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  • Heat exchangers are devices in which heat is transferred between two fluids at different temperatures without any mixing of fluids.

    Heat exchanger type

    Heat exchanger

    1. Direct heat transfer type2. Storage type3. Direct contact type

    https://www.facebook.com/100000815304058/videos/962130780490756/

    Heat exchanger

    1. Direct heat transfer typeA direct transfer type of heat exchanger is one in which the cold and hot fluids flow simultaneously through the device and heat is transferred through a wall separating the fluids

    Concentric tube heat exchangers. (a) Parallel flow. (b) Counter flow.

    hot fluid hot fluid

    cold fluid

    cold fluid

  • Heat exchanger2. Storage type heat exchangerA direct transfer type of heat exchanger is one in which the heat transfer from the hot fluid and the cold fluid occur though a coupling medium in the form of porous solid matrix. The hot and cold fluids alternatively through the matrix. The hot fluid storing heat in it and the cold fluid extracting heat from it.

    Heat exchanger3. Direct contact type heat exchanger

    A direct transfer type of heat exchanger is one in which the two fluids are not separated. If heat is to be transferred between a gas and a fluid, the gas is either bubbled through the liquid or the liquid is sprayed in the form of droplets in the gas.

  • Direct type heat exchanger1. Tubular 2. Plate3. Extended surface

    Heat exchanger

    Tubular heat exchanger1. Concentric tube 2. Shell and tube

    Concentric tube Shell and tube The heat transfer area available per unit volume 100 -500 m2/m3

    Heat exchanger

  • Plate heat exchangerSeries of large rectangular thin metal plates which are clamped together to form narrow parallel-plate channel.

    The heat transfer area available per unit volume 100-200 m2/m3

    Heat exchanger

    Extended surface heat exchangerFins attached on the primary heat transfer surface with the object of increasing the heat transfer area.

    The heat transfer area available per unit volume 700 m2/m3

    Heat exchanger

  • Classification by flow arrangementThe three basic flow arrangements:

    o Parallel flowo Counter flowo Cross flow

    Heat exchanger

    Parallel flow Counter flow

    Heat exchanger

  • Cross flow

    Both fluids unmixed One fluid mixed and the other unmixed

    Heat exchanger

    Overall heat transfer coefficient (U) and fouling factor

    Heat exchanger

    In a heat exchanger, the heat is transferred by both convection and conduction.

    q = UA (Ta –Tb)

    U is overall heat transfer coefficient Tb

    Ta

    hohi

    T1

    T2

  • Heat exchanger

    Tb

    Ta

    hohi

    T1

    T2

    1ai

    q T Th A

    1 2q T Tk A

    x

    2 bo

    q T Th A

    a bq T T

    U A

    Conv.

    Cond.

    Conv.

    Plate heat exchanger 1)

    2)

    3)

    4)

    Heat exchanger

    a bi o

    q q x q T Th A kA h A

    a bq T T

    U A

    i o

    q q q x qU A h A kA h A

    1 1 1i o

    xU h k h

    Adding above three equations (1, 2, 3)

    From (4)

    Across a plain wall

    21 h1

    kb

    h1

    U1

  • Heat exchanger

    r2

    r1Tb

    Ta

    R i R a R o

    T i To

    To

    Ti

    condxR

    kA

    21

    convo

    Rh A

    RT = Rconv1 + Rcond + Rconv2

    11

    convi

    Rh A

    Tubular heat exchanger

    Heat exchanger

    Ai = 2πriL

    oolm

    io

    iiii Ah1

    kA)rr(

    Ah1

    AU1

    oo

    i

    lm

    iio

    ii rhr

    krr)rr(

    h1

    U1

    )r/rln()rr(rio

    iolm

    โดย

    Based on inner area

    oolm

    io

    iioo Ah1

    kA)rr(

    Ah1

    AU1

    Based on outter area

    olm

    oio

    ii

    o

    o h1

    krr)rr(

    rhr

    U1

  • Heat exchanger

    oi h1

    h1

    U1

    When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, is as usually the case, the thermal resistance of the tube is negligible.

    oi AA because

    Heat exchanger

    FoulingThe performance of heat exchangers usually deteriorate with time as a result of accumulation of deposits on heat transfer surfaces, representing additional resistance, called fouling.

