Design and construction of a LiBr–water absorption machine

G.A. Florides

, S.A. Kalogirou

a,*

, S.A. Tassou

, L.C. Wrobel

Department of Mechanical Engineering, Higher Technical Institute, P.O. Box 20423, Nicosia 2152, Cyprus

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 ﬂuids are speciﬁed. These
equations are employed in a computer program, and a sensitivity analysis is performed. The diﬀerence
between the absorber LiBr inlet and outlet percentage ratio, the coeﬃcient of performance of the unit in
relation to the generator temperature, the eﬃciency of the unit in relation to the solution heat exchanger
area and the solution strength eﬀectiveness in relation to the absorber solution outlet temperature are
examined. Information on designing the heat exchangers of the LiBr–water 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.
Ó 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 and
ventilation. 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) 2483–2508

www.elsevier.com/locate/enconman

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

E-mail address:

skalogir@spidernet.com.cy

(S.A. Kalogirou).

0196-8904/03/$ - see front matter

doi:10.1016/S0196-8904(03)00006-2

Nomenclature

total heat transfer area (m

)

solution inlet concentration (mass fraction)

OUT

solution outlet concentration (mass fraction)

solution equilibrium concentration (mass fraction)

¼ X

100

, D

inside and outside diameters of tube, respectively (m)

factor equal to:

ð1:82 log

1:64Þ

correction factor depending on type of the heat exchanger

, F

fouling factors at inside and outside surfaces of tube (m

K/W)

gravitational acceleration (m/s

)

, h

heat transfer coeﬃcients for inside and outside ﬂow, respectively (W/m

latent heat of condensation (kJ/kg)

average heat transfer coeﬃcient (W/m

solution convective heat transfer coeﬃcient (W/m

thermal conductivity of tube material, solution thermal conductivity (W/m K)

factor equal to: 1

þ 3:4f

factor equal to: 11:7

þ 1:8=Pr

1=3

thermal conductivity of liquid (W/m K)

mass ﬂow rate (kg/s)

Nusselt number

¼ h

pressure (Pa)

Prandtl number

solution Prandtl number

solution Reynolds number for vertical tube

Reynolds number

¼ V

¼ 4m=pD

average overall heat transfer coeﬃcient (W/m

mean velocity (m/s)

vapour saturation temperature (

°C)

wall surface temperature (

°C)

concentration of LiBr in solution (%)

Greek symbols
C

mass ﬂow rate per wetted perimeter (kg/m s)

ﬁlm thickness (m)

logarithmic mean temperature diﬀerence (LMTD) (K)

temperature diﬀerence between hot and cold ﬂuid at inlet (K)

temperature diﬀerence between hot and cold ﬂuid at outlet (K)

density (kg/m

)

liquid density (kg/m

)

vapour density (kg/m

)

dynamic viscosity (N s/m

)

¼ mq

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

therefore, an active cooling system is required. It is preferable that such a system is not powered
by 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 the
most suitable for solar applications, since low cost solar collectors may be used to power the
generator of the machine. Such absorption units though, are not yet readily available in small
residential sizes. After a search in the world market, only one manufacturer was found com-
mercially producing LiBr–water absorption refrigerators (Yazaki of Japan). Therefore, the pos-
sibility of producing absorption air conditioning systems in small sizes for residential buildings
and 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 LiBr–water absorption machine. The necessary heat and mass transfer
equations and appropriate equations describing the properties of the working ﬂuids are speciﬁed.
These equations are employed in a computer program, and a sensitivity analysis is performed.
Information on designing the heat exchangers of the LiBr–water 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 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.

2. Absorption cooling

Absorption machines are thermally activated, and for this reason, high input (shaft) power is

not 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]. A
number of refrigerant–absorbent pairs are used, for which the most common ones are LiBr–water
and ammonia–water. These two pairs oﬀer good thermodynamic performance, and they are en-
vironmentally benign.

Absorption refrigeration system ﬂuid pairs should meet a number of important requirements,

which are [1]:

1. Absence of solid phase––The refrigerant–absorbent pair should not form a solid phase over the

range of composition and temperature to which it will be subjected. The formation of solids
may stop the ﬂow and cause problems to the equipment.

2. Volatility ratio––The refrigerant should be more volatile than the absorbent so that it can be

separated easily by heating.

absolute viscosity of liquid (N s/m

)

kinematic viscosity (m

/s)

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2485

3. Aﬃnity––The absorbent should have a strong aﬃnity with the refrigerant under the conditions

in which absorption takes place. This aﬃnity allows less absorbent to be circulated for the same
refrigerating eﬀect, 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 refrigerant–absorbent
solution. A disadvantage is that extra heat is required in the generator to separate the refrige-
rant from the absorbent.

4. Pressure––Moderate operating pressures should be used in order to avoid the use of heavy-

walled equipment and reduce the electrical power required to pump the ﬂuids from the low
pressure side to the high pressure side. Also, very low pressure (vacuum) will require the use
of large volume equipment and special means of reducing pressure drop in the refrigerant va-
pour ﬂow.

5. Stability––High chemical stability is required to avoid the undesirable formation of gases, solids

or corrosive substances.

6. Corrosion––The ﬂuids should be non-corrosive. If the ﬂuids are corrosive, corrosion inhibitors

should be used, which may inﬂuence the thermodynamic performance of the equipment.

7. Safety––Ideally, the ﬂuids must be non-toxic and non-inﬂammable.
8. Latent heat––To 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 ammonia–water pair is not suitable for use with solar collectors because of the high

temperature needed in the generator (125–170

°C). This temperature can only be obtained with

medium concentration ratio parabolic collectors, which have increased maintenance requirements
due to the need for tracking the sun.

The generator temperatures needed for the LiBr–water pair are lower (75–120

°C). These

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

3. Lithium bromide–water cooling

This type of equipment is classiﬁed by the method of heat input to the primary generator (ﬁring

method) and whether the absorption cycle is single or multiple eﬀect. The single eﬀect absorption
technology provides a peak cooling coeﬃcient of performance (COP) of approximately 0.7 and
operates with heat input temperatures in the range of 75–120

°C. The multiple eﬀect technology

gives higher COPs but can only be utilised when higher temperature heat sources are available.
Double eﬀect systems can be achieved by adding an extra stage as a topping cycle on the single
eﬀect cycle. In this way, the heat rejection from the high temperature stage is used to power the
lower temperature stage. It should be noted that the refrigerant in the LiBr–water system is water
and the LiBr acts as the absorbent, which absorbs the water vapour, thus making pumping from
the absorber to the generator easier and economic. A single eﬀect LiBr–water chiller is illus-
trated in Fig. 1, and its schematic presentation on a pressure–temperature diagram is illustrated in
Fig. 2.

