design & construction of libr_h2o machine

Design and construction of a LiBrwater absorption machine

G.A. Florides a, S.A. Kalogirou a,*, S.A. Tassou b, L.C. Wrobel b

a Department of Mechanical Engineering, Higher Technical Institute, P.O. Box 20423, Nicosia 2152, Cyprusb Department of Mechanical Engineering, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK

Received 22 July 2002; accepted 11 December 2002

Abstract

The objective of this paper is to present a method to evaluate the characteristics and performance of a

single stage lithium bromide (LiBr)water absorption machine. The necessary heat and mass transfer

equations and appropriate equations describing the properties of the working uids are specied. These

equations are employed in a computer program, and a sensitivity analysis is performed. The dierence

between the absorber LiBr inlet and outlet percentage ratio, the coecient of performance of the unit in

relation to the generator temperature, the eciency of the unit in relation to the solution heat exchangerarea and the solution strength eectiveness in relation to the absorber solution outlet temperature are

examined. Information on designing the heat exchangers of the LiBrwater absorption unit are also pre-

sented. Single pass, vertical tube heat exchangers have been used for the absorber and for the evaporator.

The solution heat exchanger was designed as a single pass annular heat exchanger. The condenser and the

generator were designed using horizontal tube heat exchangers. The calculated theoretical values are

compared to experimental results derived for a small unit with a nominal capacity of 1 kW. Finally, a cost

analysis for a domestic size absorber cooler is presented.

2003 Elsevier Science Ltd. All rights reserved.

Keywords: Absorption cooling; Lithium bromide; Sensitivity analysis; Heat exchangers

1. Introduction

In hot climates, the heating and cooling demand of domestic dwellings can be reduced sub-stantially with various measures such as good insulation, double glazing, use of thermal mass andventilation. However, due to the high summer temperatures, the cooling demand cannot be re-duced to the level of thermal comfort with passive and low energy cooling techniques, and

Energy Conversion and Management 44 (2003) 24832508www.elsevier.com/locate/enconman

*Corresponding author. Tel.: +357-22-406466; fax: +357-22-494953.

E-mail address: [email protected] (S.A. Kalogirou).

0196-8904/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0196-8904(03)00006-2

Nomenclature

A total heat transfer area (m2)CIN solution inlet concentration (mass fraction)COUT solution outlet concentration (mass fraction)CEQ solution equilibrium concentration (mass fraction) XEQ=100Di, Do inside and outside diameters of tube, respectively (m)f factor equal to: 1:82 log10 ReD 1:642F correction factor depending on type of the heat exchangerFi, Fo fouling factors at inside and outside surfaces of tube (m2 K/W)g gravitational acceleration (m/s2)hi, ho heat transfer coecients for inside and outside ow, respectively (W/m2 K)hfg latent heat of condensation (kJ/kg)hm average heat transfer coecient (W/m2 K)hs solution convective heat transfer coecient (W/m2 K)k thermal conductivity of tube material, solution thermal conductivity (W/mK)K1 factor equal to: 1 3:4fK2 factor equal to: 11:7 1:8=Pr1=3kl thermal conductivity of liquid (W/mK)M mass ow rate (kg/s)NuD Nusselt number hiDi=KP pressure (Pa)Pr Prandtl numberPrs solution Prandtl numberRe solution Reynolds number for vertical tubeReD Reynolds number VmDi=m 4m=pDilU average overall heat transfer coecient (W/m2 K)Vm mean velocity (m/s)Tv vapour saturation temperature (C)Tw wall surface temperature (C)X concentration of LiBr in solution (%)

Greek symbolsC mass ow rate per wetted perimeter (kg/m s)d lm thickness (m)DTln logarithmic mean temperature dierence (LMTD) (K)DT0 temperature dierence between hot and cold uid at inlet (K)DTL temperature dierence between hot and cold uid at outlet (K)q density (kg/m3)ql liquid density (kg/m

