the distilled water by heat transfer process from high temperature vapor to low temperature of coolant water which is flow inside the shell at 130 liter/hour volume flow rate.

    Digi-Sense 91000-00 Type K thermocouple thermometer is used to measurement the temperature in four point of H.E

    Where:

    = ( ) × (15)

    : Reynolds number in tube side

    : Fluid density in tube side (kg/m³)

    : Fluid velocity in tube side (m/s)

    : Tube inside diameter (m)

    : Fluid dynamic viscosity (kg/m².s)

    : Fluid mass flow rate inside tube (kg/s)

    : Inside tube cross sectional area (m²)

    : Number of tubes

    (inlet and outlet vapor and coolant water) by using four thermocouple wires. Type K Ten-Channals Switch-Box is used as a connection between thermometer device and thermocuple wires as shown in Fig 2: (d), (e), and (f). Data collected from experimantl test are listed in Table 1 to 4. the experimantel test proved that the water productivity for each heat exchangers is 3.8 liter/hour.

    B. Matheematical results

    The data collection from experimatel test used to achieved the hydraulic calculation. By using the Equations

    According to [15], for laminar flow inside circular tubes, the pressure drop can be calculated by using the relationship between Reynolds number (Re) and training friction factor, independent of the surface roughness.

    (3) and (12) which is represent the Reynolds number equation in shell and tube sides, the results show that the flow in two sides of each heat exchangers is lamener as shown in Table 5. By considering the heat exchangers phisical dimension and data collection from experimental test with using equations (7) and (16), the hydrulic calculation was achived as shown in Table 1 to 4.

    = 16

    (16)

    In Table 1 to 4, the symbol T refer to the temperature and the subscript h, c, i, and o are mean hot, cold, inlet, and

    For both flows laminar and turbulent, the pressure drop can

    be calculated by:

    outlet respectively. Table 5 presented the comparison between four H.Es with maximum presser drop in tube side.

    =

    (17)

    Fig. 3 and fig. 4 show the comparing between four heat

    )]

    [4 () . (

    2 2

    exchangers with respect to pressure drope in both sides shell and tube.

    Although, increase in pressur drope in heat exchanger as

  3. RESULTS AND DISCUSSIONS

    1. Experimental test

      In design the forth exchangers, it should be considered the coolant water nozzle size which is extremely depends on

      aresult of midification tubes, the pressure drop will be negelected because of its low value.

      Fig.5 show the effect of change physical dimention on weight of heat exchangers (A, B, C, D)

      Table. 1: Data collection with physical design and hydraulic calculation results from heat exchanger (A)

      Time

      min

      ,

      °C

      ,

      °C

      ,

      °C

      ,

      °C

      L/h

      L/h

      mm

      mm

      L

      m

      mm

      mm

      B

      m

      Pa

      Pa

      0

      101

      45.8

      31.5

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91486

      0.00883

      10

      100.5

      45.5

      31.5

      32.2

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91458

      0.00883

      20

      99.5

      43.4

      31.5

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91486

      0.00936

      30

      99.4

      42.3

      30.8

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91403

      0.00936

      40

      99.6

      42.7

      30.8

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91403

      0.00936

      50

      99.5

      38.5

      30.8

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91403

      0.00936

      60

      99.5

      37.9

      30.8

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91403

      0.00936

      70

      98.4

      37.6

      30.8

      32.3

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91403

      0.00936

      80

      98.6

      39.4

      30.8

      31.6

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91257

      0.00936

      90

      97.6

      38.8

      30.8

      31.6

      4

      130

      31

      25

      0.4

      100

      12.5

      2

      4

      0.08

      1.91257

      0.01031

      Table. 2: Data collection with physical design and hydraulic calculation results from heat exchanger (B)

