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Heat Exchanger Heat exchangers can be described as: they include all devices that are designed for exchanging heat. Only heat exchangers that are meant to exchange heat between two fluids are taken into account. These fluids can be gasses as well as liquids. It is still difficult to have an overview, and a classification needs to be made. It is possible to classify heat exchangers in a number of ways.

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Heat Exchanger. Heat exchangers can be described as: they include all devices that are designed for exchanging heat. Only heat exchangers that are meant to exchange heat between two fluids are taken into account. - PowerPoint PPT Presentation

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  • Heat ExchangerHeat exchangers can be described as:they include all devices that are designed for exchanging heat.Only heat exchangers that are meant to exchange heat between two fluids are taken into account. These fluids can be gasses as well as liquids. It is still difficult to have an overview, and a classification needs to be made. It is possible to classify heat exchangers in a number of ways.

  • Classification Heat Exchangers1.Classification of heat exchangers depending on the basic of the fluid paths through the heat exchanger. Difference is made between :parallel flow, counter flow and cross flow.

  • Classification cross flow air to liquid heat exchanger This is a heat exchangers that is found on the top buildingsand is for instance needed for air conditioning inside. Here a fluid is leaded between the platesat the top of the heat exchanger and flows horizontally. Air is blown vertically against theplates to cool the fluid inside.

  • Classification

  • ClassificationThe second classification made, is depending on the state of the media in the heat exchanger.Liquid-to-liquid exchangers are those in which two liquids interact. Also gas-to-gas heat exchangers like air preheaters in steam plants and helium-cooled reactor gas turbine plants have to be mentioned. These devices operate with heat transfer coefficients that are between ten and one hundred times lower than the coefficients of liquid-to-liquid exchangers. Gas to gas exchangers are general much larger and heavier if a same amount of transferred heat is demanded.

    The third type is the liquid-to-gas heat exchanger (or vice versa), usually water and air are used, for instance in automotive radiators. Because of the lower heat transfer coefficients on the gas-side there are usually fines placed on the exchanging surfaces.

  • ClassificationThe third classification method is based the purpose of heat exchanger.

    The last classification is actually the most important choice of the designer of a heat exchanging system. This is the choice what kind of construction he is going to use.

  • Classification

  • series of U-type constructions

  • Shell-and-tube-heat exchanger with one shell pass and one tube pass; cross- counterflow operation

  • Regenerative Heat Exchangers

    The regenerator represents class of heat exchangers in which heat is alternately stored and removed from a surface This heat transfer surface is usually referred to as the matrix of the regenerator. For continuous operation, the matrix must be moved into and out of the fixed hot and cold fluid streams. In this case, the regenerator is called a rotary regenerator. If, on the other hand, the hot and cold fluid streams are switched into and out of the matrix, the the regenerator is referred to as a fixed matrix regenerator.

  • Heat Transfer of Heat ExchangerHow is the heat transfer? Mechanism of ConvectionApplications . Mean fluid Velocity and Boundary and their effect on the rate of heat transfer.Fundamental equation of heat transferLogarithmic-mean temperature difference.Heat transfer Coefficients.Heat flux and Nusselt correlation Simulation program for Heat Exchanger

  • How is the heat transfer?

    Heat can transfer between the surface of a solid conductor and the surrounding medium whenever temperature gradient exists.ConductionConvectionNatural convection Forced Convection

  • Natural and forced ConvectionNatural convection occurs whenever heat flows between a solid and fluid, or between fluid layers. As a result of heat exchangeChange in density of effective fluid layers taken place, which causes upward flow of heated fluid.If this motion is associated with heat transfer mechanism only, then it is called Natural Convection

  • 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.

  • Heat Exchangers

    A device whose primary purpose is the transfer of energy between two fluids is named a Heat Exchanger.

  • Applications of Heat ExchangersHeat Exchangers prevent car engine overheating and increase efficiencyHeat exchangers are used in Industry for heat transferHeat exchangers are used in AC and furnaces

  • 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.

  • Principle of Heat ExchangerFirst Law of Thermodynamic: Energy is conserved.

  • ThTi,wallTo,wallTcRegion I : Hot Liquid-Solid ConvectionNEWTONS LAW OF CCOLINGRegion II : Conduction Across Copper WallFOURIERS LAWRegion III: Solid Cold Liquid ConvectionNEWTONS LAW OF CCOLINGTHERMALBOUNDARY LAYEREnergy moves from hot fluid to a surface by convection, through the wall by conduction, and then by convection from the surface to the cold fluid.

  • Velocity distribution and boundary layerWhen 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 = volumetric flowrateu = average mean velocity

  • In turbulent flow, there is no such distribution.

    The molecule of the flowing fluid which adjacent to the surface 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. rBoundary layer

  • Accordingly the temperature gradient is larger at the wall and through the viscous sub-layer, and small in the turbulent core.

    The reason for this is 1) Heat must transfer through the boundary layer by conduction.2) Most of the fluid have a low thermal conductivity (k)3) While in the turbulent core there are a rapid moving eddies, which they are equalizing the temperature.heatingcoolingTube wall

  • Region I : Hot Liquid Solid ConvectionRegion II : Conduction Across Copper WallRegion III : Solid Cold Liquid ConvectionU = The Overall Heat Transfer Coefficient [W/m.K]

  • Calculating U using Log Mean TemperatureHot Stream :Cold Stream:Log Mean Temperature

  • CON CURRENT FLOWCOUNTER CURRENT FLOW

    Log Mean Temperature evaluation

  • DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGERFurther Simplification:Can Be Obtained from 2 set of experimentsOne set, run for constant Pr And second set, run for constant Re

  • For laminar flowNu = 1.62 (Re*Pr*L/D)Empirical CorrelationGood To Predict within 20%Conditions: L/D > 100.6 < Pr < 16,700Re > 20,000For turbulent flow

  • ExperimentalApparatus Two copper concentric pipesInner 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 T10Hot Flow RotametersTemperature IndicatorCold Flow rotameterHeat Controller

    Switch for concurrent and countercurrent flowTemperature Controller

  • Examples of Exp. ResultsTheoretical trendy = 0.8002x 3.0841Experimental trendy = 0.7966x 3.5415Theoretical trendy = 0.3317x + 4.2533Experimental trendy = 0.4622x 3.8097Theoretical trend y = 0.026x Experimental trendy = 0.0175x 4.049Experimental Nu = 0.0175Re0.7966Pr0.4622Theoretical Nu = 0.026Re0.8Pr0.33

    Chart6

    28.45717298047.04083805167.040838051657.4101063999

    51.10350286428.45320451028.453204510282.3343495111

    73.20142891529.72469618959.7246961895105.7219043693

    95.90415902112.389850185512.3898501855128.1802163993

    120.957597868514.71608166414.716081664160.9366702419

    152.273527851518.346943110318.3469431103201.1627590435

    150.300477262518.842384223918.8423842239220.3575273563

    168.589700988422.071798045622.0717980456228.3060503899

    15.140416361615.1404163616

    11.64836494711.648364947

    9.56537355099.5653735509

    84.47297498528.80396016638.8039601663107.2757174023

    74.38931723167.77684999687.7768499968103.8721836956

    69.97919201766.45417347056.4541734705101.3063653689

    76.12972981265.86161096785.861610967898.2363930434

    74.388152219196.0455632646

    66.172429206993.8376827576

    63.852511256792.0752470177

    Experimental

    Theoretical

    Pr^X Re^Y

    Nus

    Chart1

    11.930326891

    21.7770034843

    31.867431485

    43.1034482759

    Flow Rate Calibration

    Manometer flow rate

    Calculated flow rate

    Calibration Curves

    Hot calibration curve

    Hot temp calibration curve

    50 deg C

    22.14285714290.1428571429

    33.1428571429

    60 deg C

    22.18750.1875

    33.1875

    70 deg C

    22.21428571430.2142857143

    33.2142857143

    80 deg C

    22.250.25

    33.25

    Hot calibration curve

    0000

    0000

    50

    60

    70

    80

    Manometer Value (L/min)

    Actual Value (L/min)

    Hot flow Calibration curve

    y = x + 0.25

    y = x + 0.2143

    y = x + 0.1429

    y = x + 0.1875

    Sheet1

    CALIBRATION COLD WATER

    Flowrate readingFlow (g/s)time(s)experimental flow rate (g/s)

    for 500 mL1041.9111.930326891

    2022.9621.7770034843

    3015.6931.867431485

    4011.643.1034482759

    Constant Rey

    Constant Rey #HOTCOLDHOTCOLDCOLDCOLD

    D (m)T Flow rate hot (L/min)flow rate actual hot% errorv (m/s)rho (kg/m^3)% errorviscosity hot% errorRey/D% errorT1T2T3T4T5T6T7T8T9T10deltaTlnhot% errordelta Tln coldf actual hot (g/s)% errorf cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)% errorQc (J/s)Cp hot (J/kgK)% errorCp cold (J/kg.K)density (kg/m3)densityk (W/mK)% errorkviscosity hot (Ns/m)% errorviscosityv hot (m/s)h hot% errorh coldh localh overallRey hot% errorabs errorRey coldPr hot% errorabs errorln Prhotabs errorPr coldNus hot% errorabs errorln Nushotabs error

    7.90E-0350.144.14299.65507253371.4086695802987.90.00101224825.45000E-047.33945E-012.55344E+069.68293E+0047.536.650.148.44744.1538.1532.6526.1517.459.521253385714.87270828113.66946506468.21284859.65507258681516.808647.12527.81698.212865245910.00220822641455.73401594184.16666666670.00004779924183.8888888889987.9996.290.640090.07811401520.61195.45000E-047.33945E-018.3613E-0423.19374463746844.342602310217.92321458382908.49525948682.02E+049.68E+001.95E+033.56258E+007.38090E-012.62950E-021.27048E+007.38090E-035.7171E+0084.472974985217.923384803515.14041636164.43643166050.179233848

    7.90E-03553.673.835210.42970379641.3040453725989.60.00101050935.02000E-047.96813E-012.57068E+061.04601E+0152.639.955.753.852.248.942.535.827.717.611.352734988912.866762121715.403043589563.25523210.42970384541516.808652.330.051800.38025288688.92378037031750.8678194185.61111111110.00004778274183.3333333333989.6995.630.646270.07736704470.61565.02000E-047.96813E-017.9631E-0421.50805501096085.516968012215.6584617253104.44997088882.03E+041.05E+012.12E+033.25124E+008.00560E-012.60281E-021.17904E+008.00560E-035.4114E+0074.389317231615.658652855611.6483649474.30931234590.1565865286

    7.90E-03603.43953.62711.02839812521.2332531722983.180.00101710784.66400E-048.57633E-012.59972E+061.10617E+0156.942.360.558.556.452.545.838.32917.713.250706856611.216240442916.964032871959.43323111.02839817211516.808656.531.751990.80192034537.81206747121975.74774387224187.05555555560.00004776634183.0555555556983.18995.10.650850.07682261660.618334.66400E-048.57633E-017.6822E-0420.20849756465765.311028439613.66866664493180.82838877392.05E+041.11E+012.27E+033.00045E+008.61067E-012.58359E-021.09876E+008.61067E-035.1971E+0069.979192017613.66888252799.56537355094.2481979410.1366888253

    7.90E-0365.83.17083.371711.86345167131.1464460217980.140.00102026244.29000E-049.32401E-012.61930E+061.19000E+0162.2545.2565.963.561.156.4549.541.130.617.913.24489595069.275409982419.130348576655.078967311.86345171511516.808661.17533.72180.35875348626.90628084172221.748795217841890.00004774414.18E+03980.14994.480.655520.07627532340.621314.29000E-049.32401E-017.3868E-0418.72796006246317.032973005711.5641664383171.83012329892.07E+041.19E+012.46E+032.74146E+009.35516E-012.56468E-021.00849E+009.35516E-034.9731E+0076.129729812611.56441798498.80396016634.33243885630.1156441798