3)qv vapour density (kg/m

3)l dynamic viscosity (N s/m2) mq

2484 G.A. Florides et al. / Energy Conversion and Management 44 (2003) 24832508

therefore, an active cooling system is required. It is preferable that such a system is not poweredby electricity, the production of which depends entirely on fuel.Solar energy, which is available in such climates, could be used to power an active cooling

system based on the absorption cycle. Lithium bromide (LiBr)water absorption units are themost suitable for solar applications, since low cost solar collectors may be used to power thegenerator of the machine. Such absorption units though, are not yet readily available in smallresidential sizes. After a search in the world market, only one manufacturer was found com-mercially producing LiBrwater absorption refrigerators (Yazaki of Japan). Therefore, the pos-sibility of producing absorption air conditioning systems in small sizes for residential buildingsand the economics of using such a refrigerator, assisted by solar energy, needs to be investigated.The objective of this paper is to present a method to evaluate the characteristics and perfor-

mance of a single stage LiBrwater absorption machine. The necessary heat and mass transferequations and appropriate equations describing the properties of the working uids are specied.These equations are employed in a computer program, and a sensitivity analysis is performed.Information on designing the heat exchangers of the LiBrwater absorption unit is also presented.Single pass, vertical tube heat exchangers have been used for the absorber and for the evaporator.The solution heat exchanger was designed as a single pass annular heat exchanger. The condenserand the generator were designed using horizontal tube heat exchangers. The calculated theoreticalvalues are compared to experimental results derived for a small unit with a nominal capacity of1 kW. Finally, a cost analysis for a domestic size absorber cooler is presented.

2. Absorption cooling

Absorption machines are thermally activated, and for this reason, high input (shaft) power isnot required. In this way, where power is expensive or unavailable, or where there is waste, gas,geothermal or solar heat available, absorption machines provide reliable and quiet cooling [1]. Anumber of refrigerantabsorbent pairs are used, for which the most common ones are LiBrwaterand ammoniawater. These two pairs oer good thermodynamic performance, and they are en-vironmentally benign.Absorption refrigeration system uid pairs should meet a number of important requirements,

which are [1]:

1. Absence of solid phaseThe refrigerantabsorbent pair should not form a solid phase over therange of composition and temperature to which it will be subjected. The formation of solidsmay stop the ow and cause problems to the equipment.

2. Volatility ratioThe refrigerant should be more volatile than the absorbent so that it can beseparated easily by heating.

ll absolute viscosity of liquid (N s/m2)

m kinematic viscosity (m2/s)

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 24832508 2485

3. AnityThe absorbent should have a strong anity with the refrigerant under the conditionsin which absorption takes place. This anity allows less absorbent to be circulated for the samerefrigerating eect, and therefore, sensible heat losses are less. Also, a smaller liquid heat ex-changer is required to transfer heat from the absorbent to the pressurised refrigerantabsorbentsolution. A disadvantage is that extra heat is required in the generator to separate the refrige-rant from the absorbent.

4. PressureModerate operating pressures should be used in order to avoid the use of heavy-walled equipment and reduce the electrical power required to pump the uids from the lowpressure side to the high pressure side. Also, very low pressure (vacuum) will require the useof large volume equipment and special means of reducing pressure drop in the refrigerant va-pour ow.

5. StabilityHigh chemical stability is required to avoid the undesirable formation of gases, solidsor corrosive substances.

6. CorrosionThe uids should be non-corrosive. If the uids are corrosive, corrosion inhibitorsshould be used, which may inuence the thermodynamic performance of the equipment.

7. SafetyIdeally, the uids must be non-toxic and non-inammable.8. Latent heatTo keep the circulation rate of the refrigerant and absorbent at a minimum, the

latent heat of the refrigerant should be as high as possible.

