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HEAT PERFORMANCE ANALYSISHEAT PERFORMANCE ANALYSISOF MULTIOF MULTI--FLUID HEAT EXCHANGERSFLUID HEAT EXCHANGERS

A ThesisSubmitted to the Faculty

OfPurdue University

BySang Bae Park

Advisor: Dr. S. S. Krishnan

11/13/2003

HEAT EXCHANGERSHEAT EXCHANGERS

nn Devices that provide flow of thermal energy Devices that provide flow of thermal energy between two or more fluids at different between two or more fluids at different temperatures.temperatures.

nn In a twoIn a two--fluid heat exchanger, heat transfer occurs fluid heat exchanger, heat transfer occurs between two fluids: one internal and one external.between two fluids: one internal and one external.

nn MultiMulti--fluid heat exchangers is a combination of fluid heat exchangers is a combination of several twoseveral two--fluid heat exchangers.fluid heat exchangers.

nn In a multiIn a multi--fluid heat exchanger, heat transfer fluid heat exchanger, heat transfer occurs between more than two fluids: one external occurs between more than two fluids: one external and several internal fluids.and several internal fluids.

MULTIMULTI--FLUID HEAT FLUID HEAT EXCHANGERSEXCHANGERSnn AdvantageAdvantage

–– Tighter package space while maintaining the Tighter package space while maintaining the proper temperature of vehicle thermal proper temperature of vehicle thermal management system. management system.

–– Great cost saving to car manufacturers and Great cost saving to car manufacturers and automotive suppliers.automotive suppliers.

nn DisadvantageDisadvantage–– In a multiIn a multi--fluid heat exchangers, unfavorable fluid heat exchangers, unfavorable

thermal interaction occurs between twothermal interaction occurs between two--fluid heat fluid heat exchangers operating at different temperatures.exchangers operating at different temperatures.

–– The thermal interaction is the heat from tube walls The thermal interaction is the heat from tube walls that is not delivered to external stream, but is that is not delivered to external stream, but is transferred by conduction along the fins to transferred by conduction along the fins to adjacent tubes.adjacent tubes.

PROBLEM PROBLEM IDENTIFICATIONIDENTIFICATIONnn For multiFor multi--fluid heat exchangers, tube wall fluid heat exchangers, tube wall

temperatures must first be determined for temperatures must first be determined for heat performance analysis.heat performance analysis.

nn However, LMTD and However, LMTD and ee--Ntu methods used for Ntu methods used for the analysis of twothe analysis of two--fluid heat exchangers fluid heat exchangers are not capable of evaluating tube wall are not capable of evaluating tube wall temperatures.temperatures.

nn Necessary to develop a new method to Necessary to develop a new method to predict the heat performance of multipredict the heat performance of multi--fluid fluid heat exchangers. heat exchangers.

BASIC EQUATIONS FOR MULTIBASIC EQUATIONS FOR MULTI--FLUID HEAT EXCHANGER FLUID HEAT EXCHANGER DESIGNDESIGN

iwT ,

1, +iwT

1, −iwT

ihT ,

1, +ihT

1, −ihT

1, +ihh

ihh ,

1, −ihh

1, −ich 1, −icT

ich , icT ,

1, +ich 1, +icT

walltemperature

ifq ,

1, −ifq

ibq ,

1, −ibq

iinhT )( ,iouthT )( ,

iinhh )( ,iouthh )( ,

iincT )( ,

ioutcT )( ,

iinch )( ,

ioutch )( ,

iwT ,

ihq ,

ibq ,

ifq ,

Fin Pitch

HEAT TRANSFER RATE HEAT TRANSFER RATE FROM THE FROM THE iithth LAYER LAYER -- IInn Neglecting the very small wallNeglecting the very small wall--resistance, the heat resistance, the heat

transfer rate from the transfer rate from the iithth hot fluid to the hot fluid to the iithth tube tube wall iswall is

nn The heat transfer rate fromThe heat transfer rate fromthe prime tube surface:the prime tube surface:

