Chapter SM 4: Heat and Mass Exchangers
SM 4.1 Introduction
In a number of HVAC components, water evaporates into or condenses out of an air stream.
In an evaporative cooler, a warm and relatively dry air stream is cooled through evaporation
from either a wet surface or water sprays. Such units are used for space cooling in the dry
southern western areas of the country. In a humidifier, water or steam is sprayed into an air
stream to increase the humidity level. Humidifiers are used to increase the humidity of dry and
uncomfortable air that enters the building in very cold climates. Air washers are used to
entrain particles and to clean the air flow through the spraying water into the air stream. These
units are sometimes used instead of mechanical filters. Enthalpy exchangers are devices that
exchange heat and moisture between two air streams, and often a desiccant is used as the
exchange medium. In summer these units are used to remove the heat and moisture from
incoming ventilation air and transfer it to exhaust air, which reduces the load on the cooling
coil. In winter operation the exchanger is used to preheat and humidify the ventilation air. All
of the devices described here fit specific niches in HVAC systems.
The basic thermodynamic, heat, and mass transfer principles for these devices will be
presented in this chapter. The performance of these heat and mass exchangers can usually be
expressed in terms of the parameters used for heat exchangers (Chapter 13) and cooling coils
(Chapter 14).
SM 4.2 Evaporative Coolers
An evaporative cooler is shown schematically in Figure 4.1. A warm and relatively dry air
stream, usually from the ambient, enters the device and passes over wetted pads or surfaces.
Evaporation of the water cools and humidifies the air stream. The exchange surfaces are
maintained wet by a circulating water flow. An alternative to using wetted surfaces is to spray
water into the air, but it is more difficult to control the degree of saturation in this method. The
evaporative cooler process is shown on a psychrometric diagram in Figure 4.1.
 w Tw
m
a
m
Tin
Tout
4.1
Figure 4.1 Schematic of evaporative cooler process
The air outlet state can be related to the inlet state through application of mass and energy
balances. A steady-state mass balance on the water is
 a w in  m
 wm
 a w out  0
m
(4.1)
where ma and m w are the air and water flow rates, respectively, and win and wout are the inlet
and outlet humidity ratios. Equation 4.1 relates the mass of water that evaporates to the humidity
levels. The energy balance for the process incorporates the water mass flow rate from equation
4.1
(4.2)
 a h in h out   m
 a w out w in  h w  0
m
where hin and hout are the enthalpies of the entering and leaving air /water vapor mixture,
respectively, and hw is the enthalpy of the entering water stream. For evaporator cooler
applications the last term in the energy balance is negligible (Section 4.4). The evaporative
cooling process is then essentially a constant enthalpy process for the air stream. Evaporative
cooling does not reduce the enthalpy of the air stream and thus would not reduce the load on a
cooing coil if the unit were followed by a conventional air conditioner. Evaporative coolers are
often used as the only source of cooling in very dry climates such as the Southwest. The air
stream entering the space is then cooler and more comfortable and the outlet humidity is not so
high that the air feels damp.
Because enthalpy and wet bulb lines are essentially parallel on a psychrometric chart, it is
also accurate to think of the process as occurring along a constant wet bulb line. An
effectiveness parameter is useful in characterizing the performance of an evaporative cooler. It is
convenient to define a temperature effectiveness in terms of the approach of the outlet
temperature to the wet bulb.
T T
(4.3)
  in out
Tin Twb
where Twb is the wet-bulb temperature of the inlet air stream. The effectiveness depends on the
transfer coefficients, the surface area, and air flow rate (the Ntu) in the same manner as for
sensible heat exchangers and cooling coils. Typical values of the effectiveness range between 60
to 80 %. Evaporative coolers are discussed in Section 5.7.
Evaporative coolers provide cooling at the expense of humidification of the air stream, but
are limited by the wet-bulb temperature of the air. It is possible to provide another stage of
cooling using an indirect evaporative cooler. In this device, an air stream is first cooled in an
evaporative cooler and then used as the cold flow in a heat exchanger to cool another air stream.
The cooled air stream can then be evaporatively cooled to provide a temperature lower than that
with a single stage evaporative cooler. The arrangement is shown schematically and on
psychrometric coordinates in Figure 4.2.
4.2
Water
Inlet
streams
T1
Water
T3
Ta
Supply
Tsupply
T2
Figure 4.2 Schematic operation of an indirect evaporator cooler.
The desired output is the cooled outlet air stream, which is at the humidity ratio of the incoming
ambient but at a lower temperature. The performance of the system can be determined in terms
of the effectivenesses of the evaporative cooler and heat exchanger, ec and hx, respectively. The
cold outlet temperature of the evaporative cooler, Tc, is evaluated in terms of the effectiveness
and wet bulb temperature using equation 4.3. The outlet temperature of the sensibly cooled
stream, Tout, is then given in terms of the heat exchanger effectiveness and the temperature
leaving the evaporative cooler, Tc. For equal capacitance rates for the heat exchanger, the outlet
temperature can be expressed in terms of the inlet temperature, the wet bulb temperature, and the
effectivenesses of evaporative cooler and heat exchanger as.
(4.4)
Tout  Tin   hx  ec Tin Twb 
Commercially manufactured indirect evaporative coolers usually combine the evaporation
and heat transfer effects into one unit. Water is brought in and flows down along sheets of
plastic or metal that also form passages between which the air flows. This allows the heat
transfer and evaporation to occur simultaneously. Example 4.2 illustrates the cooling that can be
obtained through an indirect evaporative cooler.
"Example 4.1 An indirect evaporative cooling system combines the evaporative cooler of example 4.1 (80
% effectiveness) with a heat exchanger of 70 % effectiveness. The air flow rate through both units is 2500
cfm and the ambient is 90 F and 5 % relative humidity. Determine the outlet state and the cooling
potential."
