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