)()( ,,, ibihihhih TTAhq −=

iibcib Ahq θ)(, =

iciwi TT ,, −=θ

2/,, ihib AA =

pitchfinperimetertubeInsideA ih ×=,

iinhT )( ,iouthT )( ,

iinhh )( ,iouthh )( ,

iincT )( ,

ioutcT )( ,

iinch )( ,

ioutch )( ,

iwT ,

ihq ,

ibq ,

ifq ,

Fin Pitch

HEAT TRANSFER RATE HEAT TRANSFER RATE FROM THE FROM THE iithth LAYER LAYER -- IIIInn The fin efficiency for the The fin efficiency for the iithth layerlayer

nn The heat transfer rate from the The heat transfer rate from the iithth fin to the fin to the iithth cold stream cold stream

Lmlmlmlmlmlm

ii

bL

iii

iif sinh

)/(sinh

1tanh,

θθη −+=

iifcfif Ahq θη )(, =

( )

−+= +1,,, sinh

1tanhii

iib

i

iificif Lmlmlm

lmAhq θθθ

( )1, )()( +−′′+′= iiifciifcif AhAhq θθηθη

areasurfacefinaofhalfA if :,

FIN EFFICIENCY FIN EFFICIENCY ??’’ AND AND BYBY--PASS EFFICIENCY PASS EFFICIENCY ??””nn When the fin conduction (k) is When the fin conduction (k) is

very much better than the wallvery much better than the wall--toto--stream heat transfer (h), the stream heat transfer (h), the byby--pass efficiency is very high. pass efficiency is very high. Thus all the heat from the tube Thus all the heat from the tube walls is conducted from one tube walls is conducted from one tube to the other and very little heat to the other and very little heat is transferred to the cold stream.is transferred to the cold stream.

nn When k is relatively poor, the byWhen k is relatively poor, the by--pass efficiency is very low and pass efficiency is very low and hence all the heat from the tube hence all the heat from the tube walls is transferred to the cold walls is transferred to the cold stream, and very little heat is stream, and very little heat is conducted from one tube to the conducted from one tube to the other.other.

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8 9 10

ml

-5

5

15

25

35

45

55

?'

?"

lmlm

i

ii

tanh=′η

Lmlm iii sinh

1=′′η

crkAhP

m ≡

OVERALL HEAT TRANSFER OVERALL HEAT TRANSFER RATE FROM THE RATE FROM THE iithth LAYERLAYER

nn The total heat transfer of the cold side:The total heat transfer of the cold side:

nn The overall surface efficiencyThe overall surface efficiency

)()()( 1,, +−′′+′+= iiifciifibicic AhAAhq θθηθη ibific AAA ,,, +=

ifibic qqq ,,, +=

( ) ( )1, )(11)( +−

′′+

′−−= ii

ic

ficci

ic

ficcic A

AAh

A

AAhq θθηθη

( )1, )()( +−′′+′= iiiccciicccic AhAhq θθηθη

( )ic

fic A

A

′−−=′ ηη 11,

ic

fic A

A

′′=′′ ηη ,

ENERGY BALANCE ON ENERGY BALANCE ON THE THE iithth TUBE LAYER TUBE LAYER -- IInn The conservation of energy requirement to the The conservation of energy requirement to the iithth

tube:tube:

wherewhere

0,1,, =−− − icicih qqq

( )iwihihhih TTAhq ,,, )( −=

( ) ( )1,,,,, )()( +−′′+−′= iwiwiccciciwicccic TTAhTTAhq ηη

( ) ( )1,,11,,11, )()( −−−−− −′′+−′= iwiwiccciciwicccic TTAhTTAhq ηη

ENERGY BALANCE ON ENERGY BALANCE ON THE THE iithth TUBE LAYER TUBE LAYER -- IIIIIInn The final form of the conservation of energy The final form of the conservation of energy

requirement to the requirement to the iithth tube:tube:

wherewhere

iiwiiwiiwi cTaTdTb =++ +− 1,,1,

iia γ= 1−= iib γ

)( ,1,1, iciiciihii TTTc ββα ++−= −−

)( 11 iiiiiid γγββα ++++−= −−

SYSTEM OF EQUATIONS FOR SYSTEM OF EQUATIONS FOR TUBE WALL TEMPERATURESTUBE WALL TEMPERATURESnn At the 1At the 1stst tube:tube:

nn At the 2At the 2ndnd tube:tube:

nn At the 3At the 3rdrd tube:tube:

. . . . .. . . . .