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

With reference to the numbering system shown in Fig. 1, at point (1), the solution is rich in

refrigerant and a pump (2) forces the liquid through a heat exchanger to the generator (3). The
temperature of the solution in the heat exchanger is increased.

EXPANSION

VALVE

GENERATOR

CONDENSER

SOLUTION

HEAT

EXCHANGER

PUMP

ABSORBER

EVAPORATOR

10,11

Fig. 1. Single eﬀect, LiBr–water absorption cycle.

CONDENSER

GENERATOR

SOLUTION HEAT
EXCHANGER

ABSORBER

EVAPORATOR

PUMP

SOLUTION
FLOW
RESTRICTOR

REFRIGERANT
FLOW
RESTRICTOR

TEMPERATURE

P
R
E
S
S
U
R
E

Fig. 2. Two shell, LiBr–water cycle cooling system [1].

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2487

In the generator, thermal energy is added and the refrigerant boils oﬀ the solution. The re-

frigerant vapour (7) ﬂows to the condenser, where heat is rejected as the refrigerant condenses.
The condensed liquid (8) ﬂows through a ﬂow restrictor to the evaporator (9). In the evaporator,
the heat from the load evaporates the refrigerant, which ﬂows back to the absorber (10). A small
portion of the refrigerant leaves the evaporator as liquid spillover (11). At the generator exit (4),
the ﬂuid consists of the absorbent–refrigerant solution, which is cooled in the heat exchanger.
From points (6)–(1), the solution absorbs refrigerant vapour from the evaporator and rejects heat
through 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 pure
water line at the left and crystallisation line at the right.

4. Design of a single eﬀect lithium bromide–water absorption cycle system

To perform estimations of equipment sizing and performance evaluation of a single-eﬀect LiBr–

water absorption cooler, basic assumptions and input values must be considered. With reference
to Figs. 1–3, the basic assumptions are:

1. The steady state refrigerant is pure water.
2. There are no pressure changes except through the ﬂow 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 in

Table 1.

CRYSTALLIS-
ATION LINE

PURE WATER
LINE

WEAK
ABSORBENT
LINE

P
R
E
S
S
U
R
E

STRONG ABSORBENT
LINE

9,10

1,2

TEMPERATURE

Fig. 3. Duhring chart of the LiBr–water absorption cycle [1].

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

4.1. Evaporator analysis

Since, in the evaporator, the refrigerant is saturated water vapour and the temperature

ðT

Þ is

assumed to be 6

°C, the saturation pressure at point 10, as calculated from curve ﬁts [2] presented

in Appendix A, is 0.934 kPa, and the enthalpy is 2511.8 kJ/kg. Since, at point 11, the refrigerant is
saturated liquid, its enthalpy is 23.5 kJ/kg. The enthalpy at point 9 is determined from the
throttling process applied to the refrigerant ﬂow restrictor, which yields that h

¼ h

To deter-

mine h

, the pressure at this point must be determined. Since, at point 4, the solution mass fraction

is 60% LiBr and the temperature at the saturated state was assumed to be 90

°C, the LiBr gives a

saturation pressure of 9.66 kPa and h

¼ 212:2 kJ/kg. Considering that the pressure at point 4 is

the same as in point 8, then h

¼ h

¼ 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 ﬂow of the refrigerant and the evaporator heat transfer
rate.

The mass balance on the evaporator is:

¼ _m

þ _m

ð1Þ

The energy balance on the evaporator is:

¼ _m

þ _m

ð2Þ

Since the evaporator output power _

is 10.0 kW and _

¼ 2:5% _m

the mass ﬂow rates can be

calculated. The results are shown in Table 2.

4.2. Absorber analysis

Since the values of _

and _

are known, mass balances around the absorber give:

¼ _m

þ _m

ð3Þ

and

¼ x

ð4Þ

Table 1
Design parameters for the single eﬀect LiBr–water absorption cooler

Parameter

Symbol

Example-value

Capacity

10 kW

Evaporator temperature

°C

Generator solution exit temperature

°C

Weak solution mass fraction

55% LiBr

Strong solution mass fraction

60% LiBr

Solution heat exchanger exit temperature

°C

Generator (desorber) vapour exit temperature

°C

Liquid carryover from evaporator

0:025 _

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2489

The mass fractions x

and x

in Eq. (4) are inputs, and therefore, _

and _

can be calculated. The

results 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 h

¼ 83 kJ/kg. The enthalpy value at point 6 is determined from the

throttling model, which gives h

¼ h

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:

þ _m

¼ _m

þ _m

ð5Þ

The temperature at point 3 is an input value (65

°C), and since the mass fraction for points 1 to 3

is the same, the enthalpy at this point is determined as 145.4 kJ/kg. Actually, the state at point 3
may be subcooled liquid. However, at the conditions of interest, the pressure has an insigniﬁcant
eﬀect on the enthalpy of the subcooled liquid, and the saturated value at the same temperature
and mass fraction can be an adequate approximation. The enthalpy at point 2 is determined from
an isentropic pump model. The minimum work input

ðwÞ can, therefore, be obtained from:

¼ _m

ðp

ð6Þ

In Eq. (6), it is assumed that the speciﬁc volume (v, m

/kg) of the liquid solution does not change

appreciably from point (1)–(2). The speciﬁc volume of the liquid solution can be obtained from a
curve ﬁt [3] (see Appendix A).

For the present study, since all variables are known (Table 2), the pump power can be calcu-

lated as:

¼ 0:29 W

Eq. (5) can now be solved for the unknown enthalpy value at point 5, giving h

¼ 144:2 kJ/kg. The

temperature at point 5 can also be determined from the enthalpy value and is 54.8

°C.