"Problem specifications"
T_a = 90 “F”
RH_a = 0.05
p_atm = 14.7 “psia”
V_dot = 2500 “cfm”
eff_EC = 0.8
eff_HX = 0.7
“Ambient temperature”
“Ambient RH”
“Ambient pressure”
“Volume flow rate”
“Evaporative cooler eff.”
“Heat exchanger eff”
"Determine the properties of the incoming air stream and the mass flow rate of the air streams"
T_wb_a = WetBulb(AirH2O,t=T_a, p=p_atm, r=RH_a) “F”
“Ambient wet-bulb”
w_a = HumRat(AirH2O,t=T_a, p=p_atm, r=RH_a) “lbm/lbm”
“Ambient humidity”
rho_a = density(AirH2O,t=T_a, p=p_atm, r=RH_a) “lbm/ft3”
“Ambient density”
cp_a = specheat(AirH2O,t=T_a, p=p_atm, r=RH_a) “Btu/lbm-F”
“Air specific heat”
4.3
m_dot = rho_a*V_dot*Convert(1/min,1/hr) “lbm/hr”
“Mass flow rate”
"For the first evaporative cooler, determine the outlet temperature. The outlet temperature will be the sink
for cooling the second air stream from the ambient."
eff_EC = (T_a -T_1)/(T_a - T_wb_a)
“Evaporative cooler eff”
"The humidity ratio of the coolant stream is"
w_2 = humrat(AirH2O,T=T_1, p=p_atm, B=T_wb_a) “lbm/lbm”
“Outlet humidity”
"For the heat exchanger, determine the outlet temperatures of the supply stream (T_3) and the stream that
was used to cool the exhaust stream (T_2). The capacitance rates of the supply and coolant stream are
equal. The effectiveness based on the supply stream is"
eff_HX = (T_a -T_3)/(T_a - T_1)
“Heat exchanger eff”
"The outlet humidity of the supply stream (w_3) equals that of the ambient since the supply stream is only
cooled sensibly."
w_3 =w_a “lbm/lbm”
“Humidity ratio”
"The outlet temperature of the coolant stream is determined. Because the supply and coolant stream
capacitance ratios are equal the energy balance reduces to"
(T_2- T_1) = (T_a - T_3) “F”
“Energy balance”
w_2 = w_1 “lbm/lbm”
“Humidity ratio”
"The supply stream is then evaporatively cooled in an evaporative cooler. The effectiveness is the same as
for the first evaporative cooler. The wet-bulb temperature that of the supply stream at state 3."
T_wb_3 = wetbulb(AirH2O,T=T_3, p=p_atm, w=w_3) “F”
“Supply wet-bulb”
eff_EC = (T_3 -T_supply)/(T_3 - T_wb_3)
“Evaporative cooler eff”
"The humidity of the supply state is"
w_supply = humrat(AirH2O,T=T_supply, p=p_atm, B=T_wb_3) “lbm/lbm”
“Supply humidity”
RH_supply = RelHum(AirH2O,T=T_supply,P=p_atm,w=w_supply)
“Supply RH”
"The sensible cooling that could be achieved for a building with a temperature of 78 F with the supply flow
is"
T_z = 78 “F”
“Zone temperature”
Cool = m_dot*cp_a*(T_z - T_supply) “Btu/hr”
“Cooling potential”
Tons = Cool*convert(Btu/hr,tons) “tons”
“Cooling potential”
Results and Discussion
The ambient has a wet bulb temperature of 55.4 F, and is cooled to 62.3 F in the first
evaporative cooler. The air stream with this temperature is then used to sensibly cool the supply
stream from the ambient from 90 F to 70.6 F. The wet-bulb temperature of this stream is reduced
to 47.0 F.
In the second evaporative cooler the supply stream is brought to a condition of 51.8 F and 70
% RH. The supply stream at this temperature could provide a cooling potential of 68,380 Btu/hr,
or 5.7 tons. This is 70 % more cooling potential than that provided by the single stage
evaporative cooler.
If the cooling potential is greater than desired, the effectiveness of the second evaporative
cooler can be decreased by reducing the water flow rate. This would increase the supply
temperature and reduce the relative humidity, and possible make for more comfortable
conditions.
Examples 4.1 and 4.2 illustrate how evaporative coolers can be employed to provide air
conditioning. The cooling cost is "free" in that only fan power is required. Fan power for an
4.4
evaporative cooler is generally small relative to the cooling benefit. Indirect evaporative coolers
have higher fan power requirements due to the pressure drop in the heat exchanger, and two
stages of evaporative cooling are the largest number of stages that is economically feasible.
4.3 Spray Dehumidifiers
Spray dehumidifiers are occasionally used to both cool and dehumidify air. A water flow is
cooled by a chiller and then introduced into the spray dehumidifier. The operation is similar to
that for a cooling tower, with the difference that the entering water stream is cold. The spray
dehumidifier differs from the evaporative cooler in that the water flow rate is high and only a
small amount of water evaporates. Inside the dehumidifier, the air becomes saturated and cooled.
A schematic of a spray dehumidifier and the psychrometric representation of the air and water
processes are shown in Figure 4.3.
Water
Tw, in
Inlet
Air
Tin
Outlet
Air Tout
Tw, out
Figure 4.3 Schematic operation of a spray dehumidifier
An effectiveness is defined in terms of enthalpies. The coldest and driest possible exit state
for the air stream is to leave in equilibrium with the water inlet state, which corresponds to
saturation at the temperature of the incoming water. The effectiveness is then defined as the
actual enthalpy change from inlet to outlet divided by the enthalpy difference between the air
inlet and saturated air at the water inlet temperature.
h in  h out

(4.5)
h in  h w,sat,in
For the conditions illustrated in Figure 4.3, the air inlet enthalpy is greater than that of saturated
air at the water inlet temperature. Energy will then be transferred from the air to the water
stream, the air will be cooled, and the humidity level will drop. The water condensed out of the
air will leave with the water flow. In this manner a cold water spray will actually dehumidify the
air. Example 4.3 illustrates the performance of a spray dehumidifier.