. . . . .. . . . .nn At the MAt the M--11thth tube:tube:

nn At the At the MMthth tube:tube:

i

1+i

2+i

1−M

M

tube

.

.

.

.

.

12,11,1 cTaTd ww ′=+′

22,22,21,2 cTaTdTb www =++

34,33,32,3 cTaTdTb www =++

1,11,12,1 −−−−−− =++ MMwMMwMMwM cTaTdTb

MMwMMwM cTdTb ′′=′′+− ,1,

THE SYSTEM OF EQUATIONS THE SYSTEM OF EQUATIONS IN MATRIX FORMIN MATRIX FORM

nn TridiagonalTridiagonal matrix formmatrix form

nn Solution using ThomasSolution using Thomas’’ AlgorithmAlgorithm

′′

′

=

′′

′

−−−−−

M

M

Mw

Mw

w

w

w

MM

MMM

cc

ccc

TT

TT

T

dbadb

adbadb

ad

1

3

2

1

,

1,

3,

2,

1,

111

333

222

11

MMMMMMMMM

ZTGP (ZEROZTGP (ZERO--THERMALTHERMAL--GRADIENT POINT)GRADIENT POINT)nn The boundary The boundary

condition for ZTGP:condition for ZTGP:

nn The location to ZTGP:The location to ZTGP:

0=dxdθ

−= +−

LmLm

mx

i

iii

i sinh/cosh

tanh1 11 θθ

−== +−

LmLm

LmLx

xi

iii

i sinh/cosh

tanh1 11* θθ

-0.25

0

0.25

0.5

0.75

1

1.25

0 1 2 3 3 4 5

x*

mL=2

mL=3

mL=5

mL=8

mL=10

THE DIRECTION OF THE DIRECTION OF THERMAL INTERACTIONTHERMAL INTERACTIONnn If If ?? i+1i+1>>?? ii, the value of x* is smaller than 0.5 , the value of x* is smaller than 0.5

and the direction of the thermal interaction and the direction of the thermal interaction is from the i+1is from the i+1thth tube to the tube to the iithth tube.tube.

nn If If ?? i+1i+1==?? ii, the value of x* is 0.5 and there is , the value of x* is 0.5 and there is no thermal interaction.no thermal interaction.

nn If If ?? i+1i+1<<?? ii, the value of x* is greater than 0.5 , the value of x* is greater than 0.5 and the direction is from the and the direction is from the iithth tube to the tube to the i+1i+1thth tube.tube.

EQUIVALENT SURFACE EQUIVALENT SURFACE AND NODAL NETWORKAND NODAL NETWORKnn Nodal network in a Nodal network in a

heat exchangerheat exchangernn Nodal network in an Nodal network in an

equivalent surfaceequivalent surface

1=j2=j

mj =

1=i

2=i

1=k5=k

nk =

xy

z

(a)

nk =

5=k1=k

1=i

2=i

1=j2=j

mj =

xy

z

(b)

THE SYSTEM OF THE SYSTEM OF EQUATIONS AT NODESEQUATIONS AT NODES

nn The system of equations for tube wall The system of equations for tube wall temperatures at nodestemperatures at nodes