Table 2
Data for single eﬀect LiBr–water cooling system

Point #

(kJ/kg)

(kg/s)

(kPa)

(

°C)

(%LiBr)

Remarks

0.053

0.934

34.9

0.053

9.66

34.9

145.4

0.053

9.66

Sub-cooled liquid

212.2

0.0486

9.66

144.2

0.0486

9.66

54.8

144.2

0.0486

0.934

44.5

2628

0.0044

9.66

Superheated steam

185.3

0.0044

9.66

44.3

Saturated liquid water

185.3

0.0044

0.934

2511.8

0.0043

0.934

Saturated vapour

23.5

0.00011

0.934

Saturated liquid water

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

Finally, the energy balance on the absorber is:

¼ _m

þ _m

ð7Þ

which gives _

¼ 13:42 kW.

4.3. Generator (desorber) analysis

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

¼ _m

þ _m

ð8Þ

and results in: _

¼ 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:

¼ _m

ðh

ð9Þ

and therefore, _

¼ 10:78 kW.

4.5. Coeﬃcient of performance

The COP is deﬁned as:

COP

ð10Þ

which gives a value of 0.704.

A summary of the energy ﬂows at the various components of the system is given in Table 3.
To ﬁnd suitable conditions for speciﬁc applications, a sensitivity analysis can be performed

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

Table 3
Energy ﬂows at the various components of the system

Description

Symbol

Capacity (evaporator output power)

10.0

Pump minimum work input

0.29

Absorber heat, rejected to the environment

13.42

Heat input to the generator

14.2

Condenser heat, rejected to the environment

10.78

Coeﬃcient of performance

COP

0.704

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2491

correlations for the ﬂuid properties shown in Appendix A. Such a sensitivity analysis is presented
below.

4.6. Sensitivity analysis

4.6.1. Eﬀect of absorber inlet LiBr percentage ratio

To check this eﬀect, the following conditions were assumed:

1. Solution heat exchanger exit temperature, T 3

¼ 55 °C.

2. Generator solution exit temperature, T 4

¼ 75 °C.

3. Condenser temperature, T 7

¼ 70 °C.

4. Evaporator capacity 10 kW.
5. Evaporator temperature 6

°C.

6. Absorber exit LiBr percentage ratio

¼ 60%.

7. Pressure in generator and condenser

¼ 4.82 kPa.

8. Pressure in absorber and evaporator

¼ 0.934 kPa.

Since the absorber exit LiBr percentage ratio is kept constant at 60%, the greater the diﬀerence

between 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 pump
mass ﬂow. On the other hand, to keep the cycle running at the speciﬁed stage, the temperature at
the exit of the absorber has to be maintained at a lower level. However, this presents diﬃculties
with the cooling water temperature of the absorber heat exchanger. Normally, this temperature
may be between 20 and 25

°C, which means that the lowest temperature at the exit of the absorber

would be around 30

°C.

47.5

52.5

57.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Absorber inlet LiBr percentage

Absorber exit temperature (˚C)

Pump mass flow (kg/s) and COP

Absorper exit temp
Pump mass flow
COP

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

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

4.6.2. Eﬀect of generator temperature

To check this eﬀect, the following conditions were assumed:

1. Solution heat exchanger exit temperature, T 3

¼ 55 °C.

2. Evaporator capacity 10 kW.
3. Evaporator temperature 6

°C.

4. Absorber inlet LiBr percentage ratio

¼ 52.5%.

5. Absorber exit LiBr percentage ratio

¼ 60%.

6. Absorber exit temperature, T 1

¼ 30:4 °C.

7. Pressure in absorber and evaporator

¼ 0.934 kPa.

As seen in Fig. 5, when the generator temperature is increased, the generator pressure is

also increased, and this has the eﬀect of lowering the COP of the unit, considering that the pressures
and temperatures at other points of the unit are kept constant. The pump mass ﬂow changes
slightly from 0.04 kg/s at a generator exit temperature of 65

°C to 0.037 kg/s at 115 °C.

4.6.3. Eﬀect of heat exchanger temperatures

To check this eﬀect, the following conditions were assumed:

1. Evaporator capacity 10 kW.
2. Evaporator temperature 6

°C.

3. Pressure in generator and condenser

¼ 4.82 kPa.

4. Absorber inlet LiBr percentage ratio

¼ 52.5%.

5. Absorber exit LiBr percentage ratio

¼ 60%.

6. Absorber exit temperature, T 1

¼ 30:4 °C.

7. Pressure in absorber and evaporator

¼ 0.934 kPa.

The solution heat exchanger increases the eﬃciency of the unit. The greater the heat exchanger

area is, the greater its eﬀect 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

100

105

110

115

Generator exit temperature, T4 (˚C)

era

ressu

)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Pump

mas

flow

(kg/s

)

and

Generator pressure

Pump mass flow

COP

Fig. 5. Eﬀect of generator temperature.

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2493

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

4.6.4. Eﬀect of solution strength

To check the solution strength eﬀectiveness, a constant diﬀerence of 6% between the absorber

inlet 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, T 4

¼ 75 °C.

0.7 2

0.74

0.76

0.78

0.8

0.82

0.84

COP

erat

˚C

Generator exit solution temp
Absorber inlet solution temp
Absorber oulet solution temp
Generator inlet solution temp

Fig. 6. Eﬀect of heat exchanger temperatures.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

absorber inlet LiBr%
Generator pressure
Absorber exit temp
COP
Pump mass flow

Pump mass flow (kg/s) - COP

Temperature (

˚C) - Pressure kPa

Absorber exit LiBr percentage ratio

Fig. 7. Eﬀect of solution strength.

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

4. Solution heat exchanger exit temperature, T 3

¼ 55 °C.

5. Pressure in absorber and evaporator

¼ 0.934 kPa.

The results shown in Fig. 7 indicate that a smaller percentage ratio in LiBr solutions will have

slightly better results, since the solution will absorb the extra water vapour more readily. The COP
for the selected conditions will vary from 0.79 to 0.75. The pump mass ﬂow will be smaller for
smaller percentage ratios in LiBr solutions and will vary from 0.038 kg/s to about 0.045 kg/s. The
main draw back is the absorber solution outlet temperature (T 1), which will have to be kept at a
low temperature for the smaller percentage ratios in LiBr solutions. As mentioned before, a
reasonable temperature at the exit of the absorber would be around 30

°C, which would result in

an 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 in

water, there is a speciﬁc minimum solution temperature for any given salt concentration. The salt
begins 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 heat
exchanger, interrupting the machine operation.