    7.90E-0370.32.9823.196312.51446985581.0868064832977.570.00102294464.02010E-049.95000E-012.64279E+061.25540E+0166.5547.6570.667.864.859.6552.543.33218.314.77642347868.371757624220.769132548352.076783183312.51446989761516.808665.12535.42389.84741157576.2612156052404.48703864190.94444444440.00004772194182.7777777778977.57993.90.659110.07585987160.623914.02010E-049.95000E-017.1379E-0417.70715689576206.325950526310.45414494683161.85486984662.09E+041.26E+012.62E+032.55618E+009.97888E-012.55078E-029.38513E-019.97888E-034.7853E+0074.388152219110.45442017957.77684999684.30929668480.1045442018

    7.90E-0375.22.801623.0337713.18491513861.0315430042974.810.00102584093.76620E-041.06208E+002.66995E+061.32276E+0170.649.975.472.268.762.955.645.533.418.717.86550495397.839738163222.120030300449.289155561713.18491517851516.808669.1537.152583.43632303645.80214746292594.31496274193.11111111110.00004769734182.7777777778974.81993.280.662470.07547511590.626533.76620E-041.06208E+006.8955E-0416.75930726595549.01888312249.75327686723203.13197197842.11E+041.32E+012.79E+032.38382E+001.06476E+002.53819E-028.68704E-011.06476E-024.6035E+0066.17242920699.75356889256.45417347054.1922638990.0975356889

    7.90E-0379.42.662262.9122613.73503739360.9902271528972.150.00102864783.56950E-041.12061E+002.69687E+061.37807E+0173.851.57975.371.665.257.847.334.419.119.50993505637.329876313623.243628499147.1858926513.73503743221516.808672.138.452731.56615969915.526140612720.903050594194.88888888890.00004767714182.8333333333972.15992.80.664720.07521964140.628423.56950E-041.12061E+006.7244E-0416.0441554445372.66345349099.17961419753197.03206044552.13E+041.38E+012.94E+032.25263E+001.12313E+002.52998E-028.12097E-011.12313E-024.4758E+0063.85251125679.17992237495.86161096784.15657591230.0917992237

    2.07124E+04

    T - T0.5656854249T-T T-T0.8T-T/T-T

    rel t-t9.5073180664rel7.881773399rel13.4453781513abs0.0463019645

    8.31890330816.611570247911.76470588240.0405228758

    852.75736995760.9375614136972.153.56950E-042.55344E+067.07106781195.7971014493100.0352941176Power Pr = 0.4621909

    5.98608915295.38720538728.46560846560.0275888133

    Flow cold = 15 g/s5.16607694024.9844236767.30593607310.0246575342

    4.52548339964.49438202256.40.0236307692

    4.0991697464.23280423285.79710144930.0220035967

    abs ln (t-t/t-t)rel ln (t-t/t-t)

    0.134453781512.6124977581

    0.117647058811.0381477773

    0.19.6019614903

    0.08465608477.5505793458

    0.07305936076.7262059391

    0.0646.423552343

    0.05797101455.9841837455

    1222

    d

    Constant Rey

    00.1792338480.179233848

    00.15658652860.1565865286

    00.13668882530.1366888253

    00.11564417980.1156441798

    00.10454420180.1045442018

    00.09753568890.0975356889

    00.09179922370.0917992237

    Ln Pr

    Ln Nu

    Concurrent new

    ConcurrenthotcoldHOTCOLD

    x0100.250.75100.250.751

    T = 52T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdeltaTlncoldf hot (L/min)f actual hot (g/s)f cold (g/s)v (m/s)f actual coldT hot meanT cold meanQh (J/s)Qc (J/s)Cp hotCp colddensity (kg/m3)densityh hoth coldA lnUUU theoryPrRe hot

    fh = 2 L/min43.844.651.949.548.246.823.432.337.740.67.902368454617.9448683589235.3157063100.728629231511.628149.3532753.076359026835.913875944181.24179.5988.82995.013656.92013742681272.21088524740.0572347574896.0872212843898.72627068863.820

    41.640.452.448.546.24420.527.432.335.213.107444863417.387343651235.30034885200.728629231521.989148.227.851239.73271945851351.2392105314180.94180.3988.39996.283629.47459482832122.44698358821244.4458870981249.54150085263.60

    39.436.652.947.844.541.2517.123.327.830.617.029102483417.7297108121235.333742375300.728629231532.350147.07523.851720.89423529461826.302250434180.64181.8989.325997.353877.89599900642813.25339601551500.03379525371507.44368832743.30

    37.6335347.143.139.616.121.325.227.725.964895025217.715221405235.34534975400.728629231542.711146.321.91979.95318127172072.3630733284180.44182.8989.65997.82926.18706850963194.89882839951379.22203033251385.48392092243.10

    average40.638.6552.5548.22545.542.912519.27526.07530.750

    T = 5241.640.452.448.546.24420.527.432.335.213.107444863417.387343651235.3157063200.728629231521.989148.227.851240.27206634521351.2392105314180.94180.3988.82996.283631.05360116772122.44698358821244.66905610251249.76650137763.10

    fc = 2042.6541.7552.749.247.145.31725.832.135.913.069068679521.6922214741351.7766584167201.068649405921.98914926.451601.97706014381737.5153533924181.14180.8988.45996.664703.7625442092187.57257682851400.80910661111407.26900786533.10

    44.343.552.8549.748.2546.517.52732.637.511.028158625122.7910263623468.2321820333201.408669580221.989149.67527.51811.62840065571838.46467284181.254180.4988.18996.386303.76265707632203.074862041548.54504087341556.44321898183.30

    4544.652.750.248.947.817.527.834.738.812.413595693123.7732793631584.6795628201.748689754521.989150.2528.151734.98770707041957.89462135754181.44180.25987.92996.25363.30558580432249.25175966361492.76177691831500.0998235253.180

    0

    fc=2044.343.552.8549.748.2546.517.52732.637.511.028158625122.7910263623468.2321820333201.408669580221.989149.67527.51811.62840065571838.46467284181.254180.4988.18996.386303.76265707632203.074862041548.54504087341556.44321898183.10

    fh=450.349.1560.1556.554.552.718.129.83842.813.130511332728.2887253008468.7447916667201.423834479921.989156.42530.452142.57407773442270.1236793694183.54179.7985995.56261.63782545572191.66407953661539.84958159421547.65908467142.90

    54.553.465.561.459.157.118.83241.346.513.491654340331.5019730509468.7911378201.428390750321.989161.332.652418.5725812545.6644737584185.54179.4982.52994.86879.03716915022206.99452394271589.80428698641598.13007960562.830

    57.7556.569.264.862.260.119.333.543.54913.007150476633.861316371468.8855430333201.432947020621.989164.6534.152624.71898083732729.4016552114187.14179.3980.74994.327743.44796542782201.41267453351637.61872575011646.45424876662.80

    AVERAGE46.777777777845.716666666756.766666666753.136111111151.111111111149.212518.386111111128.486111111135.316666666740.4

    f hot (L/min)f actual hot (L/min)Qc/Qh = .9941

    22.1429

    22.1429

    22.1429

    22.1429

    22.1429

    33.1429

    44.1429

    55.1429

    44.1429

    44.1875

    44.2009

    44.2143

    Concurrent new

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qc

    Qh

    Qh vs. Qc

    Concurrent

    000

    000

    00

    00

    Hot Current

    Cold Current

    Wall Temperature

    Flow Rate

    ConcurrentHOTCOLDHOTCOLDHOTCOLDHOTCOLD

    x0100.250.75100.250.751

    fc=fh=10T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdeltaTlncoldf hot (g/s)f actual hot (g/s)f cold (g/s)v (m/s)f actual coldT hot meanT cold meanQh (J/s)Qc (J/s)Cp (J/kgK)Cp hotCpCp colddensity (kg/m3)densityk (W/mK)kviscosity (Ns/m^2)viscosityh hoth coldAUPrRe hotNu

    35.534.552.546.6542.7538.6516.823.928.430.714.998882957516.31534581271011.85648100.244337246411.628145.57523.75686.4564603144675.9229643214183.77777777784180.34185.41666666674181.9989.9755.3620.638130.60550.000599.16E-041756.25598543631131.45886076510.0286173787635.76946424463.823238.819823506

    38.237.157.350.746.4542.4617.62631.134.0519.248863695819.00326632881012.29100.253753075711.628149.8825.825762.60054668799.7510663454184.83333333334181.34184.55555555564181988.0955.3330.643460.608610.00054788.74E-041520.28759560041149.3820813552600.45939361023.63615.870618214

    4240.162.454.949.9545.651827.5533.2536.319.934902777121.93820335751012.29100.254249692311.628154.02527.15861.0195795889.5862785154186.16666666674182.64184.08333333334180.5986.1655.31250.64820.610820.00145700058.48E-041657.42025659191107.4518859072612.41216374143.31359.4874261649

    45.744.268.159.5554.349.718.629.535.939.319.86736763824.235003081013.0368100.270357099811.628158.928.951003.765808641006.13298064188.05555555564184.54183.61111111114180983.7655.2840.65330.61380.000474268.15E-041938.76783879541133.8357739579663.7519872853.14430.3448615227

    00

    45.744.268.159.5554.349.718.629.535.939.319.86736763824.235003081013.0368100.270357099811.628158.928.951003.765808641006.13298064188.05555555564184.54183.61111111114180983.7655.2840.65330.61380.000474268.15E-041938.76783879541133.8357739579663.7519872853.14430.3448615227

    T = 7543.3539.767.658.1551.946.2518.326.431.634.6523.530282371921.89667782861013.0368150.270085301416.808656.92526.4751164.4729844161148.9700062884187.22222222224183.74184.66666666674180.8984.7555.3380.651290.608010.000488938.80E-041899.04832116411433.0729962232748.83986358843.14297.4154869322

    f2 = 104033.466.956.248.842.117.623.227.329.2531.537825262919.93848362081013.0368250.269852374727.169654.523.4251352.3521105921323.711062884186.61111111114182.84185.55555555564182985.655.3660.64650.60450.000499.23E-041645.47685322141813.1716585712777.18226628893.34288.0313347464

    37.930.266.955.447.439.717.221.824.5526.4534.498083266218.50493526221013.0368350.269524220237.530653.321.8251483.0830551041452.1274073454185.88888888894182.44186.44444444444182.9986.855.3870.64530.60170.0005059.58E-041649.69722467072143.1620070151833.39558194683.184160.6640673777

    000

    T = 7545.744.268.159.5554.349.718.629.535.939.319.86736763824.235003081013.0368100.270456071311.628158.928.951003.765808641006.132980641884184.54183.61111111114180983.455.2840.520.61380.0004658.15E-041938.76783879541133.8357739579663.7519872853.14518.5706538188

    f1=1048.948.3568.56156.752.818.531.3539.1543.516.221224095827.75761624581517.9256100.372255637411.628160.65311177.862943181215.0201694188.77777777784185.254183.16666666674179.6982.455.250.65350.61710.000467.81E-042786.40904660711195.4713412692785.8979678492.96280.5676343161

    53.754.26962.859.556.9518.834.2543.2547.9510.517104059231.26607913112527.7032100.576125192211.628162.97533.3751397.4855692281416.62877727524189.88888888894186.34115.44444444444179.3598155.2460.65520.61750.0004437.43E-045098.99866102711237.4295605216953.89546858552.8310078.8095424485

