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  • 8/11/2019 Heat Exchanger Lecture.ppt

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    Heat Transfer/Heat Exchanger How is the heat transfer?

    Mechanism of Convection

    Applications .

    Mean fluid Velocity and Boundary and their effect on the rate of heattransfer.

    Fundamental equation of heat transfer

    Logarithmic-mean temperature difference.

    Heat transfer Coefficients.

    Heat flux and Nusselt correlation

    Simulation program for Heat Exchanger

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    How is the heat transfer?

    Heat can transfer between the surface of a solid conductorand the surrounding medium whenever temperaturegradient exists.

    ConductionConvection

    Natural convection

    Forced Convection

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    Natural and forced Convection

    Natural convection occurs whenever heat flows

    between a solid and fluid, or between fluidlayers.

    As a result of heat exchange

    Change in density of effective fluid layers takenplace, which causes upward flow of heated

    fluid.

    If this motion is associated with heat transfer mechanism

    only, then it is calledNatural Convection

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    Forced Convection

    If this motion is associated by mechanical means such as

    pumps, gravity or fans, the movement of the fluid is

    enforced.

    And in this case, we then speak of Forced convection.

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    Heat Exchangers A device whose primary purpose is the transfer of energy

    between two fluids is named a Heat Exchanger.

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    Applications of Heat Exchangers

    Heat Exchangers

    prevent car engine

    overheating and

    increase efficiency

    Heat exchangers areused in Industry for

    heat transfer

    Heat

    exchangers are

    used in AC and

    furnaces

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    The closed-type exchanger is the most popular one.

    One example of this type is the Double pipe exchanger.

    In this type, the hot and cold fluid streams do not come

    into direct contact with each other. They are separated by

    a tube wall or flat plate.

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    Principle of Heat Exchanger First Law of Thermodynamic: Energy is conserved.

    generateds

    in out

    outin ewqhmhmdt

    dE

    ..

    outin

    hmhm .. h

    h

    phh TCmAQ ...

    c

    c

    pcc TCmAQ ...

    0 0 0 0

    Control Volume

    Qh

    Cross Section Area

    HOT

    COLD

    Thermal Boundary Layer

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    Q hot Q cold

    T

    h

    Ti,wall

    To,wall

    Tc

    Region I : Hot Liquid-

    Solid Convection

    NEWTONS LAW OF

    CCOLING

    dqxhh. ThTiw .dA Region II : ConductionAcross Copper Wall

    FOURIERS LAW

    dqx

    k.dT

    dr

    Region III: Solid

    Cold Liquid

    Convection

    NEWTONS LAW OF

    CCOLING

    dqxhc.TowTc .dA

    THERMAL

    BOUNDARY LAYER

    Energy moves from hot fluid

    to a surface by convection,

    through the wall by

    conduction, and then byconvection from the surface

    to the cold fluid.

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    Velocity distribution and boundary layer

    When fluid flow through a circular tube of uniform cross-

    suction and fully developed,

    The velocity distribution depend on the type of the flow.

    In laminar flow the volumetric flowrate is a function of the

    radius.

    V u2rdrr0

    rD / 2

    V = volumetric flowrate

    u = average mean velocity

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    In turbulent flow, there is no such distribution.

    The molecule of the flowing fluid which adjacent to thesurface have zero velocity because of mass-attractive

    forces. Other fluid particles in the vicinity of this layer,

    when attempting to slid over it, are slow down by viscous

    forces.

    r

    Boundary

    layer

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    Accordingly the temperature gradient is larger at the walland through the viscous sub-layer, and small in theturbulent core.

    The reason for this is

    1) Heat must transfer through the boundary layer byconduction.

    2) Most of the fluid have a low thermal conductivity (k)3) While in the turbulent core there are a rapid movingeddies, which they are equalizing the temperature.

    heating

    cooling

    Tube wall

    Twh

    Twc

    Tc

    Metalwall

    Warm fluid

    cold fluid

    qxhATqxhA(Tw T)

    qx

    k

    A(T

    w

    T)h

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    Region I : Hot Liquid

    Solid Convection

    ThTiw qxhh.Ai

    qxhhot. ThTiw .A

    Region II : Conduction

    Across Copper Wall

    qxkcopper.2L

    lnrori

    To,wallTi,wall

    qx.ln ro

    ri

    kcopper.2L

    Region III : Solid

    Cold Liquid Convection

    To,wall Tc qx

    hc.Ao

    qxhcTo,wallTc Ao+

    ThTc qx1

    hh.Ai

    ln rori

    kcopper.2L

    1

    hc.Ao

    qxU.A. T

    hT

    c

    1

    1

    .

    ln.