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 the
solution, 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 heat
input 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 also
be present, which reduce the performance of both the condenser and the absorber [4]. A direct
method for keeping the required pressure is to evacuate the vapour space periodically with a
vacuum 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 ﬂoat with
variations of load and outdoor air temperature. In this way, by using cooling water temperatures
that are below design, the unit performance is improved. However, in the solution heat exchanger
under high load conditions, the entering temperature of the dilute solution may be low enough to
reduce the temperature of the highly concentrated solution returning from the generator to the
crystallization 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 a
case, the machine may cool to ambient temperature without crystallization occurring in the

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

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2495

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

6. Heat exchangers sizing

In single pass heat exchangers, the temperature diﬀerence DT between the hot and the cold

ﬂuids is not constant but varies with distance along the heat exchanger. In the heat transfer
analysis, it is convenient to establish a mean temperature diﬀerence (DT

) between the hot and

cold ﬂuids such that the total heat transfer rate _

between the ﬂuids can be determined from the

following simple expression:

¼ AU DT

ð11Þ

For Eq. (11),

¼ F DT

¼ F

ln DT

ð12Þ

Also, for Eq. (11), the overall heat transfer coeﬃcient

ðU Þ based on the outside surface of the tube

is deﬁned as [5]:

ðD

Þð1=h

Þ þ ðD

ÞF

þ ½1=ð2kÞD

ðD

Þ þ F

þ 1=h

ð13Þ

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 of
water, which may be a cooling tower or a well.

6.1. Condenser heat exchanger design

The overall heat transfer coeﬃcient is given by Eq. (13). For this equation, the value of the

fouling factors (F

; F

) at the inside and outside surfaces of the tube can be taken as 0.09 m

K/kW

[6]. For a copper heat exchanger, k can be calculated from curve ﬁtting [5] (Appendix A). The heat
transfer coeﬃcients, h

, h

, for the inside and outside ﬂow need to be calculated.

The Petukhov–Popov equation in Ref. [7] for turbulent ﬂow inside a smooth tube gives:

ðf =8ÞRe

þ K

ðf =8Þ

1=2

ðPr

2=3

1Þ

ð14Þ

where f

¼ ð1:82 log

1:64Þ

, K

¼ 1 þ 3:4f , K

¼ 11:7 þ ð1:8=Pr

1=3

Þ.

Eq. (14) applies for Reynolds numbers 10

< Re

and Prandtl numbers, 0:5 < Pr <

2000. The Petukhov–Popov equation agrees with experimental results for the speciﬁed range
within

5%. The water properties are evaluated at a mean temperature.

The Nu number can be equated to h

, and therefore, h

can be evaluated.

NusseltÕs analysis of heat transfer for condensation on the outside surface of a horizontal tube

gives the average heat transfer coeﬃcient as [8]:

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

¼ 0:725

ðq

Þh

ðT

ÞD

0:25

ð15Þ

The physical properties in Eq. (15) should be evaluated at the mean wall surface and vapour
saturation temperatures.

The above equation is recommended in the case of condensation on a single horizontal tube,

although a comparison of the average heat transfer coeﬃcient for vertical surfaces with that found
by experiments has shown that the measured heat transfer coeﬃcient is about 20% higher than the
values suggested by theory [5].

By substituting the above values in Eq. (13), a resulting overall heat transfer coeﬃcient (U ) may

be determined.

The logarithmic mean temperature diﬀerence may be evaluated from Eq. (12), and Eq. (11) is

used to evaluate the necessary heat transfer area of the pipe.

6.2. Generator heat exchanger design

The generator provides sensible heat and the latent heat of vaporisation. The sensible heat

raises the inlet stream temperature to the saturation temperature. This amount of heat is normally
about 13% of the total heat required [4]. The heat of vaporisation consists of the heat of va-
porisation of pure water and the latent heat of mixing of the liquid solution. Typically, the heat of
mixing is about 11% of the heat of vaporisation for water/LiBr.

The above analysis indicates that the heat to be provided by the generator can be based on the

heat of vaporisation of pure water, increased by about 23% in a typical design.

Although considerable research work has been done in the past on pool boiling of liquids, data

on water/LiBr solutions are not extensive [9]. Experimental results indicate that boiling is not
signiﬁcantly aﬀected by the tube diameter but is aﬀected signiﬁcantly by the solution concen-
tration. As the solution concentration increases, the heat transfer coeﬃcient decreases. Also, the
heat transfer coeﬃcient increases as the heat ﬂux increases. Average heat transfer coeﬃcients were
found to vary between 1600 and 7500 W/m

K [9]. For the above work, stainless steel tubes were

used. The tube material also aﬀects the heat transfer coeﬃcient as shown by an empirical relation
developed by Rohsenow in Ref. [7] for nucleate boiling. Since no formula is available for cal-
culating the exact heat transfer coeﬃcient of the generator heat exchanger, the exact heat transfer
coeﬃcient needs to be determined experimentally.

6.3. Solution heat exchanger design

For the solution heat exchanger design, Eq. (13) is used to calculate the overall heat transfer

coeﬃcient. As before, the value of the fouling factors (F

; F

) at the inside and outside surfaces of

the tube are taken as 0.09 m

K/kW [6] and k for copper at a mean temperature may be evaluated.

The heat transfer coeﬃcients, h

, h

, for the inside and outside ﬂow are determined as detailed

below.

The LiBr solution properties at a mean temperature are calculated (Appendix A) and Re is

determined from

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2497

¼ 4 _m

pDl

For laminar ﬂow, the Nusselt number (Nu) is [6]:

¼ h

¼ 3:66

ð16Þ

Therefore, h

may be evaluated.

The hydraulic diameter D

for the annulus is the diﬀerence between the inside diameter of the

external tube

ðD

Þ and the outside diameter of the internal tube ðD

Þ [7].

The Reynolds number based on the hydraulic diameter and the bulk temperature properties is:

qU D

m _

For laminar ﬂow, as before Nu

¼ h

D=K

¼ 3:66, and therefore, h

may be evaluated.