  • (Log) Mean Temperature Difference

    Heat exchanger

    hot

    Where:

    cold

    dA Th

    Tc

    TdAUdq ch TTT

    Total heat transfer rate in heat exchanger TdAUq

    Heat exchanger

    If U is assumed to be a constant TdAUq

    Define mean temperature difference

    area

    m TdAA1T

    Thus:mTUAq

    This is the basic performance equation for a direct transfer type heat exchanger

  • Parallel Flow

    Heat exchanger

    Assumption1. U is a constant2. Heat exchanger is adequately

    insulated i.e. no heat loss to surrounding

    Consider in elementary area dA (B.dx)

    Heat exchanger

    dxBTUdq

    hphh dTCm

    cpcc dTCm

    ch TTT

    ch dTdT)T(d

    pccphh Cmdq

    Cmdq

    pccphh Cm1

    Cm1dxBTU

  • Heat exchanger

    L

    0pccphh

    T

    T

    dxUBCm1

    Cm1

    T)T(do

    i

    Where: i,ci,hi TTT o,co,ho TTT

    UACm1

    Cm1

    TTln

    pccphhi

    o

    UATTTTq1

    i,co,co,hi,h

    Heat exchanger

    o

    i

    oi

    TTln

    TTUAq

    This is the performance equation for a parallel-flow heat exchanger

    mTUAq

    Comparing with:

    o

    i

    oim

    TTln

    TTT

    Where:

  • Heat exchanger

    For counter flowAssumption

    1. U is a constant2. Heat exchanger is adequately

    insulated i.e. no heat loss to surrounding

    Consider an elementary area dA (B.dx)

    Heat exchanger

    dxB)TT(Udq ch

    hphh dTCm

    cpcc dTCm

    ch TTT

    ch dTdT)T(d

    pccphh Cmdq

    Cmdq

    pccphh Cm1

    Cm1dxBTU

  • Heat exchanger

    L

    0pccphh

    T

    T

    dxUBCm1

    Cm1

    T)T(do

    i

    UACm1

    Cm1

    TTln

    pccphhi

    o

    UATTTTq1

    TTln i,co,co,hi,h

    i

    o

    Where: o,ci,hi TTT i,co,ho TTT

    Heat exchanger

    o

    i

    oi

    TTln

    TTUAq

    Th,i

    Th,oTc,o

    Tc,ioT

    iT

    mTUAq

    Comparing with:

    o

    i

    oim

    TTln

    TTT

    Where:

  • Heat exchanger

    pccphh cmcm

    Special case of counter flow

    mT

    Then:i,co,co,hi,h TTTT

    i,co,ho,ci,h TTTT Or

    Substituting into the expression for , we get an indeterminate quantity

    Heat exchanger

    pTT

    o

    i

    Define

    Then:

    Apply L’ Hopital’s rulepln

    )1p(TlimT o1pm

    oo

    1pmT

    p1

    )1(TlimT

    iom TTT

    iT

    oT

  • Heat exchangerCross flowCase 1: both fluids unmixed

    Cold fluid

    Hot fluid

    Th,i

    Th,o

    Tc,i Tc,o

    B

    L

    x

    y

    Heat exchanger

    Cross flowCase 2: one fluid mixed, the other unmixed

    Cold fluid

    Hot fluid

    Th,i

    Th,o

    Tc,i Tc,o

    B

    L

    x

    y

    Th = f (x,y)Tc = f (x)

  • Heat exchanger

    Cross flowCase -: Both fluid mixed

    Cold fluid

    Hot fluid

    Th,i

    Th,o

    Tc,i Tc,o

    B

    L

    x

    y

    Th = f (y)Tc = f (x)

    Heat exchanger

    Both Th and Tc are functions of x and y

    Considering an elementary area dA (= dx dy)

    dydx)TT(Udq ch

    dydx)TT(UqB

    0

    L

    0 ch

    Comparing with mTUAq

    dydx)TT(BL1T

    B

    0

    L

    0 chm

    More complicated than before but it has been done.