′′

′

=

′′

′

−−−−−

kjM

kjM

kj

kj

kj

kjMw

kjMw

kjw

kjw

kjw

kjMkjM

kjMkjMkjM

kjkjkj

kjkjkj

kjkj

cc

c

cc

TT

T

TT

dbadb

adb

adbad

,,

,,1

,,3

,,2

,,1

,,,

,,1,

,,3,

,,2,

,,1,

,,,,

,,1,,1,,1

,,3,,3,,3

,,2,,2,,2

,,1,,1

MMMMMMMMM

HEAT TRANSFER RATE & HEAT TRANSFER RATE & FLUID TEMP. AT NODESFLUID TEMP. AT NODES

nn The heat transfer rate at nodesThe heat transfer rate at nodes

nn The fluids temperature at nodesThe fluids temperature at nodes

)()( ,,,1,,,1,,,,,, kjihkjihkjihphkjih TTcmq −= −−&

)()( ,1,,,,,,1,,,,, kjickjickjicpckjic TTcmq −− −= &

1,,,

,,,1,,,,,, )( −

− −=kjihph

kjihkjihkjih cm

qTT

&

kjicpc

kjickjickjic cm

qTT

,1,,

,,,,1,,,,, )( −

− +=&

OVERALL HEAT OVERALL HEAT TRANSFER RATETRANSFER RATE

nn HotHot--sideside

nn ColdCold--sideside

∑∑∑= = =

=M

i

m

j

n

kkjihh qQ

1 1 1,,,

∑∑∑+

= = =

=1

1 1 1,,,

M

i

m

j

n

kkjicc qQ

nk =

5=k1=k

1=i

2=i

1=j2=j

mj =

xy

z

(b)

ch QQ =

FLOW CHART FLOW CHART FOR NEW FOR NEW METHODOLOGYMETHODOLOGY

nn Thermal propertiesThermal properties–– µµ for Refor Re–– CCpp for Stfor St–– PrPr

Apply the conservation of energyrequirements to a nodal region of

each tube which has the same j and kindices.

Develop a system of equations for thetube wall temperatures at the nodes

Solve the system of equations (in atridiagonal matrix) for the tube wall

temperatures at the nodes

Convert a fin-tube surface to anequivalent surface based on the

overall efficiency

Subdivide a heat exchanger into anumber of small regions and assign

to each a reference point that is at itscenter

Define fin and overall surfaceefficiencies for a multi-fluid heat

exchanger

Calculate the outlet temperatures ofthe cold and hot fluids at the nodes

Thomas' algorithm

Calculate the local heat rate of thenodal regions

Set the outlet fluid temperatures asthe inlet temperature of the next nodal

regions in the flow direction

Integrate all the local heat rates ofeach fluid to obtain the overall heat

transfer rate

j=m and k=n?

End

No

Yes

Multi-fluid heat exchangersurface geometry, flow arrangement,

and material

Operating conditions

Thermo-physical properties of fluids

SIMULATION RESULTSSIMULATION RESULTS

nn Features of the simulation coreFeatures of the simulation corenn Operating conditionsOperating conditionsnn AssumptionsAssumptionsnn Grid independent solutionsGrid independent solutionsnn Simulation resultsSimulation resultsnn Optimization of designOptimization of design

FEATURES OF THE FEATURES OF THE SIMULATION CORESIMULATION COREnn Features of the simulation coreFeatures of the simulation core

–– 60 water tubes + 10 oil tubes60 water tubes + 10 oil tubes–– 698 mm (W) and 19 mm (d)698 mm (W) and 19 mm (d)

airwater

water

oil

oil

oil

water

header

commonfin

Wd

s

h

H

OPERATING CONDITIONSOPERATING CONDITIONS

nn Inflow conditionsInflow conditions–– Air speed: 4 Air speed: 4 m/sm/s–– Air temperature: 20 Air temperature: 20 °°CC–– Water flow rate: 5,000 l/hrWater flow rate: 5,000 l/hr–– Water temperature: 95 Water temperature: 95 °°CC–– Oil flow rate: 2 gal/minOil flow rate: 2 gal/min–– Oil temperature: 140 Oil temperature: 140 °°CC

ASSUMPTIONS ASSUMPTIONS -- II

nn The simulation core operates under steadyThe simulation core operates under steady--state, state, steadysteady--flow conditions.flow conditions.

nn There is no heat generation in the simulation There is no heat generation in the simulation core.core.

nn The temperature of each internal fluid (water or The temperature of each internal fluid (water or oil) is uniform over the flow cross section.oil) is uniform over the flow cross section.

nn The internal flow is fully developed at any flow The internal flow is fully developed at any flow cross section.cross section.

nn In a tube, the wallIn a tube, the wall--temperature distribution is temperature distribution is symmetric about the mid plane, which divides the symmetric about the mid plane, which divides the tube into two equal parts along the tube width. tube into two equal parts along the tube width.