By substituting the above values in Eq. (13), the resulting overall heat transfer coeﬃcient

ðU Þ

based on the outside surface of the tube is subsequently evaluated.

The logarithmic mean temperature is then calculated, and ﬁnally, from Eq. (11), the needed

area of the heat exchanger is determined.

6.4. Tube absorber

For this design, the solution ﬁlm can ﬂow downward either on horizontal or on vertical tubes.
The construction of the horizontal tube absorber may be more costly because of the large

length of welds, which may present problems with maintaining a vacuum. For this reason, an
alternative design with vertical tubes, housed in a cylindrical shell, may be employed, as shown in
Fig. 8. The theoretical analysis of the vertical tube absorber is presented below.

6.5. Absorber heat exchanger design

In the case of this study, the water vapour produced in the evaporator (Fig. 6) is absorbed in

the ﬂow of the LiBr–water solution and is not condensing directly on the heat exchanger tubes.
The design of the heat exchanger, therefore, requires values for the heat and mass transfer co-
eﬃcients.

A number of researchers have studied the absorption of water vapour in falling ﬁlms of LiBr–

water solutions. Morioka et al. [10] conducted experiments on steam absorption for ﬁlms ﬂowing
down a vertical pipe. They obtained experimental results, which show that for ﬁlm Reynolds
numbers in the range of 40–400, the heat transfer coeﬃcients of the ﬁlm are between 1500 and
3000 W/m

K. The average absorption of mass ﬂux (kg/m

s) is compared with the numerical

results derived from a laminar ﬂow theoretical model proposed by the authors. The agreement of
the results is good for ﬁlm Reynolds numbers up to 100, but the experimental values are far higher
above ﬁlm Reynolds numbers of 200.

Grossman [11] described a theoretical analysis of the combined heat and mass transfer process

in the absorption of gas or vapour into a laminar liquid ﬁlm. Simultaneous equations are de-
scribed that give the temperature and concentration variations at the liquid–gas interface and at
the wall. A constant temperature and an adiabatic wall case were considered. The Nusselt and

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G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

Sherwood numbers were found to depend on the Peclet and Lewis numbers as well as on the
equilibrium characteristics of the working ﬂuids.

Conlisk [12] developed a design procedure for predicting the absorption capacity of a given

tube based on the governing geometrical and physical parameters. The theoretical approach
developed can predict the amount of mass absorbed in a given length of tube.

Patnaik et al. [13] presented a model based on the solution of diﬀerential equations to calculate

the axial solution concentration and temperature distributions along a vertical tube absorber. The
absorption of water vapour into the falling ﬁlm of the solution of LiBr was modelled, employing
equations extracted from the literature, incorporating information on wavy-laminar ﬂows. The
usefulness of the model was demonstrated by generating absorber performance charts.

A practical model for absorption of vapours into a laminar ﬁlm of water and LiBr falling along

a constant temperature vertical plate was described in Andberg and Vliet [14]. The model de-
veloped considers non-isothermal absorption, and the equations showed good agreement with
experimental results. The objective of the study was to develop an eﬀective model of the ab-
sorption process in order to facilitate the study of absorber design from a theoretical viewpoint.
For this reason, some simpliﬁcations were made, like assuming that the bank of tubes of an actual
absorption unit are replaced with a constant temperature vertical ﬂat plate. Also, because of the
complexity of the problem involving the solution of momentum, energy and diﬀusion equations
with their boundary conditions, a simpliﬁed method was developed for determining the various
quantities involved. Because of the simplicity and the good agreement with experimental results,
this method was chosen for determining the number of absorber tubes required.

Cooling water inlet

Falling film

Solution outlet

Water vapour
produced in the
evaporator

Concentrated
LiBr-water
solution

Cooling water outlet

Fig. 8. Schematic representation of the vertical tube absorber.

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2499

The independent variables, which aﬀect the absorption of vapours, are solution mass ﬂow rate,

solution inlet concentration, absorber pressure and wall temperature.

The length of plate (L) is correlated to the solution mass ﬂow rate by the expression:

¼ am

ð17Þ

where a

¼ 132ðlnð100 A

Þ=86:0Þ, b ¼ 1:33, m

¼ mass ﬂow rate per unit width of plate (kg/m s)

and A

¼ ‘‘absorption percentage’’.

The ‘‘absorption percentage’’ (A

), is deﬁned as:

OUT

100

ð18Þ

Determination of the equilibrium concentration, C

, requires the solution of the following set of

expressions:

¼ 2:00755 þ 0:16976X 3:133362 0:001X

þ 1:97668 0:00001X

¼ 321:128 19:322X þ 0:374382X

2:0637 0:001X

¼ 6:21147

¼ 2886:373

¼ 337269:46

¼ ð2E=½D þ ðD

4EðC LOGðP =6894:8ÞÞÞ

0:5

Þ 459:72

¼ ð5=9ÞðAT

þ B 32Þ

The above set of expressions requires an iterative type of solution to ﬁnd C

, given T

and P .

In the case of this study, T

and P are known, and therefore, C

may be evaluated. Eq. (18) may

then be solved to calculate A

Assuming a certain length for every tube of the absorber, Eq. (17) gives the mass ﬂow m

, and

since the tube external area per meter length is known, the required number of tubes can be
calculated.

The next step is to check the area of tubes needed to cool the solution to the required level.

Patnaik et al. [13] suggest that WilkeÕs correlation, valid for a constant heat ﬂux wall with pro-
gressively decreasing diﬀerence from isothermal wall outside the entrance region, can be used for
the falling ﬁlm. It is assumed that the ﬂow is fully developed in a wavy, laminar regime and that
the bulk solution temperature proﬁle is linear with respect to the transverse coordinate. WilkeÕs
correlation is:

0:029

ðRe

0:53

0:344
s

ð19Þ

The ﬁlm thickness d (m) is given by:

3lC

1=3

ð20Þ

and the solution Reynolds number (Re

) for the vertical tube is:

¼ 4C=l

ð21Þ

2500

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

In the case of this study, the mean properties of the solution are evaluated. Assuming the number
of pipes to be used and substituting the above values into Eqs. (19)–(21), a solution convective
heat transfer coeﬃcient h

results.