      Time

      min

      ,

      °C

      ,

      °

      ,

      °C

      ,

      °C

      L/h

      L/h

      mm

      mm

      L

      m

      mm

      mm

      B

      m

      Pa

      Pa

      0

      100.5

      39.2

      31.2

      34.6

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1319

      0.00936

      10

      99.8

      38.2

      31.2

      27.2

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1361

      0.00936

      20

      99.6

      38

      31.2

      34.3

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1610

      0.00971

      30

      99.6

      38.3

      30.7

      33.2

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1629

      0.00973

      40

      98.4

      38.7

      30.7

      33.2

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1719

      0.00978

      50

      98.3

      38.5

      30.7

      33.2

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1719

      0.00978

      60

      97.7

      37.9

      30.7

      33.2

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1719

      0.00987

      70

      97.3

      37.7

      30.7

      33.4

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1707

      0.00987

      80

      96.5

      37.4

      30.7

      33.4

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1707

      0.00987

      90

      95.8

      37.2

      30.7

      33.5

      4

      130

      28

      25

      0.4

      100

      12.5

      2

      4

      0.08

      2.1707

      0.00992

      Table. 3: Data collection with physical design and hydraulic calculation results from heat exchanger (C)

      Time

      min

      ,

      °C

      ,

      °C

      ,

      °C

      ,

      °C

      L/h

      L/h

      mm

      mm

      L

      m

      mm

      mm

      B

      m

      Pa

      Pa

      0

      99.8

      46.9

      31.6

      32.2

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.1852

      0.00662

      10

      99.7

      46.5

      31.6

      32.2

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2052

      0.00662

      20

      99.4

      46

      31.6

      32.3

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2287

      0.00681

      30

      99

      45.3

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2281

      0.00681

      40

      98.6

      45.1

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2416

      0.00681

      50

      97.5

      44.5

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2416

      0.00706

      60

      97.1

      44.3

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2416

      0.00702

      70

      96.4

      43.7

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2416

      0.00702

      80

      96.6

      43.2

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2416

      0.00706

      90

      95.3

      43.4

      30.7

      31.4

      4

      130

      31

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.2416

      0.00706

      Table. 4: Data collection with physical design and hydraulic calculation results from heat exchanger (D)

      Time

      min

      ,

      °C

      ,

      °C

      ,

      °C

      ,

      °C

      L/h

      L/h

      mm

      mm

      L

      m

      mm

      p>

      mm

      B

      m

      Pa

      Pa

      0

      99.7

      40.6

      31.2

      33.5

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.5894

      0.007026

      10

      100

      40.8

      31.2

      33.3

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6119

      0.007026

      20

      99.4

      40.1

      31.2

      33.1

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6384

      0.007113

      30

      99.1

      40.3

      31.1

      32.2

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6425

      0.007131

      40

      98.6

      39.7

      30..8

      32.2

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6577

      0.007165

      50

      98.2

      39.5

      30.6

      32.2

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6577

      0.007270

      60

      97.5

      39.6

      30.6

      32.2

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6577

      0.007322

      70

      96.8

      38.9

      30.6

      32.1

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6587

      0.007391

      80

      96.3

      38.7

      30.6

      32.1

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6587

      0.007409

      90

      95.1

      38.4

      30.6

      32.1

      4

      130

      28

      25

      0.3

      100

      12.5

      2

      4

      0.06

      3.6587

      0.007444

      (d) (e) (f)

      1. (b) (c) Fig. 1: (a) , (b), and (c) fabrication stage of Heat exchanger

    Fig. 2: (d) Digi-Sense 91000-00 Type K thermocouple thermometer (e) Type K Ten-Channals Switch-Box (f) Type K thermocouple wires

    TABLE 5: COMPARING BETWEEN HEAT EXCHANGERS (A, B, C, D) WITH RESPECT TO PRESSUR DROP AND WEIGHT

    Parameters

    H.E

    (A)

    H.E

    (B)

    H.E

    (C)

    H.E

    (D)

    Shell diameter (mm)

    100

    100

    100

    100

    Number of tubes

    2

    2

    2

    2

    Parameters

    H.E

    (A)

    H.E

    (B)

    H.E

    (C)

    H.E

    (D)

    Length of tubes (m)

    0.4

    0.4

    0.3

    0.3

    ID of tubes (mm)

    25

    25

    25

    25

    OD of tubes (mm)

