Introduction (Ch 10)

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    1

    UNIT OPERATIONS II:

    HEAT TRANSFER

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    Introduction Heat transfer is the study of thermal energy (heat)

    flows Heat always flows from hot to cold

    Examples are ui!uitous"

    # heat flows in the ody# home heating$cooling systems

    # refrigerators% o&ens% appliances

    # automoiles% power plants% the sun% etc'

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    ypical *esign +rolems

    o determine"

    # o&erall heat transfer coefficient

    , e'g'% for a car radiator

    # highest (or lowest) temperature

    # e'g'% in a gas turine

    # temperature distriution (related to thermal

    stress) , e'g'% in the walls of a spacecraft

    # temperature response in time dependentheating$cooling prolems , e'g'% how long does it

    ta-e to cool down a case of soda.

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    HEAT TRANSFER

    HE/, Energy in transit

    E0+E/E# heat measured as a

    property

    HEAT TRANSFER# science in&ol&ing the

    study of principles that go&ern and the

    methods that determine the rate of heat

    transfer

    3

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    emperature 0easurement of

    a&erage -inetic

    energy ofmolecules in a

    sustance

    0easurement ofinternal thermal

    energy

    Heat hermal energy

    that is transmitted

    from one o5ect to

    another

    Energy in transit

    emperature &s Heat

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    APPLICATIONS

    Chemical engineering# process e!uipment%chemical plants

    Mechanical engineering# oilers% heat

    exchangers% turines% internal

    comustion engines Nuclear engineering# remo&al of heat

    generated y nuclear fission%

    design of nuclear rods Electrical engineering# cooling system for

    generators% motors% chips%

    transformers6

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    APPLICATIONS

    Metallurgical engineering# furnaces% heattreatment

    Civil engineering# design of suspension

    ridges% insulation of uildings%

    air conditioning Cryogenic engineering# production% storage%

    transportation of cryogenic

    li!uids Aeronautical engineering# design of space

    crafts% missiles% roc-ets

    7

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    8

    9uclear +ower +lant

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    :

    ;team

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    1=

    Ski Dubai: largest indoor ski resorts in the world

    Hydropolis: world's first underwter lu!ury resort

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    11insulators conductors

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    / metal all has a diameter that is slightly greaterthan the diameter of a hole that has een cut intoa metal plate' he coefficient of linear expansionfor the metal in the all is greater than that for theplate' >hich one (or more) of the following

    procedures can e used to ma-e the all passthrough the hole. /" raise the temperatures of the all and plate y

    the same amount

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    Answer: $ nd %

    ;ince the coefficient of linear expansion of

    the all is greater than the plate% it will

    shrin- more per change in temperature as

    the temperature of oth is lowered' /lso%

    y cooling the all you will decrease its

    si@e and y heating the plate you willincrease the si@e of the hole'

    T"er#l E!pnsion

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    hermal expansion is

    a property of the

    material

    different materials

    expand differently Engineers need to

    ta-e this into account

    in their designs"

    expansion 5oints in

    ridges

    i,metal strip

    T"er#l E!pnsion

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    his is howthermostats wor-,

    imetallic strips in

    refrigerators% o&ens%

    etc' open and close a

    switch as the

    imetallic strip ends

    one way or the otherdue to temp changes

    T"er#l E!pnsion

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    &O%ES OF HEAT TRANSFER

    &ode Trnsfer &e"nis# Rte of Trnsfer

    Condution *iffusion of energy due torandom

    molecular motion

    Con(etion *iffusion of energy due torandom

    molecular motion plusul- motion

    RditionEnergy transfer yelectromagnetic

    wa&es

    dx

    dTkAQ wallcond =

    ,

    )(

    = TThAQ SSconv

    )( 44 surrSSrad TTAQ =

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    Condution Het Trnsfer

    ?onduction is the transfer of heat ymolecular interaction

    In a gas% molecular &elocity depends on

    temperature# hot% energetic molecules collide with

    neighors% increasing their speed

    In solids% the molecules and the latticestructure &irate

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    1:

