Ch13 HT Heat Exchangers(1)

8/12/2019 Ch13 HT Heat Exchangers(1)

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Heat Transfer

Heat ExchangersDr Abdul Hai Alami

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Topics Types of Heat Exchangers The Overall Heat Transfer Coefficient Analysis of Heat Exchangers The Log Mean Temperature Difference Method (LMTD) The Effectiveness: Number of Transfer Units (NTU) Method Selection of Heat Exchangers

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Introduction

Definition: devices that facilitate exchange of heat betweentwo fluids that are at different temperatures while keeping

them from mixing with each other

Heat exchangers differ from mixing chambers:they do notallow two fluids involved to mix.

In a car radiator heat is transferred from hot water flowing throughradiator tubes to air flowing through the closely spaced thin plates

outside attached to the tubes.

Heat transfer in a heat exchanger involves convectionineach fluid and conductionthrough wall separating them

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Types of heat exchangers Attempt to match heat transfer hardware to heat transfer

requirements within specified constraints: resulted in

numerous types of innovative heat exchanger designs.

Double-pipe Parallel flow Counter flow

Cross-flow Compact Shell-and-Tube One-shell pass, two tube passes (or more)

Plate and frame5

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Double-Pipe HE Simplest type of heat exchanger: consists of two concentric

pipes of different diameters.

One fluid in a double-pipe heat exchanger flows through thesmaller pipe while the other fluid flows through the annular

space between the two pipes.

Two types of flow arrangement are possible: Parallel flow: both hot and cold fluids enter heat exchanger at sameend and move in the same direction.

Counter flow: hot and cold fluids enter heat exchanger at oppositeends and flow in opposite directions

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Parallel-flow

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Counter-flow

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Compact HE Designed to realize large heat transfer surface area per unit

volume

Area Density, !: Ratio of heat transfer surface area of a heatexchanger to its volume.

A heat exchanger with != 700 m2/m3(or 200 ft2/ft3) isclassified as being compact.

Car radiators (!= 1000 m2

/m

3

),

Glass ceramic gas turbine heat exchangers (!= 6000 m2/m3) Regenerator of a Stirling engine (!= 15,000 m2/m3) Human lung (!= 20,000 m2/m3) !!!!!!!!!!!!!!!!!!

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Cross flow: mixed and unmixed

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Shell-and-Tube HE

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Shell-and-Tube HE Most common type of heat exchanger (although Not suitable

for use in automotive and aircraft applications because of their

relatively large size and weight.)

Construction: Large number of tubes(sometimes several hundred) packed in a shell

with their axes parallel to shell. Baffles: placed in shell to force shell-side fluid to flow across shell to

enhance heat transfer and to maintain uniform spacing between tubes.

Headers: at both ends of shell, tubes open to large flow areas called,where tube-side fluid accumulates before entering the tubes and after

leaving them (good buffer and stabilizer of flow)

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Shell-and-tube: further classes

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Plate-and-FrameSometimes called just (Plate)

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Operation Hotand coldfluids flow in alternate passages: each cold fluid

stream is surrounded by two hot fluid streams, resulting in very

effective heat transfer.

Plate HE grow with increasing demand for heat transfer: simplymount more plates.

Fluids do notmix: number of very thin corrugated stainless steel platesclamped together in a frame. Every second channel is open to same

fluid. Between each pair of plates there is a rubber gasket, preventingfluids from mixing and from leaking to the surroundings

Well suited for liquid-to-liquid heat exchange applications (nopulp), provided that hot and cold fluid streams are at same

pressure

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HE with specific names

Heat exchangers are given specific names to reflectspecific application for which they are used:

Condenser: heat exchanger in which one of fluids iscooled and condenses as it flows through the heat

exchanger.

Boiler: another heat exchanger in which one of fluidsabsorbs heat and vaporizes. Space radiator/heater: heat exchanger that transfers

heat from the hot fluid to the surrounding space by

radiation

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Overall heat transfer

coefficient, U

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U HE: involves two flowing fluids

separated by solid wall.

Heat is first transferred from hotfluid to wall by convection, through

the wall by conduction, and from

wall to cold fluid again by

convection(any radiation effects areincluded in convection heat transfer

coefficients)

Thermal resistance network: twoconvection and one conduction

resistances (iis inner and ois outer

tubes)18


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Double-tube geometry

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Ufor double pipe For: Ai= "DiLand Ao= "DoL, thermal resistance of tube wall is:

where kis thermal conductivity of wall material andLis length of tube. Total thermal resistance becomes:

Aiis area of inner surface of wall that separates two fluids, andAois areaof outer surface of wall (AiandAoare surface areas of separating wall

wetted by the inner and outer fluids, respectively.)