    31

    28

    31

    28

    H.E weight (kg)

    7.5

    6.75

    6.25

    5.6

    Vapor flow rate (L/h)

    4

    4

    4

    4

    Coolant water flow

    rate (L/h)

    130

    130

    130

    130

    Water productivity

    (L/h)

    3.8

    3.8

    3.8

    3.8

    Reynolds number

    (shell)

    894.29

    818.77

    1181.1

    1066.7

    Reynolds number

    (tube)

    62.3

    64.8

    68.15

    64.7

    Flow type (shell side)

    Laminar

    Laminar

    Laminar

    Laminar

    Flow type (shell side)

    Laminar

    Laminar

    Laminar

    Laminar

    in shell side (Pa)

    1.9148

    2.1707

    3.2416

    3.65871

    in tube side (Pa)

    0.010319

    0.009925

    0.007061

    0.007444

    A

    B

    C

    D

    Type of heat exchanger

    0.007444

    0.007061

    0.01

    0.008

    0.006

    1

    0.5

    0

    1.91257

    1.5

    3.6587

    3.5

    3 3.24161

    2.5 2.17075

    2

    4

    Pressure drop in tube sid Pt

    Pressure drope in shell side Ps

    Fig.3 Effect of physical dimention on shell side pressure drop in heat exchangers (A, B, C, D)

    0.012

    0.010319

    0.009925

    A

    B

    C

    D

    Type of heat exchanger

    0.004

    0.002

    0

    Fig.4 Effect of change physical dimention on tube side pressure drop in heat exchangers (A, B, C, D)

    8

    7

    6

    5

    4

    3

    2

    1

    0

    7.5

    Type of heat exchanger

    D

    C

    B

    6.25

    5.6

    A

    6.75

    Weight of heat exchanger (kg)

    Fig.5 Effect of change physical dimention on weight of heat Exchangers (A, B, C, D)

  4. CONCLUSION

Firstly, the device is able to produce distilled water with no cost of any energy source. However, the maintenance cost still have to be determined. By studying the effect of changing length, outside tube diameter, or both modification between four heat exchangers (A, B, C, and D), the experimental and mathematical results show that:

  1. The heat exchanger D is the optimum design which has 100 mm shell diameter and two tubes with 25 mm, 28 mm, and 0.3 m as inside, outside, and length of tube respectively.

  2. Reducing thickness or length of tube will lead to reduce the heat exchanger weight and fabrication cost.

  3. Reducing thickness of tube will increase pressure drop () in both shell and tube sides.

  4. While reducing length of tubes will lead to reduction of pressure drop in tube side and increasing in shell side with same number of baffles.

  5. The effect of reducing lengthof tube on reduction

in tube side and increasing in shell side is more than effect of thickness reductions.

Finally, the experimental test show that the four heat exchangers (A, B, C, and D) produce the same amount of distilled water as 22.8 liter/day and can be reduce length and thickness of tube to a certain extent in order to reduce the weight for portable heat exchanger.

ACKNOLEDGMENTS

The financial support by University Putra Malaysia grant for post graduate (IPS) program is highly acknowledged.

REFERENCES

  1. Sathyamurthy R, Nagarajan PK, Subramani J, Vijayakumar D, Ali MA. Effect of water mass on triangular pyramid solar still using phase change material as storage medium. Energy Procedia 2014;61:2224 8.

  2. Khawaji AD, Kutubkhanah IK, Wie JM. Advances in seawater desalination technologies. Desalination 2008;221:4769. doi:10.1016/j.desal.2007.01.067.

  3. Turner NC, Rijsberman FR. Water scarcity: Fact or fiction? Agric Water Manag 2006;80:522. doi:10.1016/j.agwat.2005.07.001.

  4. El-Bahi a., Inan D. Analysis of a parallel double glass solar still with separate condenser. Renew Energy 1999;17:50921. doi:10.1016/S0960-1481(98)00768-X.

  5. Kabeel a. E. Performance of solar still with a concave wick evaporation surface. Energy 2009;34:15049. doi:10.1016/j.energy.2009.06.050.