ASSUMPTIONS ASSUMPTIONS -- IIII

nn The outer fins are insulated with side members; The outer fins are insulated with side members; the fin heat transfer to the side members is the fin heat transfer to the side members is negligible.negligible.

nn The heat transfer resistance of tube walls is The heat transfer resistance of tube walls is negligible.negligible.

nn The heat transfer resistance due to metallic The heat transfer resistance due to metallic bonding between fin and tube is negligible.bonding between fin and tube is negligible.

nn The heat transfer from the headers is negligible. The heat transfer from the headers is negligible. nn The radiation effect from the core surface is The radiation effect from the core surface is

negligible.negligible.

THE DEGREE OF GRID THE DEGREE OF GRID INDEPENDENCEINDEPENDENCEnn Depends on what we want out of the Depends on what we want out of the

solution.solution.nn If we need extreme accuracy is required, we If we need extreme accuracy is required, we

need to press the matter of grid need to press the matter of grid independence in a very detailed fashion. independence in a very detailed fashion.

nn If we can tolerate a little less precise If we can tolerate a little less precise solution, we can slightly relax the criterion solution, we can slightly relax the criterion for extreme grid independence and use for extreme grid independence and use fewer grid points thus saving computer fewer grid points thus saving computer time.time.

nn The grid independentThe grid independent--solution is less solution is less sensitive to a number of grid points.sensitive to a number of grid points.

GRID INDEPENENT GRID INDEPENENT SOLUTIONSSOLUTIONSnn Criterion for the gridCriterion for the grid--independent solution in the independent solution in the

simulation: simulation: ee=0.02 (n: number of grid points)=0.02 (n: number of grid points)

nn Along tube width, j=11Along tube width, j=11

nn Along tube length, k=4,001Along tube length, k=4,001

ε≤−

− n

nn

QQQ 2

1

IMPACT OF TUBE ASPECT RATIO IMPACT OF TUBE ASPECT RATIO ON THE THERMAL INTERACTION ON THE THERMAL INTERACTION ALONG THE COMMON FINALONG THE COMMON FIN

Impact of Aspect ratio - Water Tube

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0

x*qc

f (k

W) 1/6

1/8

1/16

Impact of Aspect ratio - Oil Tube

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0

x*

qcf

(kW

) 1/2

1/4

1/6

IMPACT OF TUBE ASPECT RATIO IMPACT OF TUBE ASPECT RATIO ON THE THERMAL INTERACTION AT ON THE THERMAL INTERACTION AT EACH TUBE LAYEREACH TUBE LAYER

Impact of Aspect ratio - Oil Tube

-100

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70

Tube layer

Q i

(kW

) 1/2

1/4

1/6

Impact of Aspect ratio - Water Tube

-100

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70

Tube layerQ

i (k

W) 1/6

1/8

1/16

IMPACT OF INTERNAL FLOW RATE IMPACT OF INTERNAL FLOW RATE ON THE THERMAL INTERACTION ON THE THERMAL INTERACTION ALONG THE COMMON FINALONG THE COMMON FIN

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.0 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0

x*

q cf

(kW

)

1 gal/min

2 gal/min

3 gal/min

4 gal/min

0.11

0.12

0.13

0.14

0.15

0.16

0.0 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0

x*

q cf

(kW

)

3000 l/h

4000 l/h

5000 l/h

6000 l/h

7000 l/h

IMPACT OF INTERNAL FLOW RATE IMPACT OF INTERNAL FLOW RATE ON THE THERMAL INTERACTION AT ON THE THERMAL INTERACTION AT EACH TUBE LAYEREACH TUBE LAYER