4.5
"Example 4.2 An air flow of 5000 L/s and at 30 C and 75 % RH enters a spray dehumidifier with an
effectiveness of 0.8 and an inlet water temperature of 10 C. Determine the outlet state of the air and the
water flow rate required for a 2 C temperature rise of the water through the spray dehumidifier."
"Problem Specifications"
p_atm = 101.3 "kPa"
T_in= 30 "C"
RH_in = 0.75
V_dot = 5000 "L/s"
eff = 0.8
T_w_in= 10 "C"
T_w_out = 12 "C"
"Atmospheric pressure"
"Air inlet temperature"
"Relative humidity"
"Air volume flow rate"
"Dehum. effectiveness"
"Water inlet temp."
"Water outlet temp"
"Properties of the air flow at inlet conditions"
m_dot_a = V_dot*rho_in*convert(L,m3) "kg/s"
"Water mass flow rate"
rho_in = density(AirH2O, T = T_in, p=p_atm, R=RH_in) "kg/m3""Air density"
w_in = HumRat(AirH2O, T = T_in, p=p_atm, R=RH_in) "kg/kg""Humidity ratio"
h_in = Enthalpy(AirH2O, T = T_in, p=p_atm, R=RH_in) "kJ/kg""Air enthalpy"
"Properties of the air flow at outlet conditions"
RH_out = 1
"Relative humidity"
w_out = HumRat(AirH2O, T = T_out , p=p_atm, R=RH_out ) "kg/kg""Humidity ratio"
h_out = Enthalpy(AirH2O, T = T_out , p=p_atm, R=RH_out ) "kJ/kg""Air enthalpy"
"Properties of the water flow"
h_w_in= Enthalpy(Water,T=T_w_in,P=p_atm) "kJ/kg"
h_w_out = Enthalpy(Water,T=T_w_out,P=p_atm) "kJ/kg"
"Water enthalpy"
"Water enthalpy"
"Spray dehumidifier effectiveness, equation 4.5"
eff = (h_in- h_out)/(h_in- h_w_sat_in)
"Defn of effectiveness"
h_w_sat_in= Enthalpy(AirH2O, T = T_w_in, p=p_atm, R=1) "kJ/kg""Sat air enth. at T_w_in"
"Mass balance on the dehumidifier to determine the rate at which moisture is condensed out of the air
stream"
m_dot_cond = m_dot_a*(w_in- w_out) "kg/s"
"Condensation flow rate"
"Energy balance on the dehumidifier to determine the water flow rate that will produce a 2 C rise in the
water temperature. The energy of the condensed water is included in the energy balance and its temperature
is taken as that of the inlet water."
m_dot_a*(h_in- h_out) + m_dot_w*h_w_in- m_dot_w*h_w_out -m_dot_cond*h_w_out = 0 "kW"
Results and Discussion:
Solving the set of equations yields the amount of moisture condensed out of the air as 0.057
kg/s, an inlet water flow rate of 27.94 kg/s, and an outlet of 28.00 kg/s. The condensate flow rate
is relatively small compared to the total water flow rate, but there still is some water addition to
the flow stream. Ultimately this condensate flow will need to be drained off.
The air temperature is dropped from 30 C to 14.2 C. Even though the air leaves at saturated
conditions, the humidity ratio is reduced from 0.0202 kgw/kga to 0.0101 kgw/kga. The air is
cooled enough and dried enough to be used for space conditioning.
A modification of the spray cooling process is to use a cold liquid desiccant solution instead
of a chilled water flow. The water in the air stream is condensed and goes into the desiccant
solution. Because of its affinity for water, at the same temperature the liquid desiccant allows the
4.6
air to be dehumidified more than with the chilled water. The desiccant will eventually become
saturated with water and must then be regenerated by heating to evaporate the absorbed water.
A spray cooler uses a chilled water or liquid desiccant flow to provide a cold and
dehumidified air stream. The end result is the same as if a conventional cooling coil were used.
The advantage of the spray cooler is that the water does not need to be as cold as with a coil
because the air does not need to be cooled to the dew point. This reduces the chiller power.
However, the water flow rate is generally significantly larger than that through a chilled water
coil, and the cooling power requirement might be more.
The water flow removes particles from the air and acts as a filter, which is usually beneficial.
Eliminators need to be placed downstream of the unit to prevent carry-over of the water, and the
water quality needs to be maintained for health and safety reasons. Because the use of cooling
coils for cooling buildings is well established, spray dehumidifiers are not widely used.
4.4 Evaporative Condensers
An evaporative condenser is a heat exchanger that is continuously cooled by a flow of
evaporating water at the same time that the refrigerant is condensed. Condensation of the
refrigerant takes place inside tubes as in a normal condenser. Water sprayed over the tubes flows
downward and evaporates into an air flow from the atmosphere that is induced by a fan and flows
upward. A schematic of an evaporative condenser is shown in Figure 4.4.
Refrigerant
Water
flow
Air
flow
Makeup water
Figure 4.4 Schematic of an evaporative condenser
Because the air is cooled by the evaporation of water the air stream can approach the wet
bulb temperature, providing a lower temperature for the heat rejection. Most of the energy
transfer goes into evaporating the water flow and so the temperature of the air stream does not
increase much. As a result, the refrigerant in an evaporative condenser is condensed at a lower
temperature than in an air-cooled condenser, reducing the chiller power. An evaporative
condenser is also a more compact device than a condenser-cooling tower combination that could
provide the same benefits.
The performance of the evaporative condenser can be represented in a manner similar to that
for a cooling coil. The heat and mass transfer processes in an evaporative condenser are the
same as in the cooling coil, with the difference that the heat and moisture flows are into the air
4.7
instead of out of the air. The detailed analysis of Section 15.3 and the analogy approach of
Section 15.4 therefore apply to the evaporative condenser. An energy balance on a section of the
evaporative condenser, similar to that of Figure 4.5, yields an equation similar to the energy
balance relation for the coil.
d hA
d hr
(4.6)
mA
 mr
d AA
d Ar
where m A and m r are the flow rates of ambient air and refrigerant, respectively, hA and hr are
the enthalpies of the moist air and refrigerant, respectively, and AA and Ar are the heat transfer
areas on the air and refrigerant side of the condenser, respectively. During the condensation
process the refrigerant temperature is constant but the enthalpy decreases as vapor condenses.