Subsequently, the cooling water properties at the mean temperature are evaluated and sub-

stituted into Eq. (14). By replacing Nu

¼ h

, h

is determined. By substituting the above

values into Eq. (13), the resulting overall heat transfer coeﬃcient (U ) based on the outside surface
of the tube is also determined. DT

also needs to be evaluated, and from Eq. (11), the resulting

length of each pipe is determined. This length needs to be equal to the initial length assumed. The
above procedure may be repeated until the pipe length matches.

6.6. Evaporator heat exchanger design

To facilitate construction, the evaporator heat exchanger may be constructed in a similar way

to the absorber heat exchanger. Fig. 9 shows a schematic representation of the vertical tube
evaporator. Water passing through the evaporator tubes supplies the required heat to vaporise the
falling ﬁlm of water around every tube.

A search of the literature has shown that the preferred construction method is to allow the liquid

to enter inside a tube. The ﬂuid inside the tube is heated by the run of ﬂuid at the outer surface of the
tube, so that progressive vaporisation occurs. The heat transfer coeﬃcient increases with distance
from the entrance, since heat is added continuously to the ﬂuid. It is also not yet possible to predict
all of the characteristics of this process quantitatively because of the great number of variables upon
which the process depends and the complexity of the various two phase ﬂow patterns that occur as
the quality of the vapour–liquid mixture increases during vaporisation [7]. Therefore, in the case of
this study, the mean heat transfer coeﬃcient needs to be determined experimentally.

Water outlet

Entering
water

Falling film

Water inlet

Entering
water

Vapour
outlet

Fig. 9. Schematic representation of the vertical tube evaporator.

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2501

7. Experimental results

To investigate the accuracy of the theoretical procedure described above for the design of the

various heat exchangers, a 1 kW model was designed and constructed [15]. The designed condi-
tions chosen are indicated in Table 4.

A summary of the experimental results is presented in Table 5.

8. General observations

Because of corrosion problems, the life expectancy of LiBr absorption machines is approximately

20 years. The presence of oxygen can greatly accelerate the degradation, and thus, leaks must be
avoided. If the vacuum must be broken for any reason, it is important to ﬁll the vapour space with
nitrogen or other inert gas to a pressure above atmospheric to avoid introduction of oxygen. Metals

Table 4
LiBr–water absorption refrigeration system calculations based on a generator temperature of 75

° C and a solution heat

exchanger exit temperature of 55

°C.

Point

(kJ/kg)

(kg/s)

(kPa)

(

°C)

%LiBr (X)

Remarks

0.00517

0.93

34.9

0.00517

4.82

34.9

124.7

0.00517

4.82

Subcooled liquid

183.2

0.00474

4.82

137.8

0.00474

4.82

51.5

137.8

0.00474

0.93

44.5

2612.2

0.000431

4.82

Superheated steam

131.0

0.000431

4.82

31.5

Saturated liquid

131.0

0.000431

0.93

2511.8

0.000421

0.93

Saturated vapour

23.45

0.000011

0.93

Saturated liquid

Description

Symbol

Capacity (evaporator output power)

1.0

Absorber heat, rejected to the environment

1.28

Heat input to the generator

1.35

Condenser heat, rejected to the environment

1.07

Coeﬃcient of performance

COP

0.74

Table 5
Overall heat transfer coeﬃcients of the various heat exchangers of the 1 kW unit

Heat exchanger

Cooling/heating water
temperature (

°C)

Overall heat transfer coeﬃcient,
U

(W/m

Entering

Leaving

Theoretically estimated

Actual value

Generator

1600–7500

2300

Condenser

28.5

2980

3265

Evaporator

–

195

Absorber

625

400

Solution heat exchanger

–

130

2502

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

like copper and iron in the presence of aqueous LiBr, which is an electrolyte, produce ions that leave
the solid surface and combine with oxygen at a distance from the surface. This leaves the solid
surface of the base metal available for more attack. By controlling the solution pH level to be
slightly basic instead of acidic, oxides are formed directly on the solid surface, forming a relatively
stable oxide coating (passivation), protecting the surface. The pH level can be controlled by adding
small amounts of hydrobromic acid (HBr). Since both elements constituting HBr are already
present within the solution, the solution properties are not signiﬁcantly altered. Corrosion inhibi-
tors can also reduce corrosion rates. Such inhibitors are lithium chromate (Li

CrO

) lithium mo-

lybdate (Li

MoO

) or lithium nitrate (LiNO

) in amounts on the order of 1% by solution weight [4].

9. Cost analysis

The unit manufactured for this project is a prototype unit, and the total cost of its construction

is about C£ 3000.

A large part of this amount was spent for purchasing ﬂow meters (C£ 500),

auxiliary equipment like vacuum pumps, glass tubes etc. (C£ 500) and experimentation with
diﬀerent types of valves and materials.

The actual cost of a working unit of 1 kW capacity can be as low as C£ 1550. A breakdown of

this cost is shown in Table 6. Based on the 1 kW unit, the cost of a 10 kW unit, which can cover
the needs of a typical insulated house, can be estimated as C£ 4300 (Table 6).

It must also be stated that the above unit cannot be produced in a basic workshop. Automatic

or semi-automatic welding machines and personnel specialised on welding components for va-
cuum are necessary. Also special equipment for weld testing and soundness is necessary. The cost
of such infrastructure is not included in the unit costing. On the other hand, the produced unit is
only a prototype, and a lot of research can be done in order to improve the eﬃciency of the heat
exchangers by using a surfactant additive, called octyl alcohol. Such an additive can increase the
heat transfer performance in the absorber. Also, other types of heat exchanging surfaces, like
rough or ﬁnned surfaces may increase the eﬃciency and reduce the size of the unit.

It must also be noted that in order to complete the requirements of a 10 kW unit, a cooling

tower or water from a well is necessary to provide adequate cooling water for the condenser and

Table 6
Comparative cost of a 1 kW and a 10 kW LiBr–water absorption unit

Item

Cost of the 1 kW unit (C£)

Cost of the 10 kW unit (C£)

Generator and condenser unit

400

Evaporator

150

1000

Absorber

150

1000

Piping

100

Pumps

370

500

Automatic controls, sensors and valves

600

700

LiBr salt

200

600

Total cost

1550

4300

Exchange rates: 1C£

¼ 1:6 US$ (July 2002).