The ammoniawater pair is not suitable for use with solar collectors because of the hightemperature needed in the generator (125170 C). This temperature can only be obtained withmedium concentration ratio parabolic collectors, which have increased maintenance requirementsdue to the need for tracking the sun.The generator temperatures needed for the LiBrwater pair are lower (75120 C). These

temperatures can be achieved with high performance at plate collectors, compound paraboliccollectors and evacuated tube collectors that are of lower cost and easier to install and operatethan medium concentration ratio parabolic collectors.

3. Lithium bromidewater cooling

This type of equipment is classied by the method of heat input to the primary generator (ringmethod) and whether the absorption cycle is single or multiple eect. The single eect absorptiontechnology provides a peak cooling coecient of performance (COP) of approximately 0.7 andoperates with heat input temperatures in the range of 75120 C. The multiple eect technologygives higher COPs but can only be utilised when higher temperature heat sources are available.Double eect systems can be achieved by adding an extra stage as a topping cycle on the singleeect cycle. In this way, the heat rejection from the high temperature stage is used to power thelower temperature stage. It should be noted that the refrigerant in the LiBrwater system is waterand the LiBr acts as the absorbent, which absorbs the water vapour, thus making pumping fromthe absorber to the generator easier and economic. A single eect LiBrwater chiller is illus-trated in Fig. 1, and its schematic presentation on a pressuretemperature diagram is illustrated inFig. 2.


A. RehmanHighlight

With reference to the numbering system shown in Fig. 1, at point (1), the solution is rich inrefrigerant and a pump (2) forces the liquid through a heat exchanger to the generator (3). Thetemperature of the solution in the heat exchanger is increased.

EXPANSION VALVE

GENERATOR

CONDENSER

SOLUTION HEAT

EXCHANGER

PUMP

ABSORBEREVAPORATOR

1

10,11

6

5

4

3

2

8

7

9

Fig. 1. Single eect, LiBrwater absorption cycle.

CONDENSER GENERATOR

SOLUTION HEAT EXCHANGER

ABSORBEREVAPORATOR

Qe Qa

QgQc

PUMPSOLUTION FLOW RESTRICTOR

REFRIGERANT FLOW RESTRICTOR

TEMPERATURE

PRESSURE

10

11

8

9

7 3 4

52

1 6

Fig. 2. Two shell, LiBrwater cycle cooling system [1].


In the generator, thermal energy is added and the refrigerant boils o the solution. The re-frigerant vapour (7) ows to the condenser, where heat is rejected as the refrigerant condenses.The condensed liquid (8) ows through a ow restrictor to the evaporator (9). In the evaporator,the heat from the load evaporates the refrigerant, which ows back to the absorber (10). A smallportion of the refrigerant leaves the evaporator as liquid spillover (11). At the generator exit (4),the uid consists of the absorbentrefrigerant solution, which is cooled in the heat exchanger.From points (6)(1), the solution absorbs refrigerant vapour from the evaporator and rejects heatthrough a heat exchanger.The above procedure can also be presented in a Duhring chart (Fig. 3). This chart is a pressure

temperature graph where the diagonal lines represent constant LiBr mass fraction, with the purewater line at the left and crystallisation line at the right.

4. Design of a single eect lithium bromidewater absorption cycle system

To perform estimations of equipment sizing and performance evaluation of a single-eect LiBrwater absorption cooler, basic assumptions and input values must be considered. With referenceto Figs. 13, the basic assumptions are:

1. The steady state refrigerant is pure water.2. There are no pressure changes except through the ow restrictors and the pump.3. At points 1, 4, 8 and 11, there is only saturated liquid.4. At point 10, there is only saturated vapour.5. Flow restrictors are adiabatic.6. The pump is isentropic.7. There are no jacket heat losses.

The method of design is demonstrated below. The design parameters considered are listed inTable 1.