The heat transfer from the refrigerant to the air stream is related to the heat transfer conductance
between the refrigerant and the condenser surface and the heat and mass transfer conductances
between the water film and the air.
The development parallels that of the cooling coil, and the energy change of the air stream is
given by an equation similar to that for a cooling coil:
d hA
U*

(4.7)
 h A  h r,sat 
d AA
mA
where hr, sat is the enthalpy of saturated air at the refrigerant temperature and U* is the overall
energy transfer conductance. To illustrate the similarity to the cooling coil, it is assumed that the
amount of superheat and subcooling is small relative to the condensation. The effect of
superheat can be included following the approach shown in Section 4.3. The similarity of the
evaporative condenser to the cooling coil leads to a definition of effectiveness similar to that for
the cooling coil:
h A,out  h A,in
(4.8)

h r,sat  h A,in




The heat transfer can then be computed as the product of effectiveness, air mass flow rate, and
the enthalpy difference times the enthalpy difference between saturated air at the refrigerant
temperature and that at the inlet:
Q   mA  h A,sat  h A,in 
(4.9)
As with the cooling coil, the effectiveness is a function of the number of transfer units and
capacitance rate ratio. The number of transfer units for a wet surface depends upon the overall
conductance and is given by
U* A A
Ntu * 
(4.10)
mA
Because the refrigerant temperature is essentially constant the capacitance rate ratio is zero.
Example 4.4 illustrates the determination of heat flow and refrigerant temperature for an
evaporative condenser.
"Example 4.3 A refrigeration system transfers 120,000 Btu/hr to the ambient using an evaporative
condenser with an effectiveness of 0.75. The air flow is 10,000 cfm and the air enters at 80 F and 40 % RH.
4.8
Determine the temperature of the condensing refrigerant. Compare the refrigerant temperature for the
evaporative condenser to that for an air-cooled condenser with the same air flow rate and effectiveness."
“The EES equations are entered sequentially and the solution can be obtained directly.”
"Problem Specifications"
Q_dot = 120000 “Btu/hr”
CFM= 10000 “cfm”
T_a = 80 “F”
RH_a= 0.4
p_atm = 14.7 “psia”
“Heat flow rate”
“Air Volume flow rate”
“Air temperature”
“Relative humidity”
“Atmospheric pressure”
"Air properties and mass flow rate"
h_a_i = Enthalpy(AirH2O, T=T_a, P=p_atm, R=RH_a) “Btu/lbm”
rho_a = density(AirH2O, T=T_a, P=p_atm,R=RH_a) “lbm/ft3”
cp_a = SpecHeat(AirH2O, T=T_a, P=p_atm, R=RH_a) “Btu/lbm-F”
T_wb = WetBulb(AirH2O, T=T_a, P=p_atm, R=RH_a) “F”
m_dot_a = CFM*rho_a*convert(1/min,1/hr) “lbm/hr”
“Air enthalpy”
“Air density”
“Specific heat”
“Wet-bulb temperature”
“Air mass flow rate”
"Evaporative condenser performance. The heat flow rate is the condenser rejection rate. The condenser
effectiveness is given by equation 4.9. This yields the enthalpy of saturated air at the refrigerant
temperature, which in turn yields the refrigerant temperature."
eff = 0.75
“Effectiveness”
Q_dot = eff*m_dot_a*(h_r_sat - h_a_i) “Btu/hr”
“Heat transfer rate”
h_r_sat = Enthalpy(AirH2O, T=T_r_EC, P=p_atm, R=1) “Btu/lbm”
“Sat air enthalpy”
"Sensible heat exchanger performance. With the same effectiveness this yields the refrigerant temperature
for the dry exchanger."
Q_dot = eff*m_dot_a*cp_a*(T_r_HX - T_a) “Btu/hr”
“Heat transfer rate”
Results and Discussion
For an evaporative condenser with an effectiveness of 0.75 transferring 120,000 Btu/hr to air
at 80 F and 40 % RH, the enthalpy of saturated air at the refrigerant temperature must be 32.4
Btu/lbm. This corresponds to a temperature of 68.1 F, which is also then the temperature at
which the refrigerant condenses. The thermal resistances between the refrigerant and air stream
are assumed negligible. The refrigerant condensing temperature is lower than the air temperature
due to the evaporation of the water from the coil surfaces into the air stream. It is higher, though,
than the wet bulb temperature of 63.5 F, which is the lowest temperature that could be achieved
with an evaporative cooler.
For an air-cooled condenser, the refrigerant temperature would be determined from the
expression for heat transfer for a sensible heat exchanger (Section 13.4). The refrigerant
temperature is 95 F.
The evaporative condenser reduces the condensing temperature of the refrigerant
significantly over that for an air-cooled condenser. For the air-cooled temperature, the
refrigerant condenses 15 F above the dry bulb air temperature, whereas with the evaporative
condenser the condensing temperature is 12 F lower than the air temperature. The lower
temperature would significantly increase the performance of the refrigerant system. Evaporative
heat transfer is more effective than "dry" heat transfer.
4.9
4.5 Enthalpy Exchangers
Enthalpy exchangers transfer both thermal energy and moisture between two air streams.
Because both the temperature and humidity of the two streams change, these devices are termed
enthalpy exchangers. Such units are commonly used for energy recovery in ventilation systems.