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2503

absorber heat exchangers. The cost of such a tower is about C£ 400. Also the installation of the
absorption unit and cooling tower will demand about C£ 100 extra cost for pumps and piping,
compared to the installation cost of a conventional 10 kW electric chiller.

10. Conclusions

A method to evaluate the characteristics and performance of a single stage LiBr–water ab-

sorption machine was presented, and the necessary heat and mass transfer equations and ap-
propriate equations describing the properties of the working ﬂuids were speciﬁed. These equations
were used in a computer program, and a sensitivity analysis was performed. This analysis shows
that the greater the diﬀerence between the absorber LiBr inlet and outlet percentage ratios is, the
smaller will be the mass circulating in the absorber. On the other hand, to keep the cycle running
at a speciﬁed stage, the temperature at the exit of the absorber has to be maintained at a lower
level when the absorber exit LiBr percentage ratio is lower.

Considering that the pressures and temperatures at other points of the unit are kept constant,

the COP of the unit is lowered when the generator temperature is increased, leading to an increase
of the generator pressure.

The solution heat exchanger increases the eﬃciency of the unit. The greater the heat exchanger

area, the greater its eﬀect is.

Finally, when checking the solution strength eﬀectiveness for a constant diﬀerence of 6% be-

tween the absorber inlet LiBr percentage ratio and absorber outlet ratio, it was found that a smaller
percentage ratio in LiBr solutions would have slightly better results. The main draw back is the
absorber solution outlet temperature (T 1), which will have to be kept at a low temperature for
smaller percentage ratios in LiBr solutions. A reasonable temperature at the exit of the absorber
would be around 30

°C, which would result in an absorber outlet LiBr percentage above 58%.

Information on designing the heat exchangers of the LiBr–water absorption unit are also

presented. The calculated theoretical values are compared to experimental results derived for a
small unit with a nominal capacity of 1 kW.

The cost for a nominal 10 kW unit that can cover the needs of a typical insulated house was

estimated to be C£ 4300. The total cost of an absorption unit together with all necessary sec-
ondary devices and installation cost is estimated as C£ 4800. The price, therefore, of a LiBr–water
absorption refrigeration unit is high compared to a similar capacity electric chiller that is only C£
1500. It should be noted, however, that the absorption units oﬀer possibilities of use of renewable
energy sources and waste heat, whereas the electric chiller uses electricity that is produced from
fossil fuels and have harmful eﬀects on the environment.

Appendix A. Material properties

A.1. LiBr solution enthalpy [4]

Range 0% < X < 40% LiBr
CT

¼ temperature (°C)

¼ enthalpy (kJ/kg)

2504

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

¼ %LiBr

¼ ðCT 9=5Þ þ 32

¼ 33:1054264, CA

¼ 0:13000636, CA

¼ 0:00097096, CB

¼ 1:0090734,

¼ 0:01377507, CB

¼ 0:000085131

¼ ½CA

þ CA

þ T ðCB

þ CB

Þ2:326

A.2. LiBr solution and refrigerant pressure and temperatures [1]

Range 45% < X < 70% LiBr
T

sol

¼ solution temperature (°C), range 5 < T

sol

175

°C

ref

¼ refrigerant saturated temperature (°C), range 15 < T

ref

110

°C

¼ saturation pressure (kPa)

¼ 2:00755, A

¼ 0:16976, A

¼ 0:003133362, A

¼ 0:0000197668

¼ 124:937, B

¼ 7:71649, B

¼ 0:152286, B

¼ 0:0007959

¼ A

þ A

¼ B

þ B

¼ 7:05, D ¼ 1596:49, E ¼ 104095:5

Log P

¼ C þ D=ðT

ref

þ 273Þ þ E=ðT

ref

þ 273Þ

ref

¼ ð2E=ðD þ ½D

4EðC log P Þ

0:5

ÞÞ 273

sol

¼ RB þ T

ref

A.3. Enthalpy of LiBr solution [1]

Range 40% < X < 70% LiBr
T

¼ solution temperature (°C)

¼ enthalpy (kJ/kg)

Solution temperature range 15

°C < T < 165 °C

¼ 2024:33, A

¼ 163:309, A

¼ 4:88161, A

¼ 0:06302948, A

¼ 0:0002913704

¼ 18:2829, B

¼ 1:1691757, B

¼ 0:03248041, B

¼ 0:0004034184, B

¼ 0:0000018520569

¼ 0:037008214, C

¼ 0:0028877666, C

¼ 0:000081313015

¼ 0:00000099116628, C

¼ 0:0000000044441207

¼ A

þ A

¼ B

þ B

¼ C

þ C

¼ RA þ T RB þ RC T

A.4. Density of LiBr solution [3]

Range 20% < X < 60%
T

¼ solution temperature (°C), 0 < T < 200 °C,

¼ LiBr solution density (kg/m

)

¼ X =100

¼ 1145:36 þ 470:84X

þ 1374:79X

ð0:333393 þ 0:571749X

Þð273 þ T Þ

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2505

A.5. Absolute viscosity of LiBr solution [3]

Range 45% < X < 65%
TK

¼ solution temperature (K)

¼ absolute viscosity (kg/m s)

¼ 494:122 þ 16:3967X 0:14511X

¼ 28606:4 934:568X þ 8:52755X

¼ 70:3848 2:35014X þ 0:0207809X

¼ A

þ ðA

=TK

Þ þ A

ðTKÞ

¼ EXPðBÞ=1000

A.6. Speciﬁc heat of LiBr solution (curve ﬁt from Ref. [1]––R

¼ 0:9997)

¼ %LiBr

¼ speciﬁc heat of LiBr solution (J/kg K)

¼ 0:0976X

37:512X þ 3825:4

A.7. Thermal conductivity of LiBr solution (Data extrapolated from Ref. [16])

¼ temperature of solution (K)

¼ %LiBr

¼ thermal conductivity of LiBr solution (W/m K)