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Uis born! In analysis of heat exchangers: convenient to combine all

thermal resistances in heat flow path from hot fluid to cold

one into a single resistance R, and to express rate of heat

transfer between the two fluids as:

U: overall heat transfer coefficient, whose unit is W/m2!C(identical to unit of ordinary convection coefficient, h)

Cancel "T in above relation:

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Why two Us: Uiand Uofor a HE?

Every heat exchanger has two heat transfer surface areasAiandAo, which are not equal to each other (normally)

Note that UiAi=UoAo, but Ui#UounlessAi=Ao Uof a heat exchanger is meaningless unless the area on

which it is based is specified.

Especially the case when one side of tube wall is finned andother side is not: surface area of finned side is several times

that of unfinned side

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Small tube thickness When wall thickness of tube is small and thermal

conductivity of tube material is high (usually the case):

thermal resistance of tube is negligible (Rwall!0) and inner

and outer surfaces of tube are almost identical (Ai!Ao!As)

Overall heat transfer coefficient simplifies to: U !Ui!Uo Individual convection heat transfer coefficients inside and

outside tube, hiand ho, are determined using convection

relations

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Udominated by smaller h

Inverse of a large number is small: When one ofconvection coefficients is much smaller than the other

(e.g. hi"ho), we have 1/hi#1/ho, and thus U!hi.

Smallerheat transfer coefficient creates abottleneckonpath of heat flow and seriously impedes heat transfer.

Situation arises frequently when one of fluids is a gas and theother is liquid: finscommonly used on gas side to enhance theproduct U.Asand thus heat transfer on that side.

Overall heat transfer coefficient ranges from 10 W/m2!C forgas-to-gas heat exchangers to about 10,000 W/m2!C for heat

exchangers involving phase changes (since gases have very low

thermal conductivities, and phase-change processes involve very

high heat transfer coefficients)

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Representative values of U U ranges from 10 W/m2!C for gas-to-gas heat exchangers to about10,000 W/m2!C for heat exchangers involving phase changes.

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Finned tubes

When tube is finned on one side to enhance heat transfer,total heat transfer surface areaon finned side becomes:

Afin: surface area of fins.

Aunfinned: area of unfinned portion of tube surface.

Short fins of high thermal conductivity: use this total areain convection resistance relationRconv= 1/hAssince fins inthis case will be very nearly isothermal.

Otherwise: determine effective surface areaAfrom26


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Fouling Factor

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Fouling Factor Performance of heat exchangers deteriorates with time as a

result of accumulation of depositson heat transfer surfaces.

Fouling factorRf: Measure of the thermal resistanceintroduced by fouling

Fouling: Layer of deposits representing additionalresistance to heat transfer and causes rate of heat transfer ina heat exchanger to decrease

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Types of fouling Precipitationof solid deposits in a fluid on the heat transfer

surfaces (Calcium-based scale in kettles). Most common type.

To avoid this potential problem, waterin power and process plantsextensively treated and its solid contents removed before it is allowed to

circulate through system (solid ashparticles in flue gasesaccumulating on

surfaces of air preheaters create similar problems)

Corrosion(chemical fouling): common in the chemical processindustry, surfaces are fouled by accumulation of products of

chemical reactions on surfaces.

Fouling can be avoided by coating metal pipes with glass or using plasticpipes instead of metal ones.

Biological fouling: HE fouled by growth of algae in warm fluids, can beprevented by chemical treatment.

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Design for Fouling

Necessary to select a larger and thus more expensive heatexchanger to ensure it meets design heat transfer requirements

even after fouling occurs.

Periodic cleaning of heat exchangers and resulting down timeare additional penalties associated with fouling.

Fouling factor is zero for new heat exchanger and increaseswith time as solid deposits build up on heat exchanger surface. Fouling factor depends on: operating temperature, velocity of

fluids, and length of service.

Fouling increases with increasing temperature and decreasingvelocity.

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Ufouling Modify relations for U to include extra resistance introduced byfouling (on both inner and outer surfaces of tube)

For unfinned shell-and-tube heat exchanger, expressed as: Ai= "DiLandAo= "DoLare areas of inner and outer surfaces Rf,iandRf,o: fouling factors at inner and outer surfaces

Get representative fouling factors from tables (high uncertainty)

Most fouling factors in table are of order of 10-4m2!C/W, equivalent tothermal resistance of a 0.2-mm-thick limestone layer(k= 2.9 W/m!C) per

unit surface area.