For example, in winter time in Northern climates the incoming ventilation flow from the
outdoors needs to be heated before it enters the space. Under very cold ambient conditions it is
also common to add humidity to the air stream, usually after the air has been heated. Enthalpy
exchangers transfer heat and moisture from the relatively warm and humid exhaust air to the
incoming ventilation air, which increases both the temperature and the moisture levels and
reduces the heating demand in winter. In a similar fashion, the enthalpy exchanger would cool
down and dehumidify the ventilation air in summer time by transferring heat and moisture
entering with the ventilation stream to the exhaust stream, which would reduce the load on the air
conditioner. To successfully employ an enthalpy exchanger, the building must be “tight” to
prevent infiltration and exfiltration. Many commercial buildings have installed enthalpy
exchangers, and they are becoming more common in well-constructed residential buildings.
There are two general classes of enthalpy exchangers, indirect and direct. Indirect enthalpy
exchangers are desiccant wheels that rotate relatively fast. As discussed in relation to Figure 4.9,
the state of the air that leaves the wheel before the fast wave exits is at the entering state of the
other air stream. Thus, if the desiccant wheel is turned fast enough so that the first wave does
not exit the bed, the state of the air exiting the wheel on the ventilation side will be at the
temperature and humidity level of the exhaust state. The incoming ventilation air would enter
the space at the same conditions as the exhaust air and would be fresh air from the ambient.
Indirect enthalpy exchangers are constructed similar to desiccant dehumidifiers. One
difference is that since the air is not dried to a very low humidity level the amount of desiccant
can be much less than for a dehumidifier. Enthalpy exchangers are commonly made from
aluminum sheets coated with a polymeric desiccant, and then wound spirally to form a matrix
with triangular air passages. A section of a rotary enthalpy exchanger is shown schematically in
Figure 4.13a.
Aluminum sheet
Desiccant-coated
foil sheets
Exhaust
air stream
Ventilation
air stream
Desiccant-coated
partition
a) Indirect enthalpy exchanger
b) Direct enthalpy exchanger
Figure 4.5a. Schematic of a rotary enthalpy exchanger surface.
4.5b. Schematic of a direct transfer enthalpy exchanger
4.10
Direct transfer enthalpy exchangers, shown in Figure 4.13b, are constructed similarly to
indirect transfer heat exchangers, but the partition that separates the two streams allows both heat
and moisture to be transferred. The separating surface is porous to water vapor and often treated
with a desiccant. Moisture is adsorbed on the high humidity side, diffuses through the surface to
the low humidity side, and then desorbs into the low humidity air stream. The pores allow
moisture to transfer from one side to another but not air molecules.
The processes that the air stream undergoes are the same for both direct and indirect enthalpy
exchangers. For an exchanger with the same flow rates and transfer coefficients for both flows,
the outlet states lie on a line connecting the two inlet states as shown on psychrometric
coordinates in Figure 4.14 for an air-conditioning situation in which the ambient is hotter and
more humid than the zone.. In an ideal exchanger, the outlet state of each stream equals the inlet
of the other. In actual exchangers the heat and mass transfer coefficients are finite and less
moisture and heat are transferred, producing a difference between the outlet and inlet states.
Exhaust
stream inlet
State 3
Ventilation
inlet
State 1
Ventilation
stream inlet
State 1
Ventilation
stream outlet
State 2
4
2
Exhaust
inlet
State 3
Exhaust
stream outlet
State 4
Figure 4.6 Processes for an enthalpy exchanger
For rotary wheels, the Lewis number is close to unity, and the convective heat and mass
transfer coefficients are then directly related (Section 5.4). The process is then as shown in
Figure 4.14. In a direct transfer device, the transfer coefficients are also equal, but the separating
surface offers more resistance to mass transfer than to heat transfer. Thus the process lines are
not along the line connecting the two inlets, but follow paths as shown in Figure 4.15. As the
mass transfer resistance becomes very large, there is no moisture transfer and the device becomes
a sensible heat exchanger only.
4.11
Mass transfer resistance
of separating surface
Infinite
Ventilation
inlet
State 1
Large
Zero
Exhaust inlet
State 3
Figure 4.7 Effect of mass transfer resistance on enthalpy exchanger processes
The performance of an enthalpy exchanger is characterized by an enthalpy effectiveness,
which is defined as the total enthalpy change of one of the streams relative to the maximum
possible total enthalpy change. For a balanced exchanger in which the mass flow rates of the
ventilation and exhaust streams are equal, the effectiveness is an enthalpy ratio only. Because
the desired state is that of the ventilation flow into the building, the effectiveness is based on the
enthalpy difference of the ventilation flow rate.
h h
h  1 2
(4.11)
h1  h 3
When the Lewis number is unity the outlet states lie on a line connecting the inlet states and
only the enthalpy effectiveness relation is needed to characterize the performance. However,
when there is an added mass transfer resistance in the matrix another effectiveness is needed. It
is conventional to define a sensible effectiveness to reflect the thermal energy exchange. The
thermal effectiveness is defined as
T T
T  1 2
(4.12)
T1  T3
The enthalpy effectiveness is always less than, or at best equal to, the sensible effectiveness. A
mass transfer effectiveness that relates the humidity ratio change to the maximum possible
change is also defined:
w  w2
(4.13)
m  1
w1  w 3
For commercially available exchangers, the enthalpy and thermal effectiveness values are
typically in the range of 0.50 to 0.75.
4.12
The enthalpy exchanger provides significant reductions in moisture as well as temperature,
and is preferable to a sensible heat exchanger for energy recovery during the air conditioning
season. The enthalpy recovery exchanger performance, in terms of reducing the load on the
compressor, is three to four times that of a sensible heat exchanger. In addition, the reduction in
design load can result in a significantly reduced installed capacity of the air conditioner, which
produces additional savings (Steich et al., 1995).
In the heating season the advantages of an enthalpy exchanger over a sensible exchanger are
not as significant. The humidity levels in winter, both inside buildings and outdoors, are low
and, relative to summer, there is not much to be gained by transferring moisture. In contrast the
temperature differences between the building zones and the ambient are much larger than in
summertime, and there can be significant savings due to heat transfer. The reduction in heating
energy through the use of an enthalpy exchanger is only 10 to 20 % greater than that obtained
using a sensible heat exchanger.