    .

    coldicopper

    i

    oo

    ihot

    o

    hrk

    r

    rr

    rh

    rU

    U = The Overall Heat Transfer Coefficient [W/m.K]

    ThTc qx

    R1R2R3

    U 1

    A.R

    r

    o

    r

    i

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    Calculating U using Log Mean Temperature

    coldhot dqdqdq

    ch TTT

    ch dTdTTd )(h

    h

    phh dTCmdq ..

    ccpcc dTCmdq ..

    Hot Stream :

    Cold Stream:

    c

    pc

    c

    h

    ph

    h

    Cm

    dq

    Cm

    dqTd

    ..

    )(

    dATUdq ..

    c

    pc

    h

    ph CmCmdATUTd

    .

    1

    .

    1...)(

    2

    1

    2

    1

    ..

    1

    .

    1.

    )( A

    Ac

    pc

    h

    ph

    T

    TdA

    CmCmU

    T

    Td

    outc

    inc

    outh

    inhch TTTTq

    AUTTq

    AU

    T

    T

    ...

    ln1

    2

    2

    1

    2

    1 ..

    )( A

    Ac

    c

    h

    hT

    T dAq

    T

    q

    T

    UT

    Td

    1

    2

    12

    ln

    .

    T

    T

    TTAUq

    Log Mean Temperature

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    CON CURRENT FLOW

    1

    2

    12

    lnT

    T

    TTTLn

    731 TTTTT in

    c

    in

    h

    1062 TTTTT out

    c

    out

    h

    COUNTER CURRENT FLOW

    1062 TTTTT in

    c

    out

    h

    731 TTTTT out

    c

    in

    h

    Umh.

    Cph. T3T6

    A.TLn

    mc.Cpc. T7T10

    A.TLn

    T1 T2T4 T5

    T3

    T7 T8 T9

    T10

    T6

    Counter - Current Flow

    T1 T2T4 T5

    T6T3

    T7

    T8 T9

    T10

    Parallel Flow

    Log Mean Temperature evaluation

    T1

    A

    1 2

    T

    2

    T

    3 T

    6

    T

    4

    T

    6

    T7

    T

    8 T

    9 T10

    WallT1

    T2

    A

    A

    1 2

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    T1

    A

    1 2

    T

    2

    T

    3 T

    6

    T

    4T6

    T

    7

    T

    8 T

    9 T10

    Wall

    qhhAiTlm

    Tlm(T3 T1) (T6 T2)

    ln(T3 T1)

    (T6 T2)

    qhcAoTlm

    Tlm(T1T7) (T2T10)

    ln(T1T7)(T2T10)

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    Nu f(Re,Pr,L /D,b /

    o)

    DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGER

    ..Dvk

    Cp .

    k

    Dh.

    Nua.Reb.PrcFurther Simplification:

    Can Be Obtained from 2 set of experiments

    One set, run for constant Pr

    And second set, run for constant Re

    q k

    A(TwT)

    h

    NuD

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    For laminar flow

    Nu = 1.62 (Re*Pr*L/D)

    Empirical Correlation

    14.0

    3/18.0 .Pr.Re.026.0

    o

    bLnNu

    Good To Predict within 20%

    Conditions: L/D > 10

    0.6 < Pr < 16,700Re > 20,000

    For turbulent flow

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    Experimental

    Apparatus

    Two copper concentric pipes

    Inner pipe (ID = 7.9 mm, OD = 9.5 mm, L = 1.05 m)

    Outer pipe (ID = 11.1 mm, OD = 12.7 mm)

    Thermocouples placed at 10 locations along exchanger, T1 through T10

    Hot Flow

    Rotameters

    Temperature

    Indicator

    Cold Flow

    rotameter

    Heat

    Controller

    Switch for concurrent

    and countercurrent

    flow

    Temperature

    Controller

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    0

    50

    100

    150

    200

    250

    150 2150 4150 6150 8150 10150 12150

    Pr^X Re^Y

    Nus

    Examples of Exp. Results

    4

    4.2

    4.4

    4.6

    4.8

    0.6 0.8 1 1.2 1.4

    ln (Pr)

    ln(Nu

    )

    2

    2.5

    3

    3.5

    4

    4.5

    5

    5.5

    6

    9.8 10 10.2 10.4 10.6 10.8 11

    ln (Re)

    ln(Nu)

    Theoretical trend

    y = 0.8002x 3.0841

    Experimental trend

    y = 0.7966x 3.5415

    Theoretical trend

    y = 0.3317x + 4.253

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