    56.256.668.563.661.559.419.636.245.950.910.202841646133.53479513193537.4808100.77986097811.628163.9535.251428.0139823041521.07786575254190.33333333334186.84182.77777777784179.25980.555.1720.65650.62370.0004397.16E-045370.875070481238.7784411448965.70327510552.813760.2827854761

    f hot (L/min)f actual hot (L/min)Qc/Qh = .9941

    0.60107592590.72

    0.60107592590.75

    0.60107592590.75

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.90161388891.1

    1.50268981481.7

    2.10376574072.3

    Flow Rate

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qh

    Qc

    Qc/Qh

    Hot stream

    000

    000

    00

    00

    hot inlet

    cold inlet

    wall

    X position

    T (C)

    Temperature Profile Con Currentf1=f2=10g/s

    Hot inlet

    753.076359026835.91387594

    974.2764037812918.511293546

    1239.73271945851351.239210531

    1351.22425537321488.978273258

    1720.89423529461826.30225043

    1869.04047206182049.516969927

    1979.95318127172072.363073328

    2143.20676995672322.392571395

    Qh (J/s)

    Qc (J/s)

    Flow Rate of the Cold Stream (g/s)

    Q (J/s)

    GRAPH

    1240.27206634521351.239210531

    1351.22425537321488.978273258

    1601.97706014381737.515353392

    1797.18058895481847.745392346

    1811.62840065571838.4646728

    1940.22389991221985.494350168

    Qh (J/s)

    Qc (J/s)

    Flow Rate of the Hot Stream (L/min)

    Q (J/s)

    countercurrent new

    1811.62840065571838.4646728

    1940.22389991221985.494350168

    2142.57407773442270.123679369

    2416.0651241652407.927829832

    2418.5725812545.664473758

    2649.9266929362711.08671393

    2624.71898083732729.401655211

    2913.89136157292894.819937345

    Qh (J/s)

    Qc (J/s)

    The Inlet Temperature of the Hot Stream (C)

    Q (J/s)

    h profile

    Con Current 10

    T = 52T3Qh (J/s)Qc (J/s)f cold (g/s)Qh (J/s)Qc (J/s)

    fh = 2 L/min51.9753.076359026835.91387594Con Current 1010Con753.076359026835.91387594

    Counter974.2764037812918.511293546

    52.41239.73271945851351.239210531Con Current 2020Con1239.73271945851351.239210531

    Counter1351.22425537321488.978273258

    52.91720.89423529461826.30225043Con Current 3030Con1720.89423529461826.30225043

    Counter1869.04047206182049.516969927

    531979.95318127172072.363073328Con Current 4040Con1979.95318127172072.363073328

    Counter2143.20676995672322.392571395

    Qh (J/s)Qc (J/s)

    T = 5252.41240.27206634521351.2392105312Con1240.27206634521351.239210531

    fc = 2052.71601.97706014381737.515353392f hot (L/min)Counter1351.22425537321488.978273258

    52.851811.62840065571838.46467283Con1601.97706014381737.515353392

    52.71734.98770707041957.8946213575Counter1797.18058895481847.745392346

    4Con1811.62840065571838.4646728

    Counter1940.22389991221985.494350168

    Qh (J/s)Qc (J/s)

    fc=2052.851811.62840065571838.464672853Con1811.62840065571838.4646728

    fh=460.152142.57407773442270.123679369Counter1940.22389991221985.494350168

    65.52418.5725812545.66447375860Con2142.57407773442270.123679369

    69.22624.71898083732729.401655211Counter2416.0651241652407.927829832

    65Con2418.5725812545.664473758

    Counter2649.9266929362711.08671393

    69Con2624.71898083732729.401655211

    Counter2913.89136157292894.819937345

    error propagation

    Counter currentCOLD

    X position0100.250.75100.250.751Nu = 0.0243 Re^.8 Pr^.4

    T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdelta Tln coldf hot (L/min)f actual hot (g/s)f cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)Qc (J/s)Q averageCp hot (J/kgK)Cp cold (J/kg.K)density (kg/m3)densityv hot (m/s)h hoth coldA lnUdelta T lnU theoryPr hotRe hotNu theory hot

    T = 5249.638.952.150.64945.542.337.531.4523.49.373915975310.8902706509235.306777551011.628148.832.85974.2764037812918.511293546946.393848663641814179.4988.57994.740.72862923153988.36471147142303.47592093160.02861737871351.340863786815.12551925352186.41080666753.800

    fh = 2 L/min47.634.352.455047.543.337.532.4527.2521.322.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.31849879683.600

    45.82952.7549.245.640.131.426.421.516.2538.551616927513.5582708004235.3435643032.350146.42523.8251869.04047206182049.5169699271959.27872099444180.44181.8989.6997.340.72862923151860.41505252384128.43132068851119.858233495622.57693544693032.50398157273.3800

    44.226.752.748.24438.228.72419.815.766.163630785113.1216471027235.358921454042.711145.4522.22143.20676995672322.3925713952232.79967067584180.24.18E+03990.03997.720.72862923151243.02104037354833.7605122304848.410899104623.24193324483356.97153820323.200

    0

    fc = 2047.634.352.455047.543.337.532.4527.2521.322.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.31849879683.200

    T = 5249.134.452.650.448.244.33731.124.616.912.887443327814.6343276514351.78975383332021.989148.4526.951797.18058895481847.7453923461822.46299065044180.94180.6988.7996.531.06864940595351.29247077073448.31715790111926.471307509420.94902271573039.94061110193.2800

    49.536.6552.851.149.24638.732.625.817.112.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.98602044933.3800

    0

    f1 = 1049.536.6552.851.149.24638.732.625.817.112.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.98602044933.200

    T = 7556.941.460.358.255.851.944.23728.41812.327068242817.5084343107468.75595833332021.989156.131.12416.0651241652407.9278298322411.99647699854183.34179.6985.16995.311.42383447997521.12095464253756.07282902972322.923130970423.90558928363525.71630921613.100

    61.144.46562.660.155.84839.930.118.514.263914838418.7784958586468.824044852021.989160.433.252649.9266929362711.086713932680.5067034334185.14179.4982.99994.631.42839075037129.0040191453942.94260557522343.739734790225.83420352983625.7008640962.900

    65.547.469.166.463.75950.742.331.719.212.99066186420.7850289141468.90801932021.989164.0534.952913.89136157292894.8199373452904.3556494594186.84179.3981.06994.051.43294702068607.47587833563803.72202691772457.138474189827.7375882423658.90596916472.8300

    average51.490909090936.736363636455.913636363653.436363636450.890909090946.672727272739.518181818233.481818181826.695454545518.6136363636

    f hot (L/min)f actual hot (L/min)

    22.1429

    22.1429

    22.1429

    22.1429

    L/min22.1429

    433.1429

    44.1429

    55.1429

    44.1429

    44.1875

    44.2009

    44.2143

    error propagation

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qc vs. Qh

    Qc

    Qh

    CounterCon

    000

    000

    00

    00

    Hot Current

    Cold Current

    Wall Temperature

    Constant Pr

    COUNTER CURRENT NEW

    L/D033.227848101399.6835443038132.9113924051

    X position0100.250.75100.250.751HOTCOLD

    T1 (Celsius)T2T3T4T5T6f actual hot (g/s)Cp hot (J/kgK)deltaTlnhotT7T8T9T10f actual cold (g/s)Cp cold (J/kg.K)delta Tln colddeltaTlnhotdelta Tln coldf hot (L/min)f actual hot (g/s)f cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)Qc (J/s)Q averageCp hot (J/kgK)Cp cold (J/kg.K)density (kg/m3)densityv hot (m/s)h hoth coldA lnUdelta T lnU theory

    T = 5249.638.952.150.64945.535.3067775541819.373915975342.337.531.4523.411.62814179.410.89027065099.373915975310.8902706509235.306777551011.628148.832.85974.2764037812918.511293546946.393848663641814179.4988.57994.740.72862923153988.36471147142303.47592093160.02861737871351.340863786815.12551925352186.4108066675

    fh = 2 L/min47.634.352.455047.543.335.3221354180.822.402090525137.532.4527.2521.321.98914179.911.489064642622.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.3184987968

    45.82952.7549.245.640.135.3435644180.438.551616927531.426.421.516.2532.35014181.813.558270800438.551616927513.5582708004235.3435643032.350146.42523.8251869.04047206182049.5169699271959.27872099444180.44181.8989.6997.340.72862923151860.41505252384128.43132068851119.858233495622.57693544693032.5039815727

    44.226.752.748.24438.235.358921454180.266.163630785128.72419.815.742.71114182.6513.121647102766.163630785113.1216471027235.358921454042.711145.4522.22143.20676995672322.3925713952232.79967067584180.24182.65990.03997.720.72862923151243.02104037354833.7605122304848.410899104623.24193324483356.9715382032

    fc = 2047.634.352.455047.543.335.3221354180.822.402090525137.532.4527.2521.321.98914179.911.489064642622.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.3184987968

    T = 5249.134.452.650.448.244.351.78975383334180.912.88744332783731.124.616.921.98914180.614.634327651412.887443327814.6343276514351.78975383332021.989148.4526.951797.18058895481847.7453923461822.46299065044180.94180.6988.7996.531.06864940595351.29247077073448.31715790111926.471307509420.94902271573039.9406111019

    49.536.6552.851.149.24668.24046783334181.212.146481285238.732.625.817.121.98914180.314.744809832912.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.9860204493

    f1 = 1049.536.6552.851.149.24668.24046783334181.212.146481285238.732.625.817.121.98914180.314.744809832912.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.9860204493

    T = 7556.941.460.358.255.851.968.75595833334183.312.327068242844.23728.41821.98914179.617.508434310712.327068242817.5084343107468.75595833332021.989156.131.12416.0651241652407.9278298322411.99647699854183.34179.6985.16995.311.42383447997521.12095464253756.07282902972322.923130970423.90558928363525.7163092161

    61.144.46562.660.155.868.824044854185.114.26391483844839.930.118.521.98914179.418.778495858614.263914838418.7784958586468.824044852021.989160.433.252649.9266929362711.086713932680.5067034334185.14179.4982.99994.631.42839075037129.0040191453942.94260557522343.739734790225.83420352983625.700864096

    65.547.469.166.463.75968.90801934186.812.99066186450.742.331.719.221.98914179.320.785028914112.99066186420.7850289141468.90801932021.989164.0534.952913.89136157292894.8199373452904.3556494594186.84179.3981.06994.051.43294702068607.47587833563803.72202691772457.138474189827.7375882423658.9059691647

    HOTL/D033.227848101399.6835443038132.9113924051COLD023.648648648670.945945945994.5945945946

    h ln03625.78610133762497.76375869933988.3647114714h ln02340.03903078771763.15440861432303.4759209316

    02479.00614456161669.5347504192314.5822676264

    Constant Pr

    00

    00

    00

    00

    COLD h ln

    graphs!!!!!!!!