CRYSTALLIS-ATION LINE

PURE WATERLINE

WEAKABSORBENTLINE

PRESSURE

STRONG ABSORBENTLINE

9,10 1,25

6

38 4

7

TEMPERATURE

Fig. 3. Duhring chart of the LiBrwater absorption cycle [1].


4.1. Evaporator analysis

Since, in the evaporator, the refrigerant is saturated water vapour and the temperature T10 isassumed to be 6 C, the saturation pressure at point 10, as calculated from curve ts [2] presentedin Appendix A, is 0.934 kPa, and the enthalpy is 2511.8 kJ/kg. Since, at point 11, the refrigerant issaturated liquid, its enthalpy is 23.5 kJ/kg. The enthalpy at point 9 is determined from thethrottling process applied to the refrigerant ow restrictor, which yields that h9 h8: To deter-mine h8, the pressure at this point must be determined. Since, at point 4, the solution mass fractionis 60% LiBr and the temperature at the saturated state was assumed to be 90 C, the LiBr gives asaturation pressure of 9.66 kPa and h4 212:2 kJ/kg. Considering that the pressure at point 4 isthe same as in point 8, then h8 h9 185:3 kJ/kg.Once the enthalpy values at all ports connected to the evaporator are known, mass and energy

balances can be applied to give the mass ow of the refrigerant and the evaporator heat transferrate.The mass balance on the evaporator is:

_mm9 _mm10 _mm11 1The energy balance on the evaporator is:

_QQe _mm10h10 _mm11h11 _mm9h9 2Since the evaporator output power _QQe is 10.0 kW and _mm11 2:5% _mm10 the mass ow rates can becalculated. The results are shown in Table 2.

4.2. Absorber analysis

Since the values of _mm10 and _mm11 are known, mass balances around the absorber give:

_mm1 _mm10 _mm11 _mm6 3and

x1 _mm1 x6 _mm6 4

Table 1

Design parameters for the single eect LiBrwater absorption cooler

Parameter Symbol Example-value

Capacity _QQe 10 kWEvaporator temperature T10 6 CGenerator solution exit temperature T4 90 CWeak solution mass fraction X1 55% LiBrStrong solution mass fraction X4 60% LiBrSolution heat exchanger exit temperature T3 65 CGenerator (desorber) vapour exit temperature T7 85 CLiquid carryover from evaporator _mm11 0:025 _mm10


The mass fractions x1 and x6 in Eq. (4) are inputs, and therefore, _mm1 and _mm6 can be calculated. Theresults are shown in Table 2.The heat transfer rate in the absorber can be determined from the enthalpy values at each of the

connected state points. At point (1), the enthalpy is determined from the input mass fraction(55%) and the assumption that the state is saturated liquid at the same pressure as the evaporator(0.934 kPa). This value is h1 83 kJ/kg. The enthalpy value at point 6 is determined from thethrottling model, which gives h6 h5.The enthalpy at point 5 is not known but can be determined from the energy balance on the

solution heat exchanger, assuming an adiabatic shell as follows:

_mm2h2 _mm4h4 _mm3h3 _mm5h5 5The temperature at point 3 is an input value (65 C), and since the mass fraction for points 1 to 3is the same, the enthalpy at this point is determined as 145.4 kJ/kg. Actually, the state at point 3may be subcooled liquid. However, at the conditions of interest, the pressure has an insignicanteect on the enthalpy of the subcooled liquid, and the saturated value at the same temperatureand mass fraction can be an adequate approximation. The enthalpy at point 2 is determined froman isentropic pump model. The minimum work input w can, therefore, be obtained from:

w _mm1v1p2 p1 6In Eq. (6), it is assumed that the specic volume (v, m3/kg) of the liquid solution does not changeappreciably from point (1)(2). The specic volume of the liquid solution can be obtained from acurve t [3] (see Appendix A).For the present study, since all variables are known (Table 2), the pump power can be calcu-

lated as:

w 0:29 WEq. (5) can now be solved for the unknown enthalpy value at point 5, giving h5 144:2 kJ/kg. Thetemperature at point 5 can also be determined from the enthalpy value and is 54.8 C.