In wintertime condensation or freezing may occur inside either an enthalpy or sensible heat
exchanger. For an enthalpy exchanger, when the ambient temperature is very low the line
connecting the ambient and building zone states may intersect the saturation line, as shown
schematically in Figure 4.4. This means that at some point in the exchanger the exhaust stream is
cooled below the local dew point, causing the moisture to condense. If the dew point is below
freezing, ice will form. Although enthalpy exchangers can accommodate some amount of
condensation and freezing, it is necessary to prevent an excessive amount of moisture from
accumulating by lowering the effectiveness. In a rotary unit, the effectiveness is reduced by
slowing the rotational speed.
Point of condensation
for a sensible heat
exchanger
Point of condensation
for an enthalpy
exchanger
Zone state
(exhaust
inlet)
Ambient state
(ventilation
inlet)
Figure 4.8 Condensation in an enthalpy exchanger during wintertime operation
The problem of condensation and freezing is accentuated in a sensible heat exchanger, as
also shown in Figure 4.16, since the zone air is cooled at a constant humidity ratio and has a
4.13
higher dew point temperature. This further lowers the energy savings of the sensible heat
recovery exchanger relative to the enthalpy exchanger, especially in very cold climates.
Example 4.6 illustrates the calculation of the performance advantage of an enthalpy
exchanger during the air-conditioning season.
"Example 4.4 In a commercial building, 5000 cfm of outdoor air at 95 F dry bulb and 75 F wet bulb are
brought into the space. The zone conditions are 75 F and 40 % RH. An exchanger is to be employed to
precondition the outdoor air using exhaust air before it enters the cooling coil. The exchanger is a direct
transfer type as shown in Figure 4.13b with passages one-eighth inch high and triangular in shape. The
effectivenesses for temperature and mass transfer are 0.75 and 0.65, respectively. The exchanger is 4 ft
long in the flow direction and 2.5 ft high. The same geometry can be used for a heat exchanger that only
transfers heat or one that transfers both heat and moisture. Determine the ventilation load for a
conventional system without an exchanger, a system using a heat recovery exchanger, and one using an
enthalpy exchanger."
"Problem specifications"
p_atm = 14.7 "psia"
V_dot = 5000 "cfm"
T_a = 95 "F"
Twb_a= 75 "F"
Eff_T = 0.75
Eff_m = 0.65
"Atmospheric pressure"
"Ventilation flow rate"
"Ambient temperature"
"Ambient wet-bulb"
“Temperature eff.”
“Humidity effectiveness”
"Determine the properties of the ambient air and the mass flow rate of the ventilation air."
h_a = Enthalpy(AirH2O,T=T_a,P=p_atm,B=Twb_a) "Btu/lbm"
"Ambient enthalpy"
w_a = HumRat(AirH2O,T=T_a,P=p_atm,B=Twb_a) "lbm/lbm"
"Ambient humidity ratio"
rho_a = density(AirH2O,T=T_a,P=p_atm,B=Twb_a) "lbm/ft3"
"Ambient density"
m_dot = V_dot*rho_a*convert(1/min,1/hr) "lbm/hr"
"Mass flow rate"
"Determine the zone air properties. "
T_z = 75 "F"
RH_z = 0.40
h_z = Enthalpy(AirH2O,T=T_z,P=p_atm,R=RH_z) "Btu/lbm"
w_z = HumRat(AirH2O,T=T_z,P=p_atm,R=RH_z) "lbm/lbm"
"Zone temperature"
"Zone relative humidity"
"Zone enthalpy"
"Zone humidity ratio"
Eff_T = (T_a - T_o)/(T_a - T_z)
"Temperature eff"
"For a heat recovery exchanger, the outlet state is at the temperature T_o and the inlet humidity ratio w_a"
h_o_HX = Enthalpy(AirH2O,T=T_o,P=p_atm,w=w_a) "Btu/lbm"
"Outlet enthalpy for HT"
Eff_m = (w_a - w_o)/(w_a - w_z)
"MT effectiveness"
"For an energy recovery exchanger, the outlet enthalpy is at the temperature T_o and the humidity ratio
w_o"
h_o = Enthalpy(AirH2O,T=T_o,P=p_atm,w=w_o)
"Outlet enthalpy for MT"
"The enthalpy effectiveness is based on the outlet enthalpy of the energy recovery exchanger"
Eff_h = (h_a - h_o)/(h_a - h_z)
"Enthalpy effectivenss"
"Determine the ventilation loads for the heat transfer and mass transfer exchangers. "
AC_ht = m_dot*(h_o_HX - h_coil)*convert(Btu/hr,tons) "tons"
"Vent load - HX exch."
AC_mt = m_dot*(h_o - h_coil)*convert(Btu/hr,tons) "tons"
"Vent load - MT exch."
"For comparison, the ventilation load for a conventional system with a coil outlet temperature of 50 F is
also determined."
T_coil = 50 "F"
"Outlet temp for coil"
h_coil = Enthalpy(AirH2O,T=T_coil,P=p_atm,R=1) "Btu/lbm"
"Outlet enthalpy for coil"
AC_conv = m_dot*(h_a - h_coil)*convert(Btu/hr,tons) "tons"
"Vent load - coil"
4.14
Results and Discussion
Without any exchanger the ambient air would be cooled and dehumidified from ambient
conditions to 50 F and saturated by passing through a coil. With a ventilation flow rate of 20,987
lbm/hr, the ventilation load without any exchanger is 31.5 tons.
For the heat transfer only exchanger, the outlet temperature is dropped from the ambient
temperature of 95 F to 80.0 F, but the humidity ratio is the same as the ambient at 0.01405
lbmw/lbma, yielding an outlet air enthalpy of 34.6 Btu/lbm. The ventilation load is 25.1 tons,
which is about 80 % of that without an exchanger.
With an enthalpy exchanger, both the temperature and humidity ratio are decreased. The
outlet temperature is 80.0 F, which is the same as for heat transfer only. The humidity ratio is
reduced from the ambient to 0.00970 lbmw/lbma, yielding an outlet air enthalpy of 29.9 Btu/lbm.