    Nus

    Counter currentCOLDHOTCOLDCOLD

    X position0100.250.75100.250.751Nu = 0.0243 Re^.8 Pr^.4

    T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdelta Tln coldf hot (g/s)f actual hot (g/s)f cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)Qc (J/s)Cp hot (J/kgK)Cp cold (J/kg.K)density (kg/m3)densityk (W/mK)kviscosity (Ns/m)viscosityv hot (m/s)h hoth coldh localh overallPr hotRe hotNu theory hot

    f1=f2=10 g/s47.22854.750.14537.433.6528.423.3518.374.842785178911.51795721061011.856481011.628146.0525.975911.6722711714746.89699130754444.64285714294184.5990995.940.6550.608890.000568.7018E-040.2443298422467.43641434041771.01850332560.0572347574318.63884964193.83412.328028336727.794593766

    49.628.558.753.648.440.1536.4530.324.2518.283.997294335611.66704162411012.291011.628149.42527.3251026.3000665392887.91024940144501.72084130024184.0555555556988.4995.580.6540.611070.0005238.4537E-040.253673489468.85958295912078.4815384871328.190152563.63787.330639880729.5660870333

    52.830.163.157.451.642.338.531.6524.6518.1132.906413122313.1164079081012.291011.628152.728.31116.33471872992.44748210674366.964183.7777777778987.4995.310.6460.612730.00058.2705E-040.2539303996322.3162720512066.4764928149237.19651158373.383961.547849315229.8857994948

    5731.5567.360.8554.4544.641.233.626.1518.4598.671322592714.40786017351013.03681011.628155.9529.8251278.44075521106.670663709743204.18E+03985994.860.6480.615210.000488.0000E-040.2700167518497.19115552097.7646462769345.25132465523.24377.36532088731.669156725

    00

    f2 = 105731.5567.360.8554.4544.641.233.626.1518.4598.671322592714.40786017351013.03681011.628155.9529.8251278.44075521106.670663709743204183.3888888889985994.860.6480.615210.000488.0000E-040.2700167518497.19115552097.7646462769345.25132465523.24377.36532088731.669156725

    T = 7553.72967.659.952.942.736.129.423.7518.31904.366666213.86502250281013.03681516.808655.1527.21421.85980660871251.85709039564380.12422360254184.1111111111985.2995.670.6450.610570.0004838.5000E-040.269961937228.65101048482465.88048810323.59696683823.284350.176716409431.8244810675

    49.225.46757.549.339.23024.921.217.85124.150460627712.48174991691013.03682527.169653.123.9251766.39165041381.623065284873.83928571434185.3333333333987996.480.6460.605310.0004489.1284E-040.2694696054545.97455738393023.0960614763394.56750427173.384690.034272378934.2069038388

    46.223.666.5556.1547.6537.126.922.619.517.282.482270133511.68682456851013.03683537.530651.82522.051687.58384156251524.01122504834395.50781254186.3055555556987.8996.9210.6430.602090.0005129.5329E-040.2692513672785.12442791493561.4716396986551.41388803823.54103.779988331531.1731541287

    000

    f1 = 105731.5567.360.8554.4544.641.233.626.1518.4598.671322592714.40786017351013.03681011.628155.9529.8251278.44075521106.670663709743204183.3888888889985994.860.6480.615210.000488.0000E-040.2700167518497.19115552097.7646462769345.25132465523.24377.36532088731.669156725

    T = 7560.135.668.26357.949.1546.237.428.2518.242.077850053115.58455209811517.92561011.628158.67532.21485.22887178451361.92958444349.35344827594183994.122994.80.6510.619010.0004647.6140E-040.36786625611354.48306142062386.7018966835764.58650597193.16226.424809882341.4516621199

    64.542.96965.461.5554.851.542.932.119.216.864429466717.81772231572527.70321011.628161.935.351636.17286294741570.99959237224159.21052631584182.7777777778993.078993.50.6540.623850.0004567.1490E-040.56911825013722.984849772408.02912566821352.49967707082.99791.475059878757.9754289242

    64.3546.268.76663.257.353.645.333.9519.316.492855398517.60754304553537.48081011.62816336.451793.29016034571668.27510892784196.9796380094182.7777777778992.6829930.65550.62550.0004426.9899E-040.77029067614172.4241572212587.65730780951479.83371369992.8313666.887200959374.9646531313

    f hot (L/min)f actual hot (L/min)

    0.60107592590.72

    0.60107592590.75

    0.60107592590.75

    0.60107592590.8

    L/min0.60107592590.8

    40.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.90161388891.1

    1.50268981481.7

    2.10376574072.3

    Nus

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qh/Qc

    Qh (J/s)

    Qc (J/s)

    000

    000

    00

    00

    hot inlet

    cold inlet

    wall

    X position

    T (C)

    Temperature Profile Counter Currentf1=f2=10g/s

    Constant Pr number (COUNTER)

    Fcold = 15 g/sF hot (L/min)T1 (Celsius)T2T3 (hot enter)T4T5T6T7T8T9T10deltaTlnhotdeltaTlncoldf actual hot (L/min)fh actual (g/s)% errorf cold (g/s)f actual cold% errorT hot meanT cold meanQh (J/s)Qc (J/s)Cp hot (J/kgK)Cp% relative errorCp cold (J/kg K)density h (kg/m3)% relative errordensity c (kg/m^3)k hot (W/mK)%relative errork cold (W/mK)viscosity h (Ns/m^2)% relative errorviscosity ch hot% errorh coldh localh overallPr hot% relative errorabsolute errorRe hot% errorabs errorNu hot% errorabs errorln Re hotabsolute errorpercent errorln Nu hotabs errorpercent errorv hot (m/s)% errorNu hot theoryln Nu theory

    Thot = 57 C1.6551.133.1556.9553.550.144.337.6530.5523.5515.126.356677547915.63739844221.837530.110521.7687074831516.80861.189867091850.62526.3751594.07855861531586.00430776334185.05555555560.00004778914184.3333333333987.760.0010123917996.690.64430.07760360080.609520.000541440.73877068560.00086292320.880576112624.74175289012769.98686608633.51692764240.74283541040.02612498398962.943475567321.78123985581952.24021655328.457172980424.74187459347.04083805169.10085396490.21781239862.39331824683.34840025460.24741874597.38916279770.36792154530.616330702121.768707506557.16994928854.0460283982

    2.6552.737.1556.9554.652.247.94133.825.915.816.164023516816.04421492032.837546.497166666714.09691629961516.80861.189867091852.42528.41761.30246978841772.127336284185.61111111110.00004778274183.7222222222986.930.0010132431996.110.646390.07735268180.613050.000525450.761252260.000823564181.366229926116.54115981983016.576222053.40248048130.76517216560.026034833614261.924093547714.11745572732013.420819773551.103502864216.54134068398.45320451029.56534861430.14117455731.47589557863.93385304410.16541340684.20487000880.41126081260.952302941314.09691633681.99897176444.4067067077

    3.6553.939.757.355.653.649.9543.135.6527.21612.369707178816.41369819843.837562.883833333310.42345276871516.80861.189867091853.62529.551934.753188551905.613580228941860.00004777834183.4444444444986.350.0010138389995.780.647750.0771902740.614780.000515220.7763673770.000804976002.053870862113.28462049943170.78098331713.32954213820.78019526070.0259769319671.130613132510.45232586472056.090672954873.201428915213.28484475459.72469618959.88690738880.10452325861.05718860854.29321494150.13284844753.09438146830.43423234111.288343126310.423452818105.29886639224.6568026536

    4.655542.457.956.154.651.444.437.228.316.410.507597855417.16369807114.837579.27058.26873385011516.80861.189867091854.6530.42157.07141270831968.82119995564186.38888888890.00004777394183.2777777778985.850.0010143531995.520.648910.07705228770.616230.000506540.7896711020.000789577877.616181051612.91876175263132.80425789233.26790067620.79342139280.025928223125222.07883689668.3063555182095.035537222995.90415902112.918991534812.389850185510.13547503420.08306355520.81953292674.56334934930.12918991532.8310327670.45023536971.62449187738.2687339123127.67526588444.849490055

    6.255.644.55856.655.452.945.8538.729.2516.68.620944481617.26336392116.3875104.66983333336.26223091981516.80861.189867091855.4531.2252234.91028133332056.6603755754186.66666666670.00004777074183.1666666667985.480.0010147339995.270.649730.07695504290.617460.000500480.79923273660.00077719948.073425708812.16607103123253.681249263.2249441050.8029290430.025894012833706.8239656616.31302709632127.9209302656120.957597868512.166314413814.71608166410.42545558740.0631302710.60553968544.79544005330.12166314412.53705901410.45997414822.14553970136.262231002160.30975028595.077107883

    8.256.246.458.157.256.454.247.1539.930.216.86.86837576917.34163160988.3875137.44316666674.76900149031516.80861.189867091856.1531.9752244.32092209722133.94818599724186.94444444440.00004776754183.0555555556985.110.0010151151995.040.650530.07686040610.618650.000494540.80883245040.0007649412539.050389020912.04843025793360.71561157883.18296082510.81247612710.025860796844792.44359894244.83710525092166.6576413305152.273527851512.048675412718.346943110310.70979473450.04837105250.45165247055.0256784290.12048675412.3974226730.46926001422.81798417084.7690015984200.38789317235.3002549541

    9.256.247.158.257.356.554.647.4540.330.6177.187409136117.28085228559.3875153.82983333334.26098535291516.80861.189867091856.432.2252318.70784382140.9508822141870.00004776694183985.040.0010151872994.940.650690.07684150670.619130.000493370.81075055230.0007601612379.622474676512.53624114173383.60295315533.17469177330.81438386370.025854177550251.71160987594.33743180892179.6337238694150.300477262512.536476641418.842384223910.82479988720.04337431810.40069394855.01263647220.12536476642.5009746290.46306966643.15427543844.2609854738219.51062784815.3914006498

    9.656.647.758.457.556.854.947.840.830.917.16.49212768417.49250146959.7875160.38454.08684546621516.80861.189867091856.6532.452350.4170272158.528475664187.11111111110.00004776564183984.890.0010153418994.840.651010.07680373570.619370.000491040.81459758880.0007577913892.858384867913.09179511523370.10717747473.15822958170.81821027110.025840958852641.53575428044.1672385532193.6983728519168.589700988413.092020422.071798045610.87126074020.04167238550.38332615265.12746795820.1309202042.55331101170.47165347983.28900922644.0868455923227.43254366795.4268536831

    % error in Qh3.282209652931188.823993488105.098445969

    % error in deltaTlnhotrel error in deltaTT - T0.565685424922.2232718873

    10.87568493012.8664692082rel T- T4.471821541114.0969162996

    8.65372284211.398789795310.4541076913

    8.19711987171.0139597252T-T T-T0.89.5140573997Power of Re

    8.73940026650.918301035rel T-T T-T4.70588235298.2255687060.7966

    8.9640004350.77278150085.33333333337.5559526569

    9.38468172750.64457520585.86080586087.9593055341

    9.68539092540.6961286722abs t-t /t-t6.72268907568.4600230711

    9.9911515340.6486383147abs t-t/t-trel T-T/T-T6.32411067197.4074074074

    0.0331803116abs ln T-T/T-T0.06324110678.2474226804

    0.0250022980.06324110678.4210526316

    0.02097753780.06324110678.8888888889

    0.02037768990.0632411067

    0.01806888760.0632411067

    0.0154048850.0632411067

    0.01686429510.0632411067

    0.01581027670.0632411067

    rel ln T-t/t-t9.8048556328

    6.8148715749

    5.7309448482

    5.5841354398

    5.0481302776

    4.477976134

    4.7846285075

    4.5618815522

    0.24741874590.2474187459

    0.16541340680.1654134068

    0.13284844750.1328484475

    0.12918991530.1291899153

    0.12166314410.1216631441

    0.12048675410.1204867541

    Ln Re

    Ln Nu

    graphs

    4.29321494154.05022035751.10473846491.1047384649

    4.56334934934.41078839010.78699674210.7869967421

    4.79544005334.66081210290.6220778480.622077848

    5.0256784294.85343721430.52000994320.5200099432

    5.01263647225.08101093510.41925255710.4192525571

    5.12746795825.30411432690.34038681220.3403868122

    5.39525135160.31246130770.3124613077

    5.43068705510.30305636910.3030563691

    Experimental

    Theoretical

    ln (Re)