Table 2

Data for single eect LiBrwater cooling system

Point # h (kJ/kg) _mm (kg/s) p (kPa) T (C) X (%LiBr) Remarks1 83 0.053 0.934 34.9 55

2 83 0.053 9.66 34.9 55

3 145.4 0.053 9.66 65 55 Sub-cooled liquid

4 212.2 0.0486 9.66 90 60

5 144.2 0.0486 9.66 54.8 60

6 144.2 0.0486 0.934 44.5 60

7 2628 0.0044 9.66 85 0 Superheated steam

8 185.3 0.0044 9.66 44.3 0 Saturated liquid water

9 185.3 0.0044 0.934 6 0

10 2511.8 0.0043 0.934 6 0 Saturated vapour

11 23.5 0.00011 0.934 6 0 Saturated liquid water


A. RehmanHighlight

Finally, the energy balance on the absorber is:

_QQa _mm10h10 _mm11h11 _mm6h6 _mm1h1 7which gives _QQa 13:42 kW.

4.3. Generator (desorber) analysis

The heat input to the generator is determined from the energy balance, which is:

_QQg _mm4h4 _mm7h7 _mm3h3 8and results in: _QQg 14:2 kW.The enthalpy at point 7 can be determined, since the temperature at this point is an input value.

In general, the state at point 7 will be superheated water vapour, and the enthalpy can be de-termined once the pressure and temperature are known.

4.4. Condenser analysis

The condenser heat can be determined from an energy balance, which gives:

_QQc _mm7h7 h8 9and therefore, _QQc 10:78 kW.

4.5. Coecient of performance

The COP is dened as:

COP _QQe_QQg

10

which gives a value of 0.704.A summary of the energy ows at the various components of the system is given in Table 3.To nd suitable conditions for specic applications, a sensitivity analysis can be performed

utilising a computer program, which follows the sequence described above and the mathematical

Table 3

Energy ows at the various components of the system

Description Symbol kW

Capacity (evaporator output power) _QQe 10.0Pump minimum work input w 0.29Absorber heat, rejected to the environment _QQa 13.42Heat input to the generator _QQg 14.2Condenser heat, rejected to the environment _QQc 10.78Coecient of performance COP 0.704


correlations for the uid properties shown in Appendix A. Such a sensitivity analysis is presentedbelow.

4.6. Sensitivity analysis

4.6.1. Eect of absorber inlet LiBr percentage ratioTo check this eect, the following conditions were assumed:

1. Solution heat exchanger exit temperature, T3 55 C.2. Generator solution exit temperature, T4 75 C.3. Condenser temperature, T7 70 C.4. Evaporator capacity 10 kW.5. Evaporator temperature 6 C.6. Absorber exit LiBr percentage ratio 60%.7. Pressure in generator and condenser 4.82 kPa.8. Pressure in absorber and evaporator 0.934 kPa.

Since the absorber exit LiBr percentage ratio is kept constant at 60%, the greater the dierencebetween the absorber LiBr inlet and outlet percentage ratios is, the smaller will be the mass cir-culating in the absorber. Additionally, as seen in Fig. 4, the COP increases with decreasing pumpmass ow. On the other hand, to keep the cycle running at the specied stage, the temperature atthe exit of the absorber has to be maintained at a lower level. However, this presents dicultieswith the cooling water temperature of the absorber heat exchanger. Normally, this temperaturemay be between 20 and 25 C, which means that the lowest temperature at the exit of the absorberwould be around 30 C.

0

5

10

1520

2530

35

40

45

45 47.5 50 52.5 55 57.500.10.20.30.40.50.60.70.80.91

Absorber inlet LiBr percentage

Abs

orbe

r ex

it te

mpe

ratu

re (

C)

Pum

p m

ass f

low

(kg/s

) and

COP

Absorper exit tempPump mass flowCOP

Fig. 4. Eect of absorber inlet LiBr percentage ratio.