  • Heat exchanger

    The integration of the three cases of cross flow has been done numerically. The results are presented in the form of a correction factor (F)

    flowcounterwastarrengementheifm

    flowcrossm

    TT

    F

    If the bulk exit temperatures on the hot side and cold side are Th,o and Tc,o, then

    i,co,ho,ci,hi,co,ho,ci,h

    flowcounterm TT/TTlnTTTT

    T

    if the arrangement was encounter-flow

    Heat exchanger

    Mean temperature difference in cross flow

    flowcounterwastarrengementheifm

    flowcrossm

    TT

    F

    For given values of Th,i; Th,o; Tc,i; Tc,o

    is the highest amongst all flow arrangements flowcounterT

    Therefore: 1F0

  • Heat exchanger

    flowcrossmflowcross TUAq

    flowcountermflowcross TUAFq

    F is plotted as a function of two parameters, R and S i,2o,2

    o,1i,1

    TTTT

    R

    i,2i,1

    i,2o,2

    TTTT

    S

    Heat exchanger

    Subscripts 1 and 2 correspond to the two fluids

    For case: 1 (both fluids unmixed) and case 3 (both fluids mixed)

    It is immaterial which subscript corresponds to the hot side and which to the cold side.

    For case: 1 and case 3

    Subscripts 1 = h2 = c

    or 1 = c2 = h

  • Heat exchanger

    However for case 2, care must be taken to see that the mixed fluid has subscript 1

    What is the parameter R?The ratio of change of temperature of the two fluids 0R

    The ratio of change in temperature of one of the fluid to the difference of inlet temperature of the two fluids 1S0

    What is the parameter S?

    Heat exchanger

    i,2o,2

    o,1i,1

    TTTT

    R

    i,2i,1

    i,2o,2

    TTTT

    S

    i,1T

    o,1T

    i,2T o,2T

    Both fluids unmixed cross flow heat exchanger

  • Heat exchangeri,1T

    o,1T

    i,2T o,2T

    i,2i,1

    i,2o,2

    TTTT

    S

    i,2o,2

    o,1i,1

    TTTT

    R

    One fluids mixed and the other unmixed

    mixed

    unmixed

    Heat exchanger

  • Heat exchanger

    Heat exchanger

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    Heat exchanger

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    Heat exchanger

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    Heat exchanger

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    Heat exchanger

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    Heat exchanger

  • Heat exchanger

    Heat exchanger

    The effectiveness - NTU methodGenerally, we encounter two type of problems:

    Given:

    hm

    cm

    o,hi,h T,T o,ci,c T,TUTwo fluids Find A?

    Type 1

    Given:hmi,hT i,cT

    Two fluids A heat exchanger A

    Type 2

    cm Find Th,o; Tc,o?

  • Heat exchanger

    Type 1

    mTUAq

    mTUqA

    Type 2

    mTUAq

    We will need a trial and error approach to solve this type of problem i.e. assuming Th,o

    ??

    Trial and error can be avoided if we adopt the alternative method called the effectiveness -NUT

    Heat exchanger

    Effectiveness of a heat exchanger =Rate of heat transfer in heat exchanger

    Maximum possible heat transfer rate

    maxqq

    )TT()Cpm()TT(Cm

    i,ci,hs

    o,hi,hphh

    )TT()Cpm()TT(Cm

    i,ci,hs

    i,co,cpcc

    i,hT

    i,cT

    T

    o,hT

    i,cT

    o,ci,h TT

    Length of heat exchanger

  • Heat exchanger

    Hence if , then pccphh CmCm spphh CmCm

    i,ci,h

    o,hi,h

    TTTT

    Hence if , then phhpcc CmCm sppcc CmCm

    i,ci,h

    i,co,c

    TTTT

    Note 1) The definition are equivalent when phhpcc CmCm 2) By definition 10

    Heat exchanger

    Effectiveness – parallel flowAssume spphh )Cm(Cm

    i,ci,h

    o,hi,h

    TTTT

    pcc

    phh

    pcc

    phh

    CmCm

    1

    CmCm

    1

    pcc

    phh

    i,ci,h

    i,co,c

    i,ci,h

    o,hi,h

    CmCm

    1TTTT

    TTTT

    pcc Cmq i,co,c TT

    pcc

    phh

    o,hi,h

    i,co,c

    CmCm

    1

    )TT()TT(

    1

  • Heat exchanger

    Effectiveness – parallel flow

    pcc

    phh

    i,ci,h

    o,co,h

    CmCm

    1TTTT

    1

    UACm1

    Cm1exp

    TTTT

    pccphhi,ci,h

    o,co,h

    Derived earlier (slide 23)