    ln (Nu)

    y = 0.8002x - 3.0841

    y = 0.7966x - 3.5415

    4.43643166054.67540231840.1792338480.179233848

    4.30931234594.64316114040.15658652860.1565865286

    4.2481979414.61814924610.13668882530.1366888253

    4.33243885634.5873767480.11564417980.1156441798

    4.30929668484.56482269620.10454420180.1045442018

    4.1922638994.54156651050.09753568890.0975356889

    4.15657591234.52260614510.09179922370.0917992237

    Experimental

    Theoretical

    ln (Pr)

    ln (Nu)

    y = 0.4622x + 3.8097

    28.45717298047.04083805167.040838051657.4101063999

    51.10350286428.45320451028.453204510282.3343495111

    73.20142891529.72469618959.7246961895105.7219043693

    95.90415902112.389850185512.3898501855128.1802163993

    120.957597868514.71608166414.716081664160.9366702419

    152.273527851518.346943110318.3469431103201.1627590435

    150.300477262518.842384223918.8423842239220.3575273563

    168.589700988422.071798045622.0717980456228.3060503899

    15.140416361615.1404163616

    11.64836494711.648364947

    9.56537355099.5653735509

    84.47297498528.80396016638.8039601663107.2757174023

    74.38931723167.77684999687.7768499968103.8721836956

    69.97919201766.45417347056.4541734705101.3063653689

    76.12972981265.86161096785.861610967898.2363930434

    74.388152219196.0455632646

    66.172429206993.8376827576

    63.852511256792.0752470177

    Experimental

    Theoretical

    Pr^X Rey^Y

    Nus

    Constant Pr#

    Pr hotPr^XRe hotln Re exp hotRey^YPr^X*Rey^YNu hotln Nu hotabs errorRey^Y*Pr^Xln reyprxNus expln Nus expRey^Y*Pr^Xln (reyprx)Nus theoryln Nus theoryXYA

    3.51692764241.78828502098962.94347556739.10085396491407.73916644732517.438864758428.45717298047.04083805162517.43886475847.830997340246.32087511163.83559272582208.0810153797.699879098557.41010639994.0502203575Experimental0.46220.79660.0184

    3.40248048131.761148373314261.92409354779.56534861432038.06622050283589.337008918651.10350286428.45320451023589.33700891868.185722787266.04380096414.19031817293166.70575042618.060447131182.33434951114.4107883901Theory0.33333333330.80.026

    3.32954213821.743597040219671.13061313259.88690738882633.08232575964591.034549823273.20142891529.72469618954591.03454982328.431860669884.47503571674.43645605544066.22709112798.3104708439105.72190436934.6608121029

    3.26790067621.72860220125222.078836896610.13547503423209.65717792965548.220462228795.90415902112.38985018555548.22046222878.6212325179102.0872565054.62582790354930.00832304978.5030959553128.18021639934.8534372143

    3.2249441051.718062493833706.82396566110.42545558744043.71022052156947.3468655381120.957597868514.7160816646947.34686553818.8461151197127.83118232594.85071050536189.87193238188.730669676160.93667024195.0810109351

    3.18296082511.707688382344792.443598942410.70979473455071.65506193548660.806428335152.273527851518.34694311038660.8064283359.0665631183159.35883828145.07115850397737.02919397938.9537730678201.16275904355.3041143269

    3.17469177331.705636432850251.711609875910.82479988725558.2333289849480.3252679372150.300477262518.84238422399480.32526793729.1569739056174.437984935.16156929138475.28951370269.0449100926220.35752735635.3952513516

    3.15822958171.701542796652641.535754280410.87126074025767.80173825939814.1614997927168.589700988422.07179804569814.16149979279.1915816726180.58057159625.19617705828781.00193807459.0803457961228.30605038995.4306870551

    Constant Rey

    Prabs errorln Nu

    3.56258E+001.79897663161.95E+042612.29532437434699.458243414484.472974985215.14041636164699.45824341448.455202513786.47003167884125.98913085618.3250610593107.27571740234.67540231844.2932149415

    3.25124E+001.72452248431.94E+042607.72605101154497.082207870374.389317231611.6483649474497.08220787038.411184067282.74631262483995.08398829398.2928198813103.87218369564.64316114044.5633493493

    3.00045E+001.66171114891.95E+042612.26337930564340.827181352669.97919201769.56537355094340.82718135268.375820203779.87122013693896.39866803348.2678079871101.30636536894.61814924614.7954400533

    2.74146E+001.59380485151.95E+042610.49046452414160.612367266276.12972981268.80396016634160.61236726628.333417546176.55526755773778.32280936268.237035488998.23639304344.5873767485.025678429

    2.55618E+001.54308018761.95E+042612.49741045794031.292994349274.38815221917.77684999684031.29299434928.301842445874.1757910963694.06012556138.214481437296.04556326464.56482269625.0126364722

    2.38382E+001.49408679471.95E+042612.5318052743903.349270870466.17242920696.45417347053903.34927087048.26959025171.8216265843609.14164452298.191225251593.83768275764.54156651055.1274679582

    2.25263E+001.45550232371.95E+042612.29478169023802.201124908263.85251125675.86161096783802.20112490828.243335421469.96050069833541.35565452598.172264886192.07524701774.52260614514.4364316605

    4.3093123459

    constant pr4.248197941

    absolute errorabs erro in Pr^xabs error in Rerel error in Pr^xabs error in Re^yrel error in Re^yrel error in Pr^xRe^yabs error in rexpryabs error in lnabs error in Pr^xRe^yabs error in NU4.3324388563

    0.02612498390.01207496761952.2402165530.67522611951555.1545565062110.4717829533110.47384649412781.11154703481.10473846492781.111547034851.17245246544.3092966848

    0.02603483360.01203330012013.42081977350.68326441231603.891025031678.696708129378.69967420932824.79653229270.78699674212824.796532292751.97625619424.192263899

    0.025976930.0120065372056.09067295480.68860733031637.881830075862.203973421362.20778479782855.98089274690.6220778482855.980892746952.55004842654.1565759123

    0.02592822310.01198402472095.03553722290.69327834321668.905308951751.996372710152.00099431612885.12980720960.52000994322885.129807209653.0863884527

    0.02589401280.01196821272127.92093026560.69661102421695.101813049641.919468028341.92525571412912.69293872580.41925255712912.692938725853.5935500726

    0.02586079680.01195286032166.65764133050.69994387871725.959477083934.03148392434.03868122452948.02429161250.34038681222948.024291612554.2436469657

    0.02585417750.01194980092179.63372386940.70060656671736.296224434431.238275215631.24613076862962.23483050790.31246130772962.234830507954.5051208813

    0.02584095880.01194369122193.69837285190.70193304521747.500123813830.297506799230.30563690552974.24414944650.30305636912974.244149446554.7260923498

    constant re

    abs Prabs Pr^xabs Reabs Re^yrel Pr^xrel Re^yrel Pr^xRe^yabs Pr^xRe^yAbs Nuabs in ln pr^xrey

    0.02629503880.01215356691.95E+031.56E+030.67558225735.96E+0159.56695397862799.324129096951.50756397540.5956695398

    0.0260280990.01203018742.12E+031.69E+030.69759527576.49E+0164.89554916522918.406195209453.69867399190.6489554917

    0.02583587530.01194134162.27E+031.81E+030.71861716656.93E+0169.28228716393007.424353071555.33660809650.6928228716

    0.02564677350.01185393872.46E+031.96E+030.74375095017.51E+0175.14485751543126.486235152357.52734672680.7514485752

    0.02550777350.01178969292.62E+032.09E+030.76403630997.99E+0179.92367345733221.95744891159.284017060.7992367346

    0.02538189180.01173151042.79E+032.22E+030.7851960428.51E+0185.07658204563320.836144957161.10338506720.8507658205

    0.02529984730.01169358942.94E+032.34E+030.80340575338.95E+0189.53522248323404.309236443862.63928995060.8953522248

    Pr^X Rey^Y

    Nus

    7.04083805167.0408380516

    8.45320451028.4532045102

    9.72469618959.7246961895

    12.389850185512.3898501855

    14.71608166414.716081664

    18.346943110318.3469431103

    18.842384223918.8423842239

    22.071798045622.0717980456

    15.140416361615.1404163616

    11.64836494711.648364947

    9.56537355099.5653735509

    8.80396016638.8039601663

    7.77684999687.7768499968

    6.45417347056.4541734705

    5.86161096785.8616109678

    Experimental

    Theoretical

    Pr^X Re^Y

    Nus

    51.172452465451.1724524654

    51.976256194251.9762561942

    52.550048426552.5500484265

    53.086388452753.0863884527

    53.593550072653.5935500726

    54.243646965754.2436469657

    54.505120881354.5051208813

    54.726092349854.7260923498

    ln Nus theory

    Nus exp

    Reynolds Number

    Nusselt Number

    0051.507563975451.5075639754

    0053.698673991953.6986739919

    0055.336608096555.3366080965

    0057.527346726857.5273467268

    0059.2840170659.28401706

    0061.103385067261.1033850672

    0062.639289950662.6392899506

    Nus theory

    Nus exp

    Prandtl Number

    Nusselt Number

    0051.172452465451.1724524654

    0051.976256194251.9762561942

    0052.550048426552.5500484265

    0053.086388452753.0863884527

    0053.593550072653.5935500726

    0054.243646965754.2436469657

    0054.505120881354.5051208813

    0054.726092349854.7260923498

    0051.507563975451.5075639754

    0053.698673991953.6986739919

    0055.336608096555.3366080965

    0057.527346726857.5273467268

    0059.2840170659.28401706

    0061.103385067261.1033850672

    0062.639289950662.6392899506

    00

    00

    00

    Nus theory

    Nus exp

    Pr^X Rey^Y

    Nusselt Number

    4.29321494159.88690738881.10473846491.1047384649

    4.563349349310.13547503420.78699674210.7869967421

    4.795440053310.42545558740.6220778480.622077848

    5.02567842910.70979473450.52000994320.5200099432

    5.012636472210.82479988720.41925255710.4192525571

    5.127467958210.87126074020.34038681220.3403868122

    Experimental

    Theoretical

    ln (Re)

    ln (Nu)

    4.43643166051.27048456350.1792338480.179233848

    4.30931234591.1790354640.15658652860.1565865286

    4.2481979411.09876218970.13668882530.1366888253

    4.33243885631.00849014710.11564417980.1156441798

    4.30929668480.93851263670.10454420180.1045442018

    4.1922638990.86870441480.09753568890.0975356889

    4.15657591230.81209666960.09179922370.0917992237

    Experimental

    Theoretical

    ln (Pr)

    ln (Nu)

    Experimental

    Theoretical

    Chart5

    4.43643166054.67540231840.1792338480.179233848

    4.30931234594.64316114040.15658652860.1565865286

    4.2481979414.61814924610.13668882530.1366888253

    4.33243885634.5873767480.11564417980.1156441798

    4.30929668484.56482269620.10454420180.1045442018

    4.1922638994.54156651050.09753568890.0975356889

    4.15657591234.52260614510.09179922370.0917992237

    Experimental

    Theoretical

    ln (Pr)

    ln (Nu)

    Chart1

    11.930326891

    21.7770034843

    31.867431485

    43.1034482759

    Flow Rate Calibration

    Manometer flow rate

    Calculated flow rate

    Calibration Curves

    Hot calibration curve

    Hot temp calibration curve

    50 deg C

    22.14285714290.1428571429

    33.1428571429

    60 deg C

    22.18750.1875

    33.1875

    70 deg C

    22.21428571430.2142857143

    33.2142857143

    80 deg C

    22.250.25

    33.25

    Hot calibration curve

    0000

    0000

    50

    60

    70

    80

    Manometer Value (L/min)