  6. Sathyamurthy R, El-Agouz SA, Dharmaraj V. Experimental analysis of a portable solar still with evaporation and condensation chambers. Desalination 2015;367:1805.

  7. Abdallah S, Badran OO. Sun tracking system for productivity enhancement of solar still. Desalination 2008;220:66976. doi:10.1016/j.desal.2007.02.047.

  8. Ahmadi P, Hajabdollahi H, Dincer I. Cost and entropy generation minimization of a cross-flow plate fin heat exchanger using multi- objective genetic algorithm. J Heat Transfer 2011;133:021801.

  9. Selba R, Kzlkan Ö, Reppich M. A new design approach for shell- and-tube heat exchangers using genetic algorithms from economic point of view. Chem Eng Process Process Intensif 2006;45:26875. doi:10.1016/j.cep.2005.07.004.

  10. McDonald, G R, Magande HL. Fundamentals of Heat Exchanger Design – Introduction to Thermo-Fluids Systems Design. 2012.

  11. Lienhard JH. A Heat Transfer Textbook. J Heat Transfer 2010;82:198. doi:10.1115/1.3246887.

  12. Incropera FP, DeWitt DP, Bergman TL, Lavine. Fundamentals of Heat and Mass Transfer 2006:1024.

  13. Kothandaraman CP. Fundamentals of heat and mass transfer (3rd edition). 2006.

  14. Pugh S, Hewitt GF, Müller–Steinhagen H. Fouling During the Use of Seawater as Coolant – The Development of a User Guide. ECI Conf Heat Exch Fouling Clean Fundam Appl 2003;RP1:619. doi:10.1080/01457630590890148.

  15. Kakac S, Liu H, Pramuanjaroenkij A. Heat exchangers: selection, rating, and thermal design. 2012.

  16. Shah RK, Sekuli DP. Fundamentals of Heat Exchanger Design 2007. doi:doi: 10.1002/9780470172605.

  17. Wen J, Yang H, Wang S, Xue Y, Tong X. Experimental investigation on performance comparison for shell-and-tube heat exchangers with different baffles. Int J Heat Mass Transf 2015;84:9907.

  18. Master BI, Chunangad KS, Pushpanathan V. Fouling mitigation using helixchanger heat exchangers 2003.

  19. Cengel Y a. Introduction to Thermodynamics and Heat Transfer 2008:865.

  20. Disegi J a., Eschbach L. Stainless steel in bone surgery. Injury 2000;31. doi:10.1016/S0020-1383(00)80015-7.

  21. Ullman DG. The Mechanical Design Process 2010:415.

  22. Pugh SJ, Hewitt GF, Müller-Steinhagen H. Fouling During the Use of Fresh Water as CoolantThe Development of a User Guide. Heat Transf Eng 2009;30:8518. doi:10.1080/01457630902753706.

  23. Tan FL, Fok SC. An educational computer-aided tool for heat exchanger design. Comput Appl Eng Educ 2006;14:7789. doi:10.1002/cae.20073.

  24. Yang J, Fan A, Liu W, Jacobi AM. Optimization of shell-and-tube heat exchangers conforming to TEMA standards with designs motivated by constructal theory. Energy Convers Manag 2014;78:46876. doi:10.1016/j.enconman.2013.11.008.

  25. Yang J, Oh SR, Liu W. Optimization of shell-and-tube heat exchangers using a general design approach motivated by constructal theory. Int J Heat Mass Transf 2014;77:114454. doi:10.1016/j.ijheatmasstransfer.2014.06.046.

  26. Patel VK, Rao RV. Design optimization of shell-and-tube heat exchanger using particle swarm optimization technique. Appl Therm Eng 2010;30:141725. doi:10.1016/j.applthermaleng.2010.03.001.

  27. Ravagnani M a SS, Caballero J a. A MINLP model for the rigorous design of shell and tube heat exchangers using the TEMA standards. Chem Eng Res Des 2007;85:142335. doi:10.1016/S0263- 8762(07)73182-9.

Leave a Reply