In absence of specific data: assume surfaces to be coated with 0.2 mm oflimestone as starting point to account for effects of fouling.

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Fouling Factors

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Nusselt Number for tubes Laminar flow (fully developed):

Developing laminar flow

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Nusselt: Turbulent

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Example: Overall Heat TransferCoefficient of a Heat Exchanger Hot oil is to be cooled in a double-tube counter-flow heat

exchanger. The copper inner tubes have a diameter of 2 cm

and negligible thickness. The inner diameter of the outer tube

(the shell) is 3 cm. Water flows through the tube at a rate of

0.5 kg/s, and the oil through the shell at a rate of 0.8 kg/s.

Taking the average temperatures of the water and the oil to be

45C and 80C, respectively, determine the overall heat

transfer coefficient of this heat exchanger.

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Solution

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Solution

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Analysis of heat exchangers

HE design tasks: You are asked to either:1. Select a heat exchanger that will achieve a specified

temperature change in a fluid stream of known mass

flow rate

Use log mean temperature difference (or LMTD) method2. Predict outlet temperatures of the hot and cold fluid

streams in a specified heat exchanger.

Use effectivenessNTU method

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Assumptions in HE anaylsis HE operate for long periods of time with no change in their operating

conditions: be modeled as steady-flowdevices

Mass flow rate of each fluid remains constant, and fluid properties such (temperatureand velocity) at any inlet or outlet remain the same.

Fluid streams experience little or no change in their velocities andelevations, and thus kinetic and potential energy changes are negligible.

Specific heat of a fluid changes with temperature but can be treated as aconstant at some average value with little loss in accuracy.

Axial heat conduction along the tube is usually insignificant and can beconsidered negligible.

Outer surface of heat exchanger is assumed to be perfectly insulated, sothat there is no heat loss to the surrounding medium

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Thermodynamics of HE

First law of thermodynamics requires that rate of heat transferfrom hot fluidbe equal to rate of heat transfer to cold one:

Subscriptsc and h: cold and hot fluids, and: #c, #h= mass flow rates Cpc, Cph= specific heats Tc,out, Th,out= outlet temperatures Tc,in, Th,in= inlet temperatures

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Heat capacity rate, C Heat capacity rate of a fluid stream represents rate of heat

transfer needed to change temperature of the stream by 1C

as it flows through HE

The product of mass flow rate and specific heat of a fluidin a single quantity:

Ch= #hCphand Cc= #cCpc

In HE: fluid with largeheat capacity ratewill experiencesmalltemperature change, and fluid with a smallheat

capacity ratewill experience a largetemperature change

doublingthe mass flow rate of a fluid while leaving everythingelse unchanged will halve the temperature change of that fluid

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Heat equations and heat capacity Heat equations:

Only time temperature rise of cold fluidis equal to temperature drop ofhot fluidis when heat capacity rates of two fluids are equal

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Condensers and boilers One of fluids in a condenser or a boiler undergoes a phase-change process, and rate of heat transfer is:

#: rate of evaporation or condensation of fluid hfg: enthalpy of vaporization of fluid at specified temperature or pressure

During phase change: ordinary fluid absorbs or releases largeamount of heat essentiallyat constant temperature

Heat capacity rateof fluid during phase-change process: mustapproach infinity since temperature change is practically zero. That is, C= #Cp$%when $T$0, so that heat transfer rate Q=#Cp$T

remains finite quantity

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Model boiling and condensation as fluids

having %heat capacity rate

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HT in HE Use Newtons law of cooling:

U: overall heat transfer coefficient, As: heat transfer area (approximated by size of HE) $Tm: appropriate average temperature difference between two fluids

U: can be determined by using average convectioncoefficients for each fluid.

$Tbetween hot and cold fluids are notconstant and varyalong heat exchanger.

Appropriate form the mean temperature difference between the twofluids is logarithmic in nature

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Log Mean Temperature Difference

(LMTD) Method Consider parallel-flow double-

pipe heat exchanger

temperature difference "Tbetween hot and cold fluids is

large at inlet of heat exchangerbut decreases exponentially

toward outlet

Temperature of cold fluid cannever exceed that of hot fluid no

matter how long the heat

exchanger is.

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Energy balance Outer surface insulated, and neglecting PE and KE Using previous figure:

Rate of heat loss from hot fluid at any section of HE = rate ofheat gain by cold fluid in that section.