4.6.2. Eect of generator temperature

To check this eect, the following conditions were assumed:

1. Solution heat exchanger exit temperature, T3 55 C.2. Evaporator capacity 10 kW.3. Evaporator temperature 6 C.4. Absorber inlet LiBr percentage ratio 52.5%.5. Absorber exit LiBr percentage ratio 60%.6. Absorber exit temperature, T1 30:4 C.7. Pressure in absorber and evaporator 0.934 kPa.

As seen in Fig. 5, when the generator temperature is increased, the generator pressure isalso increased, and this has the eect of lowering the COP of the unit, considering that the pressuresand temperatures at other points of the unit are kept constant. The pump mass ow changesslightly from 0.04 kg/s at a generator exit temperature of 65 C to 0.037 kg/s at 115 C.

4.6.3. Eect of heat exchanger temperatures

To check this eect, the following conditions were assumed:

1. Evaporator capacity 10 kW.2. Evaporator temperature 6 C.3. Pressure in generator and condenser 4.82 kPa.4. Absorber inlet LiBr percentage ratio 52.5%.5. Absorber exit LiBr percentage ratio 60%.6. Absorber exit temperature, T1 30:4 C.7. Pressure in absorber and evaporator 0.934 kPa.

The solution heat exchanger increases the eciency of the unit. The greater the heat exchangerarea is, the greater its eect will be, since useful energy can be extracted from the generator so-lution fed to the absorber and be transferred to the solution returning to the generator, where it

0

4

8

12

16

20

24

28

65 70 75 80 85 90 95 100 105 110 115Generator exit temperature, T4 (C)

Gen

era

tor

pres

sure

(kPa

)

00.10.20.30.40.50.60.70.80.9

Pum

pm

ass

flow

(kg/

s)a

nd

CO

P

Generator pressure

Pump mass flow

COP

Fig. 5. Eect of generator temperature.


will be heated to the evaporating point. As is observed in Fig. 6, the COP of the unit under thespecied conditions is increased from 0.72 to a maximum of 0.84.

4.6.4. Eect of solution strength

To check the solution strength eectiveness, a constant dierence of 6% between the absorberinlet LiBr percentage ratio and absorber outlet ratio was considered. Also, the following condi-tions were assumed:

1. Evaporator capacity 10 kW.2. Evaporator temperature 6 C.3. Generator solution exit temperature, T4 75 C.

0

10

20

30

40

50

60

70

80

0.7 2 0.74 0.76 0.78 0.8 0.82 0.84

COP

Tem

pera

ture

C

Generator exit solution tempAbsorber inlet solution tempAbsorber oulet solution tempGenerator inlet solution temp

Fig. 6. Eect of heat exchanger temperatures.

0

10

20

30

40

50

60

70

52 54 56 58 60 62 640

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

absorber inlet LiBr%Generator pressureAbsorber exit tempCOPPump mass flow P

ump

mas

s flo

w (k

g/s) -

COP

Tem

pera

ture

(C

) - Pr

essur

e kPa

Absorber exit LiBr percentage ratio

Fig. 7. Eect of solution strength.


4. Solution heat exchanger exit temperature, T3 55 C.5. Pressure in absorber and evaporator 0.934 kPa.

The results shown in Fig. 7 indicate that a smaller percentage ratio in LiBr solutions will haveslightly better results, since the solution will absorb the extra water vapour more readily. The COPfor the selected conditions will vary from 0.79 to 0.75. The pump mass ow will be smaller forsmaller percentage ratios in LiBr solutions and will vary from 0.038 kg/s to about 0.045 kg/s. Themain draw back is the absorber solution outlet temperature (T1), which will have to be kept at alow temperature for the smaller percentage ratios in LiBr solutions. As mentioned before, areasonable temperature at the exit of the absorber would be around 30 C, which would result inan absorber outlet LiBr percentage of above 58%.