-100

0

100

200

300

400

1 11 21 31 41 51 61 71

Tube layer

Q i

(kW

)

1 gal/min

2 gal/min

3 gal/min

4 gal/min

-100

-50

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70

Tube layer

Q i

(kW

)

3,000 l/h

4,000 l/h

5,000 l/h

6,000 l/h

7,000 l/h

IMPACT OF TUBE ASPECT IMPACT OF TUBE ASPECT RATIO ON THE OVERALL HEAT RATIO ON THE OVERALL HEAT TRANSFER RATETRANSFER RATE

Impact of aspect ratio - oil tube

31.10

31.15

31.20

31.25

31.30

31.35

31.40

1/2 1/4 1/6

Aspect ratio of oil tube

Qw

ater

(kW

)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Qoi

l (k

W)

water cooler

oil cooler

Impact of aspect ratio - water tube

26.00

28.00

30.00

32.00

34.00

36.00

1/6 1/8 1/16

Aspect ratio of oil tube

Qw

ater

(kW

)2.5

2.5

2.5

2.5

2.5

2.5

2.6

2.6

2.6

Qoi

l (k

W)

water cooler

oil cooler

IMPACT OF INTERNAL FLOW IMPACT OF INTERNAL FLOW RATE ON THE OVERALL HEAT RATE ON THE OVERALL HEAT TRANSFER RATETRANSFER RATE

Impact of oil flow rate

31.25

31.25

31.26

31.26

31.27

31.27

31.28

31.28

1 2 3 4

Oil flow rate (gal/min)

Qw

ater

(kW

)

2.3

2.4

2.4

2.5

2.5

2.6

2.6

2.7

Qoi

l (k

W)

water cooler

oil cooler

Impact of water flow rate

29.8

30.0

30.2

30.4

30.6

30.8

31.0

31.2

31.4

31.6

31.8

3,000 4,000 5,000 6,000 7,000

Water flow rate (l/hr)

Qw

ater

(kW

)

2.5

2.5

2.5

2.5

2.5

2.5

2.6

Qoi

l (k

W)

water cooler

oil cooler

IMPACT OF FLOW DIRECTION IMPACT OF FLOW DIRECTION ON THE OVERALL HEAT ON THE OVERALL HEAT TRANSFER RATETRANSFER RATE

TUBE WALL TEMPERATURE TUBE WALL TEMPERATURE DISTRIBUTIONDISTRIBUTION

AIR TEMPERATURE AIR TEMPERATURE DISTRIBUTIONDISTRIBUTION

INTERNAL FLUID INTERNAL FLUID TEMPERATURE DISTRIBUTIONTEMPERATURE DISTRIBUTION

OPTIMIZATION OF OPTIMIZATION OF DESIGNDESIGNnn In automotive applications of multiIn automotive applications of multi--fluid heat fluid heat

exchangers, thermal interactions between heat exchangers, thermal interactions between heat exchangers are not favorable and must be avoided or exchangers are not favorable and must be avoided or minimized if possible.minimized if possible.

nn The tube aspect ratio has more impact on the overall The tube aspect ratio has more impact on the overall thermal interaction than the flow arrangement or the thermal interaction than the flow arrangement or the flow conditions of internal and external fluids.flow conditions of internal and external fluids.

nn However, further reduction of the aspect ratio of water However, further reduction of the aspect ratio of water tube will results in the higher internal pressure drop and tube will results in the higher internal pressure drop and require more pumping power to circulate the water. It is require more pumping power to circulate the water. It is sometimes not possible to increase the pumping power sometimes not possible to increase the pumping power in vehicular applications. in vehicular applications.

nn Therefore, the most efficient way to reduce the thermal Therefore, the most efficient way to reduce the thermal interaction is to optimize the surface geometries of interaction is to optimize the surface geometries of exchanger within an acceptable range of pressure drop. exchanger within an acceptable range of pressure drop.