This is significantly lower than that for a heat transfer only exchanger. The corresponding
ventilation load is 4.8 tons, which is about 53 % of that without an exchanger.
For a system that operated 4000 hours per year, the enthalpy exchanger would produce an
energy cost savings of about $ 2,100 per year at electrical costs of $ 0.10/kWh. There is also a
reduction in the required installed coil and air conditioner capacity of about 15 tons. At a
representative incremental cost of $ 250/ton, this amounts to about $ 3,500. The savings in
operating and equipment costs would probably pay for the added cost of the heat and mass
exchanger in relatively short time.
Enthalpy exchangers significantly reduce the cost of operating air conditioning equipment.
Equally important, enthalpy exchangers allow the installed capacity of the air-conditioning
equipment to be reduced. The cooling load met by the enthalpy exchanger truly reduces the load
on the cooling coil, and the design of the system can take this into account. The reduction in cost
of the conventional equipment is often greater than the added cost of the enthalpy exchanger.
4.6 Summary
The evaporation of water into an air stream can be used to condition a building space. An
evaporative cooler provides cooling of an air stream, although with a corresponding increase in
humidity. This device is appropriate in locations such as the southwest where ambient humidity
levels are low. Indirect evaporative coolers use evaporative cooled air as a heat rejection source,
and produce cooling without humidification. These devices extend the climate range for which
evaporation alone can be used for space conditioning. The cost of operation of these devices is
roughly an order of magnitude less than cooling with conventional cooling units. In combination
with conventional cooling systems, evaporative coolers reduce the maximum load on the system.
This allows smaller capacity and lower cost cooling equipment to be installed.
Evaporative condensers allow refrigeration equipment to reject heat to air at the wet bulb
temperature instead of the higher dry bulb temperature as in dry condensers. Evaporative
condensers thus allow the cooling equipment to operative more efficiently. The reduction in
compressor power is less than the parasitic power for the extra fans and pumps of the evaporative
condenser.
4.15
Enthalpy exchangers pre-condition incoming ventilation air by transferring heat and moisture
to the exhaust air steam, significantly reducing the enthalpy of the incoming air. The
corresponding ventilation load on the heating or cooling system is significantly reduced. The
reduction in humidity level has a much larger impact on energy savings during the cooling
seasons than the heating season. Enthalpy exchangers are more effective than sensible
exchangers during the cooling system, while sensible heat exchangers are nearly as effective
during winter and are somewhat less costly. Installing an enthalpy exchanger reduces the
maximum load on the air-conditioning equipment and allows smaller equipment to be installed.
4.7 Nomenclature
A
h
w
W
area
specific enthalpy
mass flow rate
number of transfer units for heat
transfer
number of transfer units for mass
transfer
heat flow rate
temperature
overall unit mass transfer
conductance
humidity ratio
moisture content


effectiveness
relative humidity
m
Ntu
Ntu*
Q
T
U*
Subscripts
A
ambient state
a
air
ec
evaporative cooler
f
liquid phase
g
vapor phase
h
enthalpy
hx
heat exchanger
in
in, inlet
m
mass transfer
out
out, outlet
r
refrigerant
sat
saturation conditions
T
temperature
w
water
wb
wet-bulb
z
zone
4.8 References
ASHRAE Handbook, HVAC Systems and Equipment, Chapter 19, ASHRAE, Atlanta GA, 2004
Duffie, J. A., W. A. Beckman, and J. W. Mitchell, “Solar Cooling,” in Solar Energy Technology
Handbook, W.C. Dickenson (Ed.), Marcel Dekker, New York, 1980.
Evaporative Cooling, Munters Corporation, Fort Meyers, FL, 1994.
Hollands, K. G. T., "Analysis and Design of Evaporative Cooler Pads," Mechanical and
Chemical Engineering Transactions, p 55 - 61, 1970
Indirect Evaporative Cooling, Vari-Cool, Santal Rosa, CA, 1980.
Jalalzadeh-Azar, A., S. Slayzak, R. Judkoff, T. Schaffhauser, and R. DeBlasio, “Performance
Assessment of a Desiccant Cooling System in a CHP Application Incorporating an IC
Engine,” IJDER, 2005
Jurinak, J., J. W. Mitchell, W. A. Beckman, "Open-Cycle Desiccant Air Conditioning as an
Alternative to Vapor Compression Cooling in Residential Applications," ASME Trans., 106,
252-260 (1984).
4.16
Klein, H., S.A. Klein, J. W. Mitchell, "Analysis of Regenerative Enthalpy Exchangers,"
International Journal of Heat Transfer, (1989).
Lowenstein, A., S. Slayzak, and E. Kozubal, “A Zero Carryover Liquid-Desiccant Air
Conditioner For Solar Applications,” Proceedings Of Isec2006 ASME International Solar
Energy Conference July 8-13, 2006, Denver, Co
Maclaine-Cross, I. L. and P. J. Banks, "Coupled Heat and Mass Transfer in RegeneratorsPredictions Using an Analogy with Heat Transfer," International Journal of Heat and Mass
Transfer, Vol 15, no. 6, pg 1225 - 1242, 1972.
Manley, D. L., K. L. Bowlen, and B. M. Cohen, "Evaluation of Gas-Fired Desiccant-Based Space
Conditioning for Supermarkets," Trans. ASHRAE, V 91, Pt 1, 1985.
Peterson, J. L., "An Effectiveness Model for Indirect Evaporative Coolers," Trans. ASHRAE, V
99, Pt 2, 1993.
Steich, G., Mitchell, J.W., Klein, S.A., "Performance of Rotary Heat and Mass Exchangers" Int.
J. of HVAC and Refrigerating Research, 308,17, (1995).
SuperAire Design Manual, Cargocaire Corporation, Amesbury, MA.