Temperature change of the hot fluid is a negative quantity, andso a negative sign is added

Solving equations above for dThand dTcgives:47

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Energy balance II Taking temperature difference Rate of heat transfer in differential section of heat

exchanger can also be expressed:

Substituting into temperature difference above, rearrange: Solving for #cCpcand #hCphand substituting:

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LMTD Where:

Here$T1and$T2: temperature difference between two fluidsat two ends (inlet and outlet) of heat exchanger.

Makes no difference which end of HE is designated as inlet or outlet

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Why log scale?

Temperature difference between two fluids decreases from$T1atinletto $T2at outlet:Tempting to use arithmetic mean temperature

$Tam= 1/2($T1+ $T2)as average temperature difference

Logarithmic mean temperature difference $Tlmis obtained bytracing actual temperature profileof fluids along heat exchanger

and is exact representation of average temperature differencebetween hot and cold fluids.It truly reflects the exponential

decay of the local temperature difference.

Note: $Tlmis always less than "Tam50


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Why log scale? using "Tamin calculations instead of "Tlmoverestimates rate of

heat transfer in a heat exchanger between the two fluids.

When "T1differs from "T2by no more than 40 % error in usingarithmetic mean temperature difference is less than 1%.

Error increases to undesirable levels when "T1differs from "T2by greater amounts

Should always use the logarithmic mean temperature differencewhen determining the rate of heat transfer in a heat exchanger

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Counter-Flow Heat Exchangers

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Hot and cold fluids enter HE fromopposite ends, and outlet temperature

of cold fluid mayexceed outlet

temperature of hot fluid.

limiting case: cold fluid will be heatedto inlet temperature of hot fluid.

Outlet temperature of cold fluid cannever exceed inlet temperature of hotfluid (violates second law of

thermodynamics)

LMTD works with CF HE, just note"T1and "T2are calculated from T

diagram above


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Counter flow vs. Parallel flow For specified inlet and outlet temperatures, LMTD for a

counter-flow heat exchanger is alwaysgreaterthan that for a

parallel-flow heat exchanger.

That is:$Tlm,CF>$Tlm,PF: smaller surface area (and thus a smallerheat exchanger) needed to achieve a specified heat transfer rate in a

counter-flow heat exchanger.

Common practice to use counter-flow arrangements in heat exchangers For counter-flow heat exchanger, temperature difference

between hot and cold fluids remains constant along heat

exchanger when heat capacity rates of two fluids are equal:

("T= constantwhen Ch= Ccor&hCph= &cCpc).

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Multipass and Cross-Flow Heat Exchangers:

Use of a Correction Factor

LMTD $Tlmrelation is limited to parallel-flow and counter-flow heat exchangers only.

Similar relations are developed for cross-flow and multipass shell-and-tube heat exchangers, but resulting expressions are too complicated

because of complex flow conditions

Convenient to relate equivalenttemperature difference to logmean temperature differencerelation for counter-flow caseas:

F: correction factor (depends on geometry of HE and the inlet andoutlet temperatures of hot and cold fluid streams).

$Tlm,CF: LMTD for counter-flow heat exchanger [$Tl= Th,in- Tc,out]and [$T2= Th,out-Tc,in]

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Multipass and Cross-Flow Heat Exchangers:Use of a Correction Factor

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Correction factor,F Correction factor is less than unity for cross-flow and

multipass shell- and-tube heat exchanger, F '1.

Limiting value of F= 1 corresponds to counter-flow heat exchanger.Thus,Ffor HE is a measure of deviation of the "Tlmfrom the

corresponding values for counter-flow case.

The correction factorFfor common cross-flowand shell-and-tubeHE configurations is given in Figure, versus twotemperature ratios P and R defined as:

Subscripts 1 and 2 represent inlet and outlet, respectively. Shell-and-tube heat exchanger, Tandtrepresent the shell- and tube-

side temperatures, respectively

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Correction factor Makes no difference hot or the cold fluid flows through

the shell or the tube.

Determination of correction factor F requiresavailabilityof inlet and outlet temperatures for both cold and hot

fluids.

Note that value ofPranges from 0 to 1. Value of R ranges from 0 to infinity ( R= 0corresponding to the

phase-change (condensation or boiling) on shell-sideand R $%to

phase-change ontube side.

Correction factor is F= 1 for both of these limiting cases.(correction factor for a condenser or boiler is F = 1, regardless of

the configuration of the heat exchanger)

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Example

Steam in the condenser of a power plant is to be condensedat a temperature of 30C with cooling water from a nearby

lake, which enters the tubes of the condenser at 14C and

leaves at 22C. The surface area of the tubes is 45 m2, and

the overall heat transfer coefficient is 2100 W/m2!C.