    STEA%) HEAT CON%UCTION IN

    PLANE *ALLS

    Heat transfer

    , temperature gradient

    , not in the direction where no

    change in temperature

    , normal to the wall surface

    , no significant heat transfer in other

    directions

    , If in and outside remain constant

    Stedy nd one+di#ensionl

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    2=

    Ener,y -lne for t"e wll

    rate of

    heat transfer

    into the wall

    rate of

    heat transfer

    out of the wall

    rate of change

    of the energy

    of the wall, A

    dt

    dEQQ walloutin =

    0=dt

    dEwall

    consQwallcond =

    ,

    steady operationB since there is no change in the

    temperature of the wall with time at any point

    he rate of heat transfer through the wall is constant

    If there is no heat generation

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    21

    FOURIER.S LA* OF HEAT

    CON%UCTION

    wallcondQ ,

    dx

    dTkAQ wallcond =

    ,

    (>)

    and / constant% then

    dx

    dT constant also

    emperature through the wall &aries linearly

    with x' emperature distriution in the wall

    under steady conditions is a straight line'

    ==

    =

    2

    1,0

    T

    TTwallcond

    L

    x kAdTdxQ

    L

    TTkAQ wallcond

    21

    ,

    =

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    Con(etion Het Trnsfer

    ?on&ection is mo&ement of heat with a fluid E'g'% when cold air sweeps past a warm

    ody% it draws away warm air near the ody

    and replaces it with cold air

    ody

    T

    ThTThq body == )(

    a&erage heat transfer coefficient (>$m2,C)=h

    !

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    2

    NE*TON.S LA* OF COOLIN/ FOR

    CON0ECTION HEAT TRANSFER RATE

    )(

    = TThAQ SSconv

    conv

    S

    convR

    TTQ

    =

    S

    conv

    hA

    R 1=

    convR

    h

    ?on&ection resistance of surface

    (>)

    (=? $ >)

    ?on&ection heat transfer

    coefficient

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    23

    adiation Heat ransfer

    hermal radiation is emission of energy as

    electromagnetic wa&es

    Intensity depends on ody temperature and

    surface characteristics

    Important mode of heat transfer at hightemperatures and natural con&ection prolems

    Examples"

    # toaster% grill% roiler

    # fireplace# sunshine

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    RA%IATION

    rad

    surrSsurrSSradrad

    RTTTTAhQ ==

    )(

    Srad

    rad

    AhR

    1=

    )( surrSS

    rad

    radTTA

    Qh

    =

    radconvcombined hhh +=

    )( 44 surrSSrad TTAQ =

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    26

    ONE DIMENSIONAL STEADY HEAT

    FLOW

    ate of

    heat con&ection

    from the wall

    ate of

    heat con&ection

    into the wall

    ate of

    heat conduction

    through the wall

    A A

    )()( 22221

    111

    =

    == TTAhL

    TTkATTAhQ

    Ah

    TT

    kAL

    TT

    Ah

    TTQ

    2

    2221

    1

    11

    /1//1

    =

    =

    =

    2,

    2221

    1,

    11

    convwallconv R

    TT

    R

    TT

    R

    TTQ

    =

    =

    =

    adding the numerators and denominators

    totalR

    TTQ 21 =

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    he thermal resistance networ- for heat transfer through a plane wall

    su5ected to con&ection on oth sides and the electrical analogy

    THER&AL RESISTANCE NET*OR1

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    HE0/D E;I;/9?E

    wall

    wallcondR

    TTQ 21

    ,

    =

    kA

    LRwall=

    (>)

    (=? $ >)