    Actual Value (L/min)

    Hot flow Calibration curve

    y = x + 0.25

    y = x + 0.2143

    y = x + 0.1429

    y = x + 0.1875

    Sheet1

    CALIBRATION COLD WATER

    Flowrate readingFlow (g/s)time(s)experimental flow rate (g/s)

    for 500 mL1041.9111.930326891

    2022.9621.7770034843

    3015.6931.867431485

    4011.643.1034482759

    Constant Rey

    Constant Rey #HOTCOLDHOTCOLDCOLDCOLD

    D (m)T Flow rate hot (L/min)flow rate actual hot% errorv (m/s)rho (kg/m^3)% errorviscosity hot% errorRey/D% errorT1T2T3T4T5T6T7T8T9T10deltaTlnhot% errordelta Tln coldf actual hot (g/s)% errorf cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)% errorQc (J/s)Cp hot (J/kgK)% errorCp cold (J/kg.K)density (kg/m3)densityk (W/mK)% errorkviscosity hot (Ns/m)% errorviscosityv hot (m/s)h hot% errorh coldh localh overallRey hot% errorabs errorRey coldPr hot% errorabs errorln Prhotabs errorPr coldNus hot% errorabs errorln Nushotabs error

    7.90E-0350.144.14299.65507253371.4086695802987.90.00101224825.45000E-047.33945E-012.55344E+069.68293E+0047.536.650.148.44744.1538.1532.6526.1517.459.521253385714.87270828113.66946506468.21284859.65507258681516.808647.12527.81698.212865245910.00220822641455.73401594184.16666666670.00004779924183.8888888889987.9996.290.640090.07811401520.61195.45000E-047.33945E-018.3613E-0423.19374463746844.342602310217.92321458382908.49525948682.02E+049.68E+001.95E+033.56258E+007.38090E-012.62950E-021.27048E+007.38090E-035.7171E+0084.472974985217.923384803515.14041636164.43643166050.179233848

    7.90E-03553.673.835210.42970379641.3040453725989.60.00101050935.02000E-047.96813E-012.57068E+061.04601E+0152.639.955.753.852.248.942.535.827.717.611.352734988912.866762121715.403043589563.25523210.42970384541516.808652.330.051800.38025288688.92378037031750.8678194185.61111111110.00004778274183.3333333333989.6995.630.646270.07736704470.61565.02000E-047.96813E-017.9631E-0421.50805501096085.516968012215.6584617253104.44997088882.03E+041.05E+012.12E+033.25124E+008.00560E-012.60281E-021.17904E+008.00560E-035.4114E+0074.389317231615.658652855611.6483649474.30931234590.1565865286

    7.90E-03603.43953.62711.02839812521.2332531722983.180.00101710784.66400E-048.57633E-012.59972E+061.10617E+0156.942.360.558.556.452.545.838.32917.713.250706856611.216240442916.964032871959.43323111.02839817211516.808656.531.751990.80192034537.81206747121975.74774387224187.05555555560.00004776634183.0555555556983.18995.10.650850.07682261660.618334.66400E-048.57633E-017.6822E-0420.20849756465765.311028439613.66866664493180.82838877392.05E+041.11E+012.27E+033.00045E+008.61067E-012.58359E-021.09876E+008.61067E-035.1971E+0069.979192017613.66888252799.56537355094.2481979410.1366888253

    7.90E-0365.83.17083.371711.86345167131.1464460217980.140.00102026244.29000E-049.32401E-012.61930E+061.19000E+0162.2545.2565.963.561.156.4549.541.130.617.913.24489595069.275409982419.130348576655.078967311.86345171511516.808661.17533.72180.35875348626.90628084172221.748795217841890.00004774414.18E+03980.14994.480.655520.07627532340.621314.29000E-049.32401E-017.3868E-0418.72796006246317.032973005711.5641664383171.83012329892.07E+041.19E+012.46E+032.74146E+009.35516E-012.56468E-021.00849E+009.35516E-034.9731E+0076.129729812611.56441798498.80396016634.33243885630.1156441798

    7.90E-0370.32.9823.196312.51446985581.0868064832977.570.00102294464.02010E-049.95000E-012.64279E+061.25540E+0166.5547.6570.667.864.859.6552.543.33218.314.77642347868.371757624220.769132548352.076783183312.51446989761516.808665.12535.42389.84741157576.2612156052404.48703864190.94444444440.00004772194182.7777777778977.57993.90.659110.07585987160.623914.02010E-049.95000E-017.1379E-0417.70715689576206.325950526310.45414494683161.85486984662.09E+041.26E+012.62E+032.55618E+009.97888E-012.55078E-029.38513E-019.97888E-034.7853E+0074.388152219110.45442017957.77684999684.30929668480.1045442018

    7.90E-0375.22.801623.0337713.18491513861.0315430042974.810.00102584093.76620E-041.06208E+002.66995E+061.32276E+0170.649.975.472.268.762.955.645.533.418.717.86550495397.839738163222.120030300449.289155561713.18491517851516.808669.1537.152583.43632303645.80214746292594.31496274193.11111111110.00004769734182.7777777778974.81993.280.662470.07547511590.626533.76620E-041.06208E+006.8955E-0416.75930726595549.01888312249.75327686723203.13197197842.11E+041.32E+012.79E+032.38382E+001.06476E+002.53819E-028.68704E-011.06476E-024.6035E+0066.17242920699.75356889256.45417347054.1922638990.0975356889

    7.90E-0379.42.662262.9122613.73503739360.9902271528972.150.00102864783.56950E-041.12061E+002.69687E+061.37807E+0173.851.57975.371.665.257.847.334.419.119.50993505637.329876313623.243628499147.1858926513.73503743221516.808672.138.452731.56615969915.526140612720.903050594194.88888888890.00004767714182.8333333333972.15992.80.664720.07521964140.628423.56950E-041.12061E+006.7244E-0416.0441554445372.66345349099.17961419753197.03206044552.13E+041.38E+012.94E+032.25263E+001.12313E+002.52998E-028.12097E-011.12313E-024.4758E+0063.85251125679.17992237495.86161096784.15657591230.0917992237

    2.07124E+04

    T - T0.5656854249T-T T-T0.8T-T/T-T

    rel t-t9.5073180664rel7.881773399rel13.4453781513abs0.0463019645

    8.31890330816.611570247911.76470588240.0405228758

    852.75736995760.9375614136972.153.56950E-042.55344E+067.07106781195.7971014493100.0352941176Power Pr = 0.4621909

    5.98608915295.38720538728.46560846560.0275888133

    Flow cold = 15 g/s5.16607694024.9844236767.30593607310.0246575342

    4.52548339964.49438202256.40.0236307692

    4.0991697464.23280423285.79710144930.0220035967

    abs ln (t-t/t-t)rel ln (t-t/t-t)

    0.134453781512.6124977581

    0.117647058811.0381477773

    0.19.6019614903

    0.08465608477.5505793458

    0.07305936076.7262059391

    0.0646.423552343

    0.05797101455.9841837455

    1222

    d

    Constant Rey

    00.1792338480.179233848

    00.15658652860.1565865286

    00.13668882530.1366888253

    00.11564417980.1156441798

    00.10454420180.1045442018

    00.09753568890.0975356889

    00.09179922370.0917992237

    Ln Pr

    Ln Nu

    Concurrent new

    ConcurrenthotcoldHOTCOLD

    x0100.250.75100.250.751

    T = 52T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdeltaTlncoldf hot (L/min)f actual hot (g/s)f cold (g/s)v (m/s)f actual coldT hot meanT cold meanQh (J/s)Qc (J/s)Cp hotCp colddensity (kg/m3)densityh hoth coldA lnUUU theoryPrRe hot

    fh = 2 L/min43.844.651.949.548.246.823.432.337.740.67.902368454617.9448683589235.3157063100.728629231511.628149.3532753.076359026835.913875944181.24179.5988.82995.013656.92013742681272.21088524740.0572347574896.0872212843898.72627068863.820

    41.640.452.448.546.24420.527.432.335.213.107444863417.387343651235.30034885200.728629231521.989148.227.851239.73271945851351.2392105314180.94180.3988.39996.283629.47459482832122.44698358821244.4458870981249.54150085263.60

    39.436.652.947.844.541.2517.123.327.830.617.029102483417.7297108121235.333742375300.728629231532.350147.07523.851720.89423529461826.302250434180.64181.8989.325997.353877.89599900642813.25339601551500.03379525371507.44368832743.30

    37.6335347.143.139.616.121.325.227.725.964895025217.715221405235.34534975400.728629231542.711146.321.91979.95318127172072.3630733284180.44182.8989.65997.82926.18706850963194.89882839951379.22203033251385.48392092243.10

    average40.638.6552.5548.22545.542.912519.27526.07530.750

    T = 5241.640.452.448.546.24420.527.432.335.213.107444863417.387343651235.3157063200.728629231521.989148.227.851240.27206634521351.2392105314180.94180.3988.82996.283631.05360116772122.44698358821244.66905610251249.76650137763.10

    fc = 2042.6541.7552.749.247.145.31725.832.135.913.069068679521.6922214741351.7766584167201.068649405921.98914926.451601.97706014381737.5153533924181.14180.8988.45996.664703.7625442092187.57257682851400.80910661111407.26900786533.10

    44.343.552.8549.748.2546.517.52732.637.511.028158625122.7910263623468.2321820333201.408669580221.989149.67527.51811.62840065571838.46467284181.254180.4988.18996.386303.76265707632203.074862041548.54504087341556.44321898183.30

    4544.652.750.248.947.817.527.834.738.812.413595693123.7732793631584.6795628201.748689754521.989150.2528.151734.98770707041957.89462135754181.44180.25987.92996.25363.30558580432249.25175966361492.76177691831500.0998235253.180

    0

    fc=2044.343.552.8549.748.2546.517.52732.637.511.028158625122.7910263623468.2321820333201.408669580221.989149.67527.51811.62840065571838.46467284181.254180.4988.18996.386303.76265707632203.074862041548.54504087341556.44321898183.10

    fh=450.349.1560.1556.554.552.718.129.83842.813.130511332728.2887253008468.7447916667201.423834479921.989156.42530.452142.57407773442270.1236793694183.54179.7985995.56261.63782545572191.66407953661539.84958159421547.65908467142.90

    54.553.465.561.459.157.118.83241.346.513.491654340331.5019730509468.7911378201.428390750321.989161.332.652418.5725812545.6644737584185.54179.4982.52994.86879.03716915022206.99452394271589.80428698641598.13007960562.830

    57.7556.569.264.862.260.119.333.543.54913.007150476633.861316371468.8855430333201.432947020621.989164.6534.152624.71898083732729.4016552114187.14179.3980.74994.327743.44796542782201.41267453351637.61872575011646.45424876662.80

    AVERAGE46.777777777845.716666666756.766666666753.136111111151.111111111149.212518.386111111128.486111111135.316666666740.4

    f hot (L/min)f actual hot (L/min)Qc/Qh = .9941

    22.1429

    22.1429

    22.1429

    22.1429

    22.1429

    33.1429

    44.1429

    55.1429

    44.1429

    44.1875

    44.2009

    44.2143

    Concurrent new

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qc

    Qh

    Qh vs. Qc

    Concurrent

    000

    000

    00

    00

    Hot Current

    Cold Current

    Wall Temperature

    Flow Rate

    ConcurrentHOTCOLDHOTCOLDHOTCOLDHOTCOLD

    x0100.250.75100.250.751

    fc=fh=10T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdeltaTlncoldf hot (g/s)f actual hot (g/s)f cold (g/s)v (m/s)f actual coldT hot meanT cold meanQh (J/s)Qc (J/s)Cp (J/kgK)Cp hotCpCp colddensity (kg/m3)densityk (W/mK)kviscosity (Ns/m^2)viscosityh hoth coldAUPrRe hotNu