Determine themass flow rate of the cooling water needed

and the rate of condensation of the steamin the condenser.

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Solution

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Example II A counter-flow double-pipe heat exchanger is to heat water

from 20C to 80C at a rate of 1.2 kg/s. The heating is to be

accomplished by geothermal water available at 160C at a

mass flow rate of 2 kg/s. The inner tube is thin-walled and has

a diameter of 1.5 cm. If the overall heat transfer coefficient of

the heat exchanger is 640 W/m2!C, determine the length of the

heat exchanger required to achieve the desired heating.

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Solution

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Example III A 2-shell passes and 4-tube passes heat exchanger is used to heat

glycerin from 20C to 50C by hot water, which enters the thin-

walled 2-cm-diameter tubes at 80C and leaves at 40C. The total

length of the tubes in the heat exchanger is 60 m. The convection

heat transfer coefficient is 25 W/m2!C on the glycerin (shell) side

and 160 W/m2!C on the water (tube) side. Determine the rate of

heat transfer in the heat exchanger (a) before any fouling occurs

and (b) after fouling with a fouling factor of 0.0006 m2!C/ W

occurs on the outer surfaces of the tubes.

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Solution

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LMTD procedure

LMTD method: very suitable for determining sizeof HE to realizeprescribed outlet temperatureswhen mass flow rates and inlet and

outlet temperatures of hot and cold fluids are specified.

With LMTD method: task is to selecta heat exchanger that willmeet prescribed heat transfer requirements.

Procedure to be followed: Select type of heat exchanger suitable for the application. Find unknown inlet or outlet temperature and HT rate using energy balance. Calculate log mean temperature difference "Tlmand correction factor F Obtain (select or calculate) value of overall heat transfer coefficient U. Calculate the heat transfer surface area As

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Effectiveness-NTU Method If determination of heat transfer rateand outlet

temperatures of the hot and cold fluidsfor prescribed fluid

mass flow rates and inlet temperatures when the type and

size of the heat exchanger are specified.

The heat transfer surface area A of heat exchanger in thiscase is known, but outlet temperatures are not.

Task: determine heat transfer performance of a specifiedheat exchangerorto determine if a heat exchangeravailable in storage will do the job.

LMTD method can still be used for this alternativeproblem, but procedure would require tedious iterations,

and thus it is not practical

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NTU method formulation To eliminate iterations from the solution of HT rate without

knowing outlet temperatures,KaysandLondoncame up with a

method in 1955 called effectivenessNTU method, greatly

simplified heat exchanger analysis.

This method is based on a dimensionless parameter called theheat transfer effectiveness (, defined as

actual HT rate in HE can be determined from an energybalance on hot or cold fluids and can be expressed as:

Cc= #cCpcand Ch= #cCphare heat capacity rates of cold and hot fluids68


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NTU method formulation Maximum possible heat transfer ratein HE: maximum

temperature difference is difference between inlet temperatures

of hot and cold fluids:

HT in HE will reach its maximum value when: Cold fluid is heated to inlet temperature of hot fluid Hot fluid is cooled to inlet temperature of cold fluid. Two limiting conditions will not be reached simultaneouslyunless heat capacity rates of hot and cold fluids are identical

(i.e., Cc= Ch)

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NTU method formulation WhenCc#Ch(usually case): fluid with smaller heat capacity

rate will experience a larger temperature change, and it will be

the first to experience maximum temperature, at which point the

heat transfer will come to a halt.

Maximum possible heat transfer rate in a heat exchanger is Cmin is the smallerofCc= #cCpcand Ch= #cCph

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Example Cold water enters a counter-flow heat exchanger at 10C ata rate of 8 kg/s, where it is heated by a hot water stream that

enters the heat exchanger at 70C at a rate of 2 kg/s.

Assuming the specific heat of water to remain constant at

Cp = 4.18 kJ/kg!C, determine the maximum heat transfer

rate and the outlet temperatures of the cold and the hot water

streams for this limiting case.