    *epends on the geometry

    and the thermal properties

    of the medium

    eR

    VVI 21

    = A

    LR ee =

    eR 21 VV eElectrical resistance oltage differenceacross the resistance

    Electrical

    conducti&ity

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    2:

    t"rou," two+lyer plne

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    =

    THER&AL RESISTANCE

    NET*OR1S

    )11

    )((21

    21

    2

    21

    1

    21

    21RR

    TTR

    TT

    R

    TTQQQ +=

    +

    =+=

    totalR

    TT

    Q

    21

    =

    21

    111

    RRRtotal+=

    21

    21

    RR

    RRRtotal

    +=

    esistances are parallel

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    1

    totalR

    TTQ = 1

    convconvtotal RRRR

    RRRRRR ++

    +=++= 3

    21

    21312

    33

    3

    3Ak

    LR =

    3

    1

    hARconv =

    11

    11

    Ak

    LR =

    22

    22

    Ak

    LR =

    ?F0

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    2

    Totl T"er#l Resistne

    totalRTTQ 21

    =

    AhAk

    L

    Ak

    L

    AhR

    RRRRR

    total

    convwallwallconvtotal

    22

    2

    1

    1

    1

    2,2,1,1,

    11+++=

    +++=

    TUAQ =

    totalRUA

    1=

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    ?onduction Example

    ?ompute the heat transfer through the wall

    of a home"

    shingles

    -A='14 >$m2,C

    sheathing

    -A='14 >$m2,C

    fierglas

    insulation

    -A='==3 >$m2

    ,C

    2x6 stud

    -A='14 >$m2,C

    sheetroc-

    -A='3 >$m2,C

    outA 2= outA 68

    /lthough slight% youcan see the thermal

    ridging effect

    through the studs

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    3

    T"er#l Contt Resistne

    a!contact QQQ +=

    er"acec TAhQ int=

    er"ace

    cT

    AQh

    int

    /

    =

    (>$m2=?)

    (m2=?$ >)

    AQ

    T

    hR

    er"ace

    c

    c

    /

    1 int

    ==

    h?" thermal contact conductance

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    4

    hermal contact resistance is in&erse of

    thermal contact conduction%

    *epends on

    ;urface roughness%

    0aterial properties%

    emperature and pressure at interface% ype of fluid trapped at interface

    T"er#l Contt Resistne

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    6

    Effet of #etlli

    otin,s on

    t"er#l ontt

    ondutne

    or soft metals with

    smoot surfaces athigh pressures

    hermal contact

    conductance

    hermal contact

    resistance

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    7

    HE/ ?F9*?IF9 I9 ?JDI9*E;

    /9* ;+HEE;

    ;teady,state heat conduction

    Heat is lost from a hot,

    water pipe to the air outside

    in the radial direction'

    Heat transfer from a long

    pipe is one dimensional

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    8

    A LON/ C)LIN%ERICAL PIPE

    dr

    dTkAQ cylcond =

    ,

    ourierKs law of conduction

    =

    cylcondQ

    ,constant

    ==

    = 21

    2

    1

    , T

    TT

    r

    rr

    cylcondkdTdr

    A

    Q

    rLA 2=

    )/ln(2

    12

    21

    ,rr

    TTLkQ

    cylcond

    =

    cyl

    cylcondR

    TTQ 21

    ,

    =

    Lk

    rrRcyl

    2

    )/ln( 12=

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    :

    F ;+HEE;

    24 rA =

    krr

    rrRs!h

    21

    12

    4

    =

    s!h

    s!hcondR

    TTQ 21,=

    including con&ection

    2

    2

    221

    12

    4

    1

    4 hrkrr

    rrRtotal

    +

    =

    totalR

    TTQ = 1

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    3=

    CRITICAL RA%IUS OF INSULATION

    )2(

    1

    2

    )/ln(

    2

    12

    11

    LrhLk

    rr

    TT

    RR

    TTQ

    convins

    +

    =

    +

    =

    0/ 2 = drQd

    h

    kr cylindercr =,

    hermal conducti&ity

    External con&ection heat

    transfer coefficient

    show

    ?JDI9*E

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    31

    CHOSIN/ INSULATION THIC1NESS

    cr

    cr

    cr

    rr

    rr

    rr

    >=