    35.534.552.546.6542.7538.6516.823.928.430.714.998882957516.31534581271011.85648100.244337246411.628145.57523.75686.4564603144675.9229643214183.77777777784180.34185.41666666674181.9989.9755.3620.638130.60550.000599.16E-041756.25598543631131.45886076510.0286173787635.76946424463.823238.819823506

    38.237.157.350.746.4542.4617.62631.134.0519.248863695819.00326632881012.29100.253753075711.628149.8825.825762.60054668799.7510663454184.83333333334181.34184.55555555564181988.0955.3330.643460.608610.00054788.74E-041520.28759560041149.3820813552600.45939361023.63615.870618214

    4240.162.454.949.9545.651827.5533.2536.319.934902777121.93820335751012.29100.254249692311.628154.02527.15861.0195795889.5862785154186.16666666674182.64184.08333333334180.5986.1655.31250.64820.610820.00145700058.48E-041657.42025659191107.4518859072612.41216374143.31359.4874261649

    45.744.268.159.5554.349.718.629.535.939.319.86736763824.235003081013.0368100.270357099811.628158.928.951003.765808641006.13298064188.05555555564184.54183.61111111114180983.7655.2840.65330.61380.000474268.15E-041938.76783879541133.8357739579663.7519872853.14430.3448615227

    00

    45.744.268.159.5554.349.718.629.535.939.319.86736763824.235003081013.0368100.270357099811.628158.928.951003.765808641006.13298064188.05555555564184.54183.61111111114180983.7655.2840.65330.61380.000474268.15E-041938.76783879541133.8357739579663.7519872853.14430.3448615227

    T = 7543.3539.767.658.1551.946.2518.326.431.634.6523.530282371921.89667782861013.0368150.270085301416.808656.92526.4751164.4729844161148.9700062884187.22222222224183.74184.66666666674180.8984.7555.3380.651290.608010.000488938.80E-041899.04832116411433.0729962232748.83986358843.14297.4154869322

    f2 = 104033.466.956.248.842.117.623.227.329.2531.537825262919.93848362081013.0368250.269852374727.169654.523.4251352.3521105921323.711062884186.61111111114182.84185.55555555564182985.655.3660.64650.60450.000499.23E-041645.47685322141813.1716585712777.18226628893.34288.0313347464

    37.930.266.955.447.439.717.221.824.5526.4534.498083266218.50493526221013.0368350.269524220237.530653.321.8251483.0830551041452.1274073454185.88888888894182.44186.44444444444182.9986.855.3870.64530.60170.0005059.58E-041649.69722467072143.1620070151833.39558194683.184160.6640673777

    000

    T = 7545.744.268.159.5554.349.718.629.535.939.319.86736763824.235003081013.0368100.270456071311.628158.928.951003.765808641006.132980641884184.54183.61111111114180983.455.2840.520.61380.0004658.15E-041938.76783879541133.8357739579663.7519872853.14518.5706538188

    f1=1048.948.3568.56156.752.818.531.3539.1543.516.221224095827.75761624581517.9256100.372255637411.628160.65311177.862943181215.0201694188.77777777784185.254183.16666666674179.6982.455.250.65350.61710.000467.81E-042786.40904660711195.4713412692785.8979678492.96280.5676343161

    53.754.26962.859.556.9518.834.2543.2547.9510.517104059231.26607913112527.7032100.576125192211.628162.97533.3751397.4855692281416.62877727524189.88888888894186.34115.44444444444179.3598155.2460.65520.61750.0004437.43E-045098.99866102711237.4295605216953.89546858552.8310078.8095424485

    56.256.668.563.661.559.419.636.245.950.910.202841646133.53479513193537.4808100.77986097811.628163.9535.251428.0139823041521.07786575254190.33333333334186.84182.77777777784179.25980.555.1720.65650.62370.0004397.16E-045370.875070481238.7784411448965.70327510552.813760.2827854761

    f hot (L/min)f actual hot (L/min)Qc/Qh = .9941

    0.60107592590.72

    0.60107592590.75

    0.60107592590.75

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.90161388891.1

    1.50268981481.7

    2.10376574072.3

    Flow Rate

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qh

    Qc

    Qc/Qh

    Hot stream

    000

    000

    00

    00

    hot inlet

    cold inlet

    wall

    X position

    T (C)

    Temperature Profile Con Currentf1=f2=10g/s

    Hot inlet

    753.076359026835.91387594

    974.2764037812918.511293546

    1239.73271945851351.239210531

    1351.22425537321488.978273258

    1720.89423529461826.30225043

    1869.04047206182049.516969927

    1979.95318127172072.363073328

    2143.20676995672322.392571395

    Qh (J/s)

    Qc (J/s)

    Flow Rate of the Cold Stream (g/s)

    Q (J/s)

    GRAPH

    1240.27206634521351.239210531

    1351.22425537321488.978273258

    1601.97706014381737.515353392

    1797.18058895481847.745392346

    1811.62840065571838.4646728

    1940.22389991221985.494350168

    Qh (J/s)

    Qc (J/s)

    Flow Rate of the Hot Stream (L/min)

    Q (J/s)

    countercurrent new

    1811.62840065571838.4646728

    1940.22389991221985.494350168

    2142.57407773442270.123679369

    2416.0651241652407.927829832

    2418.5725812545.664473758

    2649.9266929362711.08671393

    2624.71898083732729.401655211

    2913.89136157292894.819937345

    Qh (J/s)

    Qc (J/s)

    The Inlet Temperature of the Hot Stream (C)

    Q (J/s)

    h profile

    Con Current 10

    T = 52T3Qh (J/s)Qc (J/s)f cold (g/s)Qh (J/s)Qc (J/s)

    fh = 2 L/min51.9753.076359026835.91387594Con Current 1010Con753.076359026835.91387594

    Counter974.2764037812918.511293546

    52.41239.73271945851351.239210531Con Current 2020Con1239.73271945851351.239210531

    Counter1351.22425537321488.978273258

    52.91720.89423529461826.30225043Con Current 3030Con1720.89423529461826.30225043

    Counter1869.04047206182049.516969927

    531979.95318127172072.363073328Con Current 4040Con1979.95318127172072.363073328

    Counter2143.20676995672322.392571395

    Qh (J/s)Qc (J/s)

    T = 5252.41240.27206634521351.2392105312Con1240.27206634521351.239210531

    fc = 2052.71601.97706014381737.515353392f hot (L/min)Counter1351.22425537321488.978273258

    52.851811.62840065571838.46467283Con1601.97706014381737.515353392

    52.71734.98770707041957.8946213575Counter1797.18058895481847.745392346

    4Con1811.62840065571838.4646728

    Counter1940.22389991221985.494350168

    Qh (J/s)Qc (J/s)

    fc=2052.851811.62840065571838.464672853Con1811.62840065571838.4646728

    fh=460.152142.57407773442270.123679369Counter1940.22389991221985.494350168

    65.52418.5725812545.66447375860Con2142.57407773442270.123679369

    69.22624.71898083732729.401655211Counter2416.0651241652407.927829832

    65Con2418.5725812545.664473758

    Counter2649.9266929362711.08671393

    69Con2624.71898083732729.401655211

    Counter2913.89136157292894.819937345

    error propagation

    Counter currentCOLD

    X position0100.250.75100.250.751Nu = 0.0243 Re^.8 Pr^.4

    T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdelta Tln coldf hot (L/min)f actual hot (g/s)f cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)Qc (J/s)Q averageCp hot (J/kgK)Cp cold (J/kg.K)density (kg/m3)densityv hot (m/s)h hoth coldA lnUdelta T lnU theoryPr hotRe hotNu theory hot

    T = 5249.638.952.150.64945.542.337.531.4523.49.373915975310.8902706509235.306777551011.628148.832.85974.2764037812918.511293546946.393848663641814179.4988.57994.740.72862923153988.36471147142303.47592093160.02861737871351.340863786815.12551925352186.41080666753.800

    fh = 2 L/min47.634.352.455047.543.337.532.4527.2521.322.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.31849879683.600

    45.82952.7549.245.640.131.426.421.516.2538.551616927513.5582708004235.3435643032.350146.42523.8251869.04047206182049.5169699271959.27872099444180.44181.8989.6997.340.72862923151860.41505252384128.43132068851119.858233495622.57693544693032.50398157273.3800

    44.226.752.748.24438.228.72419.815.766.163630785113.1216471027235.358921454042.711145.4522.22143.20676995672322.3925713952232.79967067584180.24.18E+03990.03997.720.72862923151243.02104037354833.7605122304848.410899104623.24193324483356.97153820323.200

    0

    fc = 2047.634.352.455047.543.337.532.4527.2521.322.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.31849879683.200

    T = 5249.134.452.650.448.244.33731.124.616.912.887443327814.6343276514351.78975383332021.989148.4526.951797.18058895481847.7453923461822.46299065044180.94180.6988.7996.531.06864940595351.29247077073448.31715790111926.471307509420.94902271573039.94061110193.2800

    49.536.6552.851.149.24638.732.625.817.112.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.98602044933.3800

    0

    f1 = 1049.536.6552.851.149.24638.732.625.817.112.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.98602044933.200

    T = 7556.941.460.358.255.851.944.23728.41812.327068242817.5084343107468.75595833332021.989156.131.12416.0651241652407.9278298322411.99647699854183.34179.6985.16995.311.42383447997521.12095464253756.07282902972322.923130970423.90558928363525.71630921613.100

    61.144.46562.660.155.84839.930.118.514.263914838418.7784958586468.824044852021.989160.433.252649.9266929362711.086713932680.5067034334185.14179.4982.99994.631.42839075037129.0040191453942.94260557522343.739734790225.83420352983625.7008640962.900

    65.547.469.166.463.75950.742.331.719.212.99066186420.7850289141468.90801932021.989164.0534.952913.89136157292894.8199373452904.3556494594186.84179.3981.06994.051.43294702068607.47587833563803.72202691772457.138474189827.7375882423658.90596916472.8300

    average51.490909090936.736363636455.913636363653.436363636450.890909090946.672727272739.518181818233.481818181826.695454545518.6136363636

    f hot (L/min)f actual hot (L/min)

    22.1429

    22.1429

    22.1429

    22.1429

    L/min22.1429

    433.1429

    44.1429

    55.1429

    44.1429

    44.1875

    44.2009

    44.2143

    error propagation

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qc vs. Qh

    Qc

    Qh

    CounterCon

    000

    000

    00

    00

    Hot Current

    Cold Current

    Wall Temperature

    Constant Pr

    COUNTER CURRENT NEW

    L/D033.227848101399.6835443038132.9113924051

    X position0100.250.75100.250.751HOTCOLD

    T1 (Celsius)T2T3T4T5T6f actual hot (g/s)Cp hot (J/kgK)deltaTlnhotT7T8T9T10f actual cold (g/s)Cp cold (J/kg.K)delta Tln colddeltaTlnhotdelta Tln coldf hot (L/min)f actual hot (g/s)f cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)Qc (J/s)Q averageCp hot (J/kgK)Cp cold (J/kg.K)density (kg/m3)densityv hot (m/s)h hoth coldA lnUdelta T lnU theory