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Solution

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Finding maximum Q. Determination of Q!max requires availability of inlet

temperature of the hot and cold fluids and their mass flow

rates(usually specified)

Then, once effectiveness of heat exchanger is known,actual heat transfer rate Q!can be determined from:

Effectiveness of HE enables us to determine heat transferrate withoutknowing outlet temperatures of fluids Effectiveness of HE depends on geometryof HE as well

as flow arrangement(different types of heat exchangers

have different effectiveness relations)

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Effectiveness, (, development Effectiveness, (, relation for double-pipe parallel-flow heat

exchanger: from LMTD equations:

Solving for Th,out: Rearranging Which simplifies to:

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Manipulate the definition of effectiveness to obtain solving for (gives the following relation for effectiveness of a

parallel-flow HE:

Taking either Ccor Chto be Cmin(both approaches give sameresult), relation above can be expressed more conveniently as:

Effectiveness, (, development

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Number of transfer units NTU

Effectiveness relations of HE typically involve dimensionlessgroup UAs/Cmin. This quantity is: number of transfer units

NTU and is expressed as

U: overall heat transfer coefficient,As: heat transfer surface area of HE. NTU is proportional to As: for specified values of U and Cmin, value of

NTU is measure of the heat transfer surface area As(larger NTU, the

larger heat exchanger)

Convenient to define another dimensionless quantity calledthe capacity ratio,c:

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(=f(UAs/Cmin, Cmin/Cmax) =f(NTU, c)

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Better than graphs

(no reading errors)

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Graphical form

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Graphical form

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Graphical form

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observations from effectiveness relations andcharts Value of the effectiveness ranges from 0 to 1:

Increases rapidly with NTU for small values (up to about NTU=1.5) but rather slowly for larger values.

Use of a heat exchanger with a large NTU (usually larger than 3)and thus a large size cannot be justified economically, since a large

increase in NTU in this case corresponds to a small increase in

effectiveness.

A heat exchanger with a very high effectiveness may be highlydesirable from a heat transfer point of view but rather undesirablefrom an economical point of view.

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observations from effectiveness relations and

charts For a given NTU and capacity ratio c= Cmin/Cmax, counter-flowheat

exchanger has highest effectiveness, followed closely by cross-flow

heat exchangerswith both fluids unmixed (lowest effectiveness values

are encountered in parallel-flow heat exchangers)

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observations from effectiveness relations andcharts The effectiveness of a heat exchanger is independent of capacity ratio

cfor NTU values of less than about 0.3.

Value of capacity ratio c ranges between 0 and 1, for a given NTU,effectiveness becomes a maximum for c= 0 and a minimum for c= 1.

The case c = Cmin/Cmax$0 corresponds to Cmax $%, which isrealized during a phase-change process in a condenser or boiler. All

effectiveness relations in this case reduce to (regardless of the type of

heat exchanger)

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Determination of temps and HT

Once the quantities c= Cmin/CmaxandNTU= UAs/Cminhavebeen evaluated, effectiveness (can be determined from

either charts or (preferably) effectiveness relation for

specified type of heat exchanger.

Then the rate of heat transfer Q!and the outlet temperaturesTh, out and Tc, out can be determined from

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Determination of temps and HT When all inlet and outlet temperatures are specified, sizeof

heat exchanger can easily be determined using LMTD

method.

Alternatively, it can also be determined from effectivenessNTU method by first evaluating the effectiveness (from its

definition and then the NTU from the appropriate NTU

relation in tables (given for NTUf(() next)

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Dr Abdul Hai Alami

NTUf(()

86

Same as previous but here

NTUf(()


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Dr Abdul Hai Alami

Example, use NTU A counter-flow double-pipe heat exchanger is to heat waterfrom 20C to 80C at a rate of 1.2 kg/s. The heating is to be

accomplished by geothermal water available at 160C at a

mass flow rate of 2 kg/s. The inner tube is thin-walled and has

a diameter of 1.5 cm. If the overall heat transfer coefficient of

the heat exchanger is 640 W/m2!C, determine the length of the

heat exchanger required to achieve the desired heating.

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Dr Abdul Hai Alami

Solution

88


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Example II Hot oil is to be cooled by water in a 1-shell-pass and 8-tube-passesheat exchanger. The tubes are thin-walled and are made of copper with

an internal diameter of 1.4 cm. The length of each tube pass in the heat

exchanger is 5 m, and the overall heat transfer coefficient is 310 W/m2

!C. Water flows through the tubes at a rate of 0.2 kg/s, and the oil

through the shell at a rate of 0.3 kg/s. The water and the oil enter at

temperatures of 20C and 150C, respectively. Determine the rate of

heat transfer in the heat exchanger and the outlet temperatures of the

water and the oil.

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Dr Abdul Hai Alami

Solution

90

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Ch13 HT Heat Exchangers(1)