    UACm1

    Cm1

    TTln

    pccphhi

    o

    Heat exchanger

    pcc

    phh

    phhpcc

    phh

    CmCm

    1Cm

    UACmCm

    1exp1

    Substituting

  • Heat exchanger

    If we had assumed initially sppcc )Cm(Cm

    phh

    pcc

    pccphh

    pcc

    CmCm

    1Cm

    UACmCm

    1exp1

    , then

    We combine the two expressions for

    bp

    sp

    spbp

    sp

    CmCm

    1Cm

    UACmCm

    1exp1

    Heat exchanger

    Define two new parameters

    Capacity ratio (C)

    max

    min

    bp

    sp

    CCor

    )Cm()Cm(

    C

    Number of transfer unit (NTU)

    minsp CUAor

    )Cm(UANTU

    Note: 1) Both are dimensionless2)3) NTU

    10 0

  • Heat exchanger

    Effectiveness – parallel flow

    C1NTUC1exp1

    Effectiveness – counter flow

    NTUC11expC1

    NTUC1exp1

    Heat exchanger

    Special casesCapacity rate (m.Cp) is infinite either on the hot side or the cold side

    0C

    For this solution, we obtain the relation

    NTUexp1

  • Heat exchanger

    Heat exchanger

  • Heat exchanger

    Heat exchanger

  • Heat exchanger

    Heat exchanger

    Situation: Light lubricating oil (Cp=2090 J/kg-K) is cooled with water in a small heat

    exchanger. Oil flow = 0.5 kg/s, inlet T = 375 K Water flow = 0.2 kg/s, inlet T = 280 K

    Part 1: If desired outlet temperature of the oil is 350 K, and you know the estimated

    overall heat transfer coefficient, U = 250 W/m²-K, from manufacturer’s data for this type of heat exchanger

    Find: Required heat transfer area for a parallel flow heat exchanger and compare to the area needed for a counter flow heat exchanger.

    Example

  • Heat exchanger

    LMTDSolution, Part 1:

    K375T in,oil

    K350T in,oil

    K280T in,water

    ?T out,water K.Kg/J181,4C c,p

    C/qTT and

    TT Cq

    ci,co,c

    o,hi,hh

    W125,26

    )350375(090,25.0

    K311

    )181,42.0/(125,26280

    Heat exchanger

    • For parallel flow, 95Ti 39To

    63)39/95ln(

    3995T/Tln

    TTToi

    oiPFm,

    • For counter flow, 64Ti 70To

    67)70/64ln(

    7064T/Tln

    TTToi

    oiCFm,

    95Ti 39To

    70To

    64Ti

  • Heat exchanger

    • For parallel flow,

    • For counter flow,

    2PF,mPF m66.1)TU/(qA

    2CF,mCF m56.1)TU/(qA

    Heat exchanger

    Part 2:• Use -NTU method to determine the required NTU and heat transfer

    area for parallel and counter flowSolution

    K.Kg/J181,4C c,p

    K/W104520905.0Cm phh

    sppcc )Cm(K/W2.836181,42.0Cm

    To determine the minimum heat capacity rate,

  • Heat exchanger• Then

    W440,79)280375(2.836

    )TT(Cq i,ci,hminmax

    W26,125 TT Cq o,hi,hh • The effectiveness is

    33.0440,79/125,26q/q max

    With 8.0

    045,12.836

    )Cm()Cm(

    Cbp

    sp

    Heat exchanger

    Parallel flow Counter flow

    2PFminPF m84.1U/NTUCA

    2CFminCF m67.1U/NTUCA

    0.55 0.50

  • Heat exchanger

    Heat exchanger

  • Heat exchanger

    Heat exchanger

  • Heat exchanger

    Heat exchanger

  • Heat exchanger

    Other consideration in designing heat exchangers

    1. Pressure drop on either sides2. Size restriction3. Stress consideration4. Servicing requirements5. Materials of construction6. System operation7. Cost