    T = 5249.638.952.150.64945.535.3067775541819.373915975342.337.531.4523.411.62814179.410.89027065099.373915975310.8902706509235.306777551011.628148.832.85974.2764037812918.511293546946.393848663641814179.4988.57994.740.72862923153988.36471147142303.47592093160.02861737871351.340863786815.12551925352186.4108066675

    fh = 2 L/min47.634.352.455047.543.335.3221354180.822.402090525137.532.4527.2521.321.98914179.911.489064642622.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.3184987968

    45.82952.7549.245.640.135.3435644180.438.551616927531.426.421.516.2532.35014181.813.558270800438.551616927513.5582708004235.3435643032.350146.42523.8251869.04047206182049.5169699271959.27872099444180.44181.8989.6997.340.72862923151860.41505252384128.43132068851119.858233495622.57693544693032.5039815727

    44.226.752.748.24438.235.358921454180.266.163630785128.72419.815.742.71114182.6513.121647102766.163630785113.1216471027235.358921454042.711145.4522.22143.20676995672322.3925713952232.79967067584180.24182.65990.03997.720.72862923151243.02104037354833.7605122304848.410899104623.24193324483356.9715382032

    fc = 2047.634.352.455047.543.335.3221354180.822.402090525137.532.4527.2521.321.98914179.911.489064642622.402090525111.4890646426235.3221352021.989147.87529.41351.22425537321488.9782732581420.10126431564180.84179.9989995.80.72862923152314.58226762643539.49690708811240.016074847418.24859304182719.3184987968

    T = 5249.134.452.650.448.244.351.78975383334180.912.88744332783731.124.616.921.98914180.614.634327651412.887443327814.6343276514351.78975383332021.989148.4526.951797.18058895481847.7453923461822.46299065044180.94180.6988.7996.531.06864940595351.29247077073448.31715790111926.471307509420.94902271573039.9406111019

    49.536.6552.851.149.24668.24046783334181.212.146481285238.732.625.817.121.98914180.314.744809832912.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.9860204493

    f1 = 1049.536.6552.851.149.24668.24046783334181.212.146481285238.732.625.817.121.98914180.314.744809832912.146481285214.7448098329468.24046783332021.989149.427.91940.22389991221985.4943501681962.85912504014181.24180.3988.3996.271.40866958026129.64187500453677.62403703522116.550050681620.62238360023325.9860204493

    T = 7556.941.460.358.255.851.968.75595833334183.312.327068242844.23728.41821.98914179.617.508434310712.327068242817.5084343107468.75595833332021.989156.131.12416.0651241652407.9278298322411.99647699854183.34179.6985.16995.311.42383447997521.12095464253756.07282902972322.923130970423.90558928363525.7163092161

    61.144.46562.660.155.868.824044854185.114.26391483844839.930.118.521.98914179.418.778495858614.263914838418.7784958586468.824044852021.989160.433.252649.9266929362711.086713932680.5067034334185.14179.4982.99994.631.42839075037129.0040191453942.94260557522343.739734790225.83420352983625.700864096

    65.547.469.166.463.75968.90801934186.812.99066186450.742.331.719.221.98914179.320.785028914112.99066186420.7850289141468.90801932021.989164.0534.952913.89136157292894.8199373452904.3556494594186.84179.3981.06994.051.43294702068607.47587833563803.72202691772457.138474189827.7375882423658.9059691647

    HOTL/D033.227848101399.6835443038132.9113924051COLD023.648648648670.945945945994.5945945946

    h ln03625.78610133762497.76375869933988.3647114714h ln02340.03903078771763.15440861432303.4759209316

    02479.00614456161669.5347504192314.5822676264

    Constant Pr

    00

    00

    00

    00

    COLD h ln

    graphs!!!!!!!!

    Nus

    Counter currentCOLDHOTCOLDCOLD

    X position0100.250.75100.250.751Nu = 0.0243 Re^.8 Pr^.4

    T1 (Celsius)T2T3T4T5T6T7T8T9T10deltaTlnhotdelta Tln coldf hot (g/s)f actual hot (g/s)f cold (g/s)f actual cold (g/s)T hot meanT cold meanQh (J/s)Qc (J/s)Cp hot (J/kgK)Cp cold (J/kg.K)density (kg/m3)densityk (W/mK)kviscosity (Ns/m)viscosityv hot (m/s)h hoth coldh localh overallPr hotRe hotNu theory hot

    f1=f2=10 g/s47.22854.750.14537.433.6528.423.3518.374.842785178911.51795721061011.856481011.628146.0525.975911.6722711714746.89699130754444.64285714294184.5990995.940.6550.608890.000568.7018E-040.2443298422467.43641434041771.01850332560.0572347574318.63884964193.83412.328028336727.794593766

    49.628.558.753.648.440.1536.4530.324.2518.283.997294335611.66704162411012.291011.628149.42527.3251026.3000665392887.91024940144501.72084130024184.0555555556988.4995.580.6540.611070.0005238.4537E-040.253673489468.85958295912078.4815384871328.190152563.63787.330639880729.5660870333

    52.830.163.157.451.642.338.531.6524.6518.1132.906413122313.1164079081012.291011.628152.728.31116.33471872992.44748210674366.964183.7777777778987.4995.310.6460.612730.00058.2705E-040.2539303996322.3162720512066.4764928149237.19651158373.383961.547849315229.8857994948

    5731.5567.360.8554.4544.641.233.626.1518.4598.671322592714.40786017351013.03681011.628155.9529.8251278.44075521106.670663709743204.18E+03985994.860.6480.615210.000488.0000E-040.2700167518497.19115552097.7646462769345.25132465523.24377.36532088731.669156725

    00

    f2 = 105731.5567.360.8554.4544.641.233.626.1518.4598.671322592714.40786017351013.03681011.628155.9529.8251278.44075521106.670663709743204183.3888888889985994.860.6480.615210.000488.0000E-040.2700167518497.19115552097.7646462769345.25132465523.24377.36532088731.669156725

    T = 7553.72967.659.952.942.736.129.423.7518.31904.366666213.86502250281013.03681516.808655.1527.21421.85980660871251.85709039564380.12422360254184.1111111111985.2995.670.6450.610570.0004838.5000E-040.269961937228.65101048482465.88048810323.59696683823.284350.176716409431.8244810675

    49.225.46757.549.339.23024.921.217.85124.150460627712.48174991691013.03682527.169653.123.9251766.39165041381.623065284873.83928571434185.3333333333987996.480.6460.605310.0004489.1284E-040.2694696054545.97455738393023.0960614763394.56750427173.384690.034272378934.2069038388

    46.223.666.5556.1547.6537.126.922.619.517.282.482270133511.68682456851013.03683537.530651.82522.051687.58384156251524.01122504834395.50781254186.3055555556987.8996.9210.6430.602090.0005129.5329E-040.2692513672785.12442791493561.4716396986551.41388803823.54103.779988331531.1731541287

    000

    f1 = 105731.5567.360.8554.4544.641.233.626.1518.4598.671322592714.40786017351013.03681011.628155.9529.8251278.44075521106.670663709743204183.3888888889985994.860.6480.615210.000488.0000E-040.2700167518497.19115552097.7646462769345.25132465523.24377.36532088731.669156725

    T = 7560.135.668.26357.949.1546.237.428.2518.242.077850053115.58455209811517.92561011.628158.67532.21485.22887178451361.92958444349.35344827594183994.122994.80.6510.619010.0004647.6140E-040.36786625611354.48306142062386.7018966835764.58650597193.16226.424809882341.4516621199

    64.542.96965.461.5554.851.542.932.119.216.864429466717.81772231572527.70321011.628161.935.351636.17286294741570.99959237224159.21052631584182.7777777778993.078993.50.6540.623850.0004567.1490E-040.56911825013722.984849772408.02912566821352.49967707082.99791.475059878757.9754289242

    64.3546.268.76663.257.353.645.333.9519.316.492855398517.60754304553537.48081011.62816336.451793.29016034571668.27510892784196.9796380094182.7777777778992.6829930.65550.62550.0004426.9899E-040.77029067614172.4241572212587.65730780951479.83371369992.8313666.887200959374.9646531313

    f hot (L/min)f actual hot (L/min)

    0.60107592590.72

    0.60107592590.75

    0.60107592590.75

    0.60107592590.8

    L/min0.60107592590.8

    40.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.60107592590.8

    0.90161388891.1

    1.50268981481.7

    2.10376574072.3

    Nus

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Qh/Qc

    Qh (J/s)

    Qc (J/s)

    000

    000

    00

    00

    hot inlet

    cold inlet

    wall

    X position

    T (C)

    Temperature Profile Counter Currentf1=f2=10g/s

    Constant Pr number (COUNTER)

    Fcold = 15 g/sF hot (L/min)T1 (Celsius)T2T3 (hot enter)T4T5T6T7T8T9T10deltaTlnhotdeltaTlncoldf actual hot (L/min)fh actual (g/s)% errorf cold (g/s)f actual cold% errorT hot meanT cold meanQh (J/s)Qc (J/s)Cp hot (J/kgK)Cp% relative errorCp cold (J/kg K)density h (kg/m3)% relative errordensity c (kg/m^3)k hot (W/mK)%relative errork cold (W/mK)viscosity h (Ns/m^2)% relative errorviscosity ch hot% errorh coldh localh overallPr hot% relative errorabsolute errorRe hot% errorabs errorNu hot% errorabs errorln Re hotabsolute errorpercent errorln Nu hotabs errorpercent errorv hot (m/s)% errorNu hot theoryln Nu theory

    Thot = 57 C1.6551.133.1556.9553.550.144.337.6530.5523.5515.126.356677547915.63739844221.837530.110521.7687074831516.80861.189867091850.62526.3751594.07855861531586.00430776334185.05555555560.00004778914184.3333333333987.760.0010123917996.690.64430.07760360080.609520.000541440.73877068560.00086292320.880576112624.74175289012769.98686608633.51692764240.74283541040.02612498398962.943475567321.78123985581952.24021655328.457172980424.74187459347.04083805169.10085396490.21781239862.39331824683.34840025460.24741874597.38916279770.36792154530.616330702121.768707506557.16994928854.0460283982

    2.6552.737.1556.9554.652.247.94133.825.915.816.164023516816.04421492032.837546.497166666714.09691629961516.80861.189867091852.42528.41761.30246978841772.127336284185.61111111110.00004778274183.7222222222986.930.0010132431996.110.646390.07735268180.613050.000525450.761252260.000823564181.366229926116.54115981983016.576222053.40248048130.76517216560.026034833614261.924093547714.11745572732013.420819773551.103502864216.54134068398.45320451029.56534861430.14117455731.47589557863.93385304410.16541340684.20487000880.41126081260.952302941314.09691633681.99897176444.4067067077

    3.6553.939.757.355.653.649.9543.135.6527.21612.369707178816.41369819843.837562.883833333310.42345276871516.80861.189867091853.62529.551934.753188551905.613580228941860.00004777834183.4444444444986.350.0010138389995.780.647750.0771902740.614780.000515220.7763673770.000804976002.053870862113.28462049943170.78098331713.32954213820.78019526070.0259769319671.130613132510.45232586472056.090672954873.201428915213.28484475459.72469618959.88690738880.10452325861.05718860854.29321494150.13284844753.09438146830.43423234111.288343126310.423452818105.29886639224.6568026536

    4.655542.457.956.154.651.444.437.228.316.410.507597855417.16369807114.837579.27058.26873385011516.80861.189867091854.6530.42157.07141270831968.82119995564186.38888888890.00004777394183.2777777778985.850.0010143531995.520.648910.07705228770.616230.000506540.7896711020.000789577877.616181051612.91876175263132.80425789233.26790067620.79342139280.025928223125222.07883689668.3063555182095.035537222995.90415902112.918991534812.389850185510.13547503420.08306355520.81953292674.56334934930.12918991532.8310327670.45023536971.62