For T P 313
K

¼ 0:3081ðX =100Þ þ 0:62979

¼ 0:3191795ðX =100Þ þ 0:65388

¼ ððK

Þ=20ÞðT 313Þ

¼ K

þ D

For T < 313
K

¼ 0:3081ðX =100Þ þ 0:62979

¼ 0:291897ðX =100Þ þ 0:59821

¼ ððK

Þ=20Þð313 T Þ

¼ K

þ D

A.8. Saturation pressure of water vapour (curve ﬁts from data presented in Ref. [2]––R

¼ 0:9999)

¼ saturation pressure (kPa)

¼ temperature (°C)

¼ 0:000000000002T

0:000000003T

þ 0:0000002T

þ 0:00003T

þ 0:0014T

þ 0:0444T

þ 0:6108

A.9. Saturated water–vapour enthalpy (curve ﬁts from data presented in Ref. [2]––R

¼ 0:9999)

¼ vapour enthalpy (kJ/kg)

¼ temperature (°C)

¼ 0:00125397T

þ 1:88060937T þ 2500:559

2506

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

A.10. Latent heat of condensation of water vapour (curve ﬁt Ref. [1]––R

¼ 0:9999Þ

¼ latent heat of condensation (kJ/kg)

¼ saturation temperature (°C)

¼ 0:00132635T

2:29983657T þ 2500:43063

A.11. Density of saturated water (curve ﬁt Ref. [1]––R

¼ 0:9986)

¼ density of saturated water (kg/m

)

¼ saturation temperature (°C)

¼ 1=ð0:00001147965T

0:00297197798T

þ 0:28077931731T

11:83083758T

þ 202:9035477661Þ

A.12. Enthalpy of superheated steam (curve ﬁts from data presented in Ref. [2]––R

¼ 0:992)

¼ enthalpy of superheated steam (kJ/kg),

ref

¼ refrigerant (water) saturated temperature [see Section 2] (°C)

actual

¼ temperature of vapour (°C)

¼ pressure of vapour (kPa)

¼ degrees of superheat (°C)

¼ T

actual

ref

SH1

¼ 32:508 lnðP Þ þ 2513:2

SH2

¼ 0:00001P

0:1193P þ 2689

¼ ððH

SH2

SH1

Þ=100ÞT þ H

SH1

A.13. Water properties (curve ﬁts from data presented in Ref. [2])

¼ temperature of water (°C)

¼ thermal conductivity (W/m K) [R

¼ 0:9999]

¼ absolute viscosity (N s/m

) (kg/m s) [R

¼ 0:9999]

¼ kinematic viscosity (m

/s) [R

¼ 0:9999]

¼ density (kg/m

) [R

¼ 0:9999]

¼ speciﬁc heat (J/kg K) [R

¼ 0:9994]

¼ 6:5104167D

)10T

þ 0:00000018923611T

2:671875E

)05T

þ 0:0027103175T þ 0:5520119

¼ 0:000001ð0:000031538716146T

8:913055428199999D

)03T

þ 0:9795876934T

55:4567974T þ 1791:74424Þ

¼ 0:0001ð3:1770833333ð10

ÞT

0:0000089652777778T

þ 0:00098270833333T

0:055322222222T þ 1:7876666667Þ

¼ 0:000015451T

0:0059003T

0:019075T þ 1002:3052

¼ 0:000003216145833T

0:000798668982T

þ 0:0780295139T

3:0481614T

þ 4217:7377

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

2507

A.14. Thermal conductivity of copper (curve ﬁt Ref. [5]––R

=1)

copper

¼ thermal conductivity of copper (W/m K)

¼ temperature (°C)

copper

¼ 4:583333E

)09T

2:916667E

)06T

þ 6:541667E

)04T

0:1108333T þ 386

References

[1] ASHRAE, Handbook of Fundamentals. Atlanta, 1997.
[2] Rogers GFC, Mayhew YR. Thermodynamic and transport properties of ﬂuids: SI units. 4th ed. UK: Blackwell

Publishers; 1992.

[3] Lee RJ, DiGuilio RM, Jeter SM, Teja AS. Properties of lithium bromide–water solutions at high temperatures and

concentration. II. Density and viscocity. ASHRAE Trans 1990;96(Pt. 1):709–28.

[4] Herold EK, Radermacher R, Klein SA. Absorption chillers and heat pumps. CRS Press; 1996.
[5] Ozisik M. Heat transfer––a basic approach. McGraw-Hill Book Company; 1985.
[6] Howell RH, Sauer JH, Coad JW. Principles of HVAC. ASHRAE, Refrigeration Equipment, Section 18.21, 1998.
[7] Kreith F, Bohn MS. Principles of heat transfer. 5th ed. PWS Publishing Company; 1997.
[8] Nusselt in Ozisik M. Heat transfer––a basic approach. McGraw-Hill Book Company; 1985.
[9] Varma HK, Mehrotra RK, Agrawal KN. Heat transfer during pool boiling of LiBr–water solutions at

subatmospheric pressures. Int Commun Heat Mass Transf 1994;21(4):539–48.

[10] Morioka I, Kiyota M, Nakao R. Absorption of water vapor into a ﬁlm of aqueous solution of LiBr falling along

a vertical pipe. JSME Int J, Ser B 1993;36(2):351–6.

[11] Grossman G. Simultaneous heat and mass transfer in ﬁlm absorption under laminar ﬂow. Int J Heat Mass Transf

1983;26(3):357–71.

[12] Conlisk AT. Falling ﬁlm absorption on a cylindrical tube. AICHE J 1992;38(11):1716–28.
[13] Patnaik V, Perez-Blanco H, Ryan WA. A simple analytical model for the design of vertical tube absorbers.

ASHRAE Trans: Res 1993:69–80.

[14] Andberg JW, Vliet GC. Design guidelines for water–lithium bromide absorbers. ASHRAE Trans 1983;89(Part

1B):220–32.

[15] Kalogirou S, Florides G, Tassou S. Design and construction of a lithium bromide water absorption refrigerator.

In: Proceedings of CLIMA 2000 International Conference on CD-ROM, Naples, 2001.

[16] Abdullagatov IM, Magomedov UB. Measurements of thermal conductivity of aqueous LiCl and LiBr solutions.

Phys Chem 1997;101(4):708–11.

2508

G.A. Florides et al. / Energy Conversion and Management 44 (2003) 2483–2508

Document Outline

Design and construction of a LiBr-water absorption machine

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