IMPORTANCE OF IMPORTANCE OF ACCURACY EVALUATIONACCURACY EVALUATIONnn The new method is completely different from LMTD and The new method is completely different from LMTD and

ee--NtuNtu methods in that it first determines the methods in that it first determines the temperatures of tube walls and calculates overall heat temperatures of tube walls and calculates overall heat transfer rate using the wall temperatures.transfer rate using the wall temperatures.

nn Assumptions made for the simulation model Assumptions made for the simulation model development may introduce some errors into the development may introduce some errors into the calculations.calculations.

nn Therefore, the question about the accuracy of the Therefore, the question about the accuracy of the simulation model is inevitable.simulation model is inevitable.

nn The accuracy of the simulation model was defined byThe accuracy of the simulation model was defined by

where S and T denote the simulation and the where S and T denote the simulation and the experiment, respectively.experiment, respectively.

T

TSAccuracy

−−= 1

AVERAGE ACCURACYAVERAGE ACCURACY

nn The average accuracy of the simulation model: The average accuracy of the simulation model: 0.975. 0.975.

0.90

0.92

0.94

0.96

0.98

1.00

2.0 2.5 3.0 3.5 4.0 4.5 5.0

Air speed (m/sec)

Acc

urac

y

2,000 (l/hr) 5,000 (l/hr)

6,000 (l/hr) 7,000 (l/hr)

EVALUATION OF EVALUATION OF SIMULATION MODELSIMULATION MODEL

nn The assumptions used for the The assumptions used for the simulation model are reasonable.simulation model are reasonable.

nn The simulation model is capable of The simulation model is capable of predicting the heat performance of predicting the heat performance of heat exchangers that is accurate heat exchangers that is accurate enough for the initial product enough for the initial product development. development.

CONCLUSIONSCONCLUSIONS

nn The new method is capable of evaluatingThe new method is capable of evaluating–– The heat performance of multiThe heat performance of multi--fluid heat exchanger as fluid heat exchanger as

well as twowell as two--fluid heat exchangers.fluid heat exchangers.–– The heat transfer rate due to thermal interaction.The heat transfer rate due to thermal interaction.–– The different flow arrangement (coThe different flow arrangement (co-- and counterand counter--flow).flow).

nn The error of the new method is less than 6%, The error of the new method is less than 6%, which is accurate enough for initial product which is accurate enough for initial product development.development.

nn With knowledge of tube wall temperatures, the With knowledge of tube wall temperatures, the existence and the direction of the thermal existence and the direction of the thermal interaction can readily be determined using ZTGP.interaction can readily be determined using ZTGP.

RECOMMENDATIONS RECOMMENDATIONS -- II

nn The new method presents only the rating The new method presents only the rating problem that is concerned with the problem that is concerned with the determination of the heat transfer rates and determination of the heat transfer rates and the flow outlet temperatures.the flow outlet temperatures.

nn This new method involves some This new method involves some assumptions and simplifications and doesnassumptions and simplifications and doesn’’t t consider all the factors that need to be consider all the factors that need to be considered for a complete heat exchanger considered for a complete heat exchanger design. design.

RECOMMENDATIONS RECOMMENDATIONS -- IIII

nn Recommended to consider some other important factors:Recommended to consider some other important factors:–– Pressure drop limitation of each fluid, which determines Pressure drop limitation of each fluid, which determines

the pumping power.the pumping power.–– Influence of poor flow distribution on exchanger Influence of poor flow distribution on exchanger

performance. performance. –– Optimum distribution of thermal resistance and flowOptimum distribution of thermal resistance and flow--

friction power on surfaces.friction power on surfaces.–– Uncertainty of proper thermal contact between the Uncertainty of proper thermal contact between the

extended and prime surfaces.extended and prime surfaces.–– Thermal stress and construction problemsThermal stress and construction problems–– Allowance for fouling.Allowance for fouling.

nn Any or all of these factors may have a profound influence Any or all of these factors may have a profound influence on the complete design of a multion the complete design of a multi--fluid heat exchanger. fluid heat exchanger.