5. Crystallization

LiBr is a salt, and in its solid state, it has a crystalline structure. When LiBr is dissolved inwater, there is a specic minimum solution temperature for any given salt concentration. The saltbegins to leave the solution and crystallize below this minimum temperature.In an absorption machine, if the solution concentration is too high or the solution temperature

is reduced too low, crystallization may occur. This is most likely to occur in the solution heatexchanger, interrupting the machine operation. 1 In such a case, the concentrated solution tem-perature needs to be raised above its saturation point so that the salt crystals will return to thesolution, freeing the machine.The most frequent cause of crystallization is air leakage into the machine, which results in

increased pressure in the evaporator. This, in turn, results in higher evaporator temperatures and,consequently, lower capacities. At high load conditions, the control system increases the heatinput to the generator, resulting in increased solution concentrations to the point where crys-tallization may occur. Non-absorbable gases, like hydrogen, produced during corrosion, can alsobe present, which reduce the performance of both the condenser and the absorber [4]. A directmethod for keeping the required pressure is to evacuate the vapour space periodically with avacuum pump.Excessively cold condenser water, coupled with a high load condition, is another cause for

crystallization. In modern designs, the cooling tower water temperature is allowed to oat withvariations of load and outdoor air temperature. In this way, by using cooling water temperaturesthat are below design, the unit performance is improved. However, in the solution heat exchangerunder high load conditions, the entering temperature of the dilute solution may be low enough toreduce the temperature of the highly concentrated solution returning from the generator to thecrystallization point.A third reason is electric power failure. During normal shutdown, the machine undergoes a

dilution cycle, which lowers the concentration of the solution throughout the machine. In such acase, the machine may cool to ambient temperature without crystallization occurring in the

1 Absorption Refrigeration. Trane Air Conditioning Clinic. The Trane Company, La Crosse, Wisconsin 54601.


solutions. Crystallization is most likely to occur when the machine is stopped while operating atfull load, when highly concentrated solutions are present in the solution heat exchanger.

6. Heat exchangers sizing

In single pass heat exchangers, the temperature dierence DT between the hot and the colduids is not constant but varies with distance along the heat exchanger. In the heat transferanalysis, it is convenient to establish a mean temperature dierence (DTm) between the hot andcold uids such that the total heat transfer rate _QQ between the uids can be determined from thefollowing simple expression:

_QQ AU DTm 11For Eq. (11),

DTm F DTln F DT0 DTLln DT0=DTL

12

Also, for Eq. (11), the overall heat transfer coecient U based on the outside surface of the tubeis dened as [5]:

U 1Do=Di1=hi Do=DiFi 1=2kDo lnDo=Di Fo 1=ho 13

The above equations can be used in a computer program for designing the unit heat exchangers.For the design of the heat exchangers, the cooling water inlet and outlet temperatures must be

assumed. The cooling water inlet temperature depends exclusively on the available source ofwater, which may be a cooling tower or a well.

6.1. Condenser heat exchanger design

The overall heat transfer coecient is given by Eq. (13). For this equation, the value of thefouling factors (Fi; Fo) at the inside and outside surfaces of the tube can be taken as 0.09 m2 K/kW[6]. For a copper heat exchanger, k can be calculated from curve tting [5] (Appendix A). The heattransfer coecients, hi, ho, for the inside and outside ow need to be calculated.The PetukhovPopov equation in Ref. [7] for turbulent ow inside a smooth tube gives:

NuD f =8ReDPrK1 K2f =81=2Pr2=3 1

14

where f 1:82 log10 ReD 1:642, K1 1 3:4f , K2 11:7 1:8=Pr1=3.Eq. (14) applies for Reynolds numbers 104 < ReD < 5 106 and Prandtl numbers, 0:5 < Pr

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