Tanaka, O., "An Analysis of Simultaneous Heat and Water Vapour Exchange through a Total
Heat Exchanger of the Paper Plate Fin Type," report of Mitsubishi Corporation, 1982.
4.9 Problems
Problems in English units
4.1 A supply air temperature lower than 65 F and a humidity ratio lower than 0.006 lbmw/lbma
can provide satisfactory conditions in an occupied space.
a. On a psychrometric chart show the region of ambient conditions for which an
evaporative cooler would be suitable and the values of effectivenesses that are needed
to achieve the desired supply state.
b. On a psychrometric chart show the region of ambient conditions for which a single
stage indirect evaporative cooler would be suitable and the values of effectivenesses
that are needed to achieve the desired supply state.
c. Draw some conclusions from your results.
4.2 A single stage indirect evaporative cooler consists of a 90 % effectiveness evaporative
cooler and a 75 % effectiveness heat exchanger. The system is designed to be the sole
cooling source for a building load of 10 tons of cooling with a SHR of 0.8 at ambient
conditions of 80 F and 20 % RH. The zone set temperature is to be 75 F with the humidity
within the ASHRAE comfort zone.
a. Determine the air flow rate (cfm) and zone humidity level (RH and humidity ratio) at
design conditions.
b. For operating ambient conditions between 70 and 90 F and 20 and 40 % relative
humidity, the system uses the indirect evaporative cooler to precool air that then enters
the coil of a vapor compression system. Determine the energy savings of the combined
system over a conventional air-conditioning system.
4.17
4.3
4.4
4.5
4.6
4.7
c. Draw some conclusions from your results.
An air flow of 500 cfm and at 90 F and 65 % RH enters a spray dehumidifier with an
effectiveness of 0.8. The chilled water temperature is 45 F and the flow rate is 6000
lbm/hr.
a. Determine the outlet state of the air, the amount of water condensed, and the
temperature rise of the water flow.
b. Determine and plot on psychrometric coordinates the air outlet state as the spray dryer
effectiveness is varied between 0 and 1.0.
c. Draw some conclusions from your results.
An evaporative condenser with an effectiveness of 0.7 operates with 30,000 cfm of air at a
condition of 85/70 (dry bulb/wet bulb).
a. Determine the condenser capacity (Btu/hr and tons) and the amount of water
evaporated for a condensing temperature of 78 F.
b. For the capacity found in part a, determine and plot the condensing temperature over
the range of effectiveness of 0.2 to 0.9.
c. Draw some conclusions from your results.
An evaporative condenser is to be designed for an air conditioner that rejects 500,000
Btu/hr. The design conditions are 95/80 (dry bulb/wet bulb) and the design effectiveness is
0.7. The evaporative condenser is to be compared to a dry condenser with the same
effectiveness.
a. Determine the condensing temperatures and air flow rates for the evaporative and dry
condensers at design conditions.
b. At the design air flow rates, determine the condensing temperatures for the two units
over an range of ambient temperature and humidity representative of operation.
c. Draw some conclusions from your results.
A commercial building application has an outdoor air requirement of 10,000 cfm. In
summer time the average conditions are 85 F dry bulb, and 65 F wet bulb for 2000 hours
per year. In winter the average conditions are 25 F and 80 % RH for 1000 hours. The zone
is maintained at 75 F and 40 % RH in summer and 70 F and 20 % in winter. The air
conditioner has a COP of 3.4 and electrical costs are $ 0.11/kWh, and heating costs are $
10/106 Btu. Determine the seasonal energy savings for
a. An enthalpy exchanger with a heat transfer effectiveness of 0.7 and a mass transfer
effectiveness of 0.65
b. A sensible heat exchanger with an effectiveness of 0.7.
c. Plot the processes for both exchangers and for both seasons on psychrometric
coordinates.
d. Draw some conclusions from your results.
An exchanger is considered for a commercial building operation in Washington D.C. to
recover exhaust heat in the air-conditioning season. The indoor conditions are 70 F and 45
% RH, the average summer ambient conditions are 85 F and 60 % RH, and the flow rate is
4000 cfm. There are 1900 hours of operation for the unit. A sensible heat exchanger
4.18
would cost $ 7000, and an enthalpy exchanger would cost $ 8000. Both would have an
effectiveness of 0.7. Determine whether either exchanger is cost effective and, if so, which
one is the more cost effective. The cooling system has a COP of 3 and electrical costs are
$0.085/kWh.
Problems in SI Units:
4.8 A supply air temperature lower than 18 C and a humidity ratio lower than 0.006 kgw/kga
can provide satisfactory conditions in an occupied space.
a. On a psychrometric chart show the region of ambient conditions for which an
evaporative cooler would be suitable and the values of effectivenesses that are needed
to achieve the desired supply state.
b. On a psychrometric chart show the region of ambient conditions for which a single
stage indirect evaporative cooler would be suitable and the values of effectivenesses
that are needed to achieve the desired supply state.
c. Draw some conclusions from your results.
4.9 A single stage indirect evaporative cooler consists of a 90 % effectiveness evaporative
cooler and a 75 % effectiveness heat exchanger. The system is designed to be the sole
cooling source for a building load of 40 kW of cooling with a SHR of 0.8 at ambient
conditions of 27 C and 20 % RH. The zone set temperature is to be 24 C with the humidity
within the ASHRAE comfort zone.
a. Determine the air flow rate (L/s) and zone humidity level (RH and humidity ratio) at
design conditions.
b. For operating ambient conditions between 20 and 35 C and 20 and 40 % relative
humidity, the system uses the indirect evaporative cooler to precool air that then enters
the coil of a vapor compression system. Determine the energy savings of the combined
system over a conventional air-conditioning system.
c. Draw some conclusions from your results.
4.10 An air flow of 500 L/s and at 35 C and 60 % RH enters a spray dehumidifier with an
effectiveness of 0.8. The chilled water temperature is 7 C and the flow rate is 1.5 kg/s.
a. Determine the outlet state of the air, the amount of water condensed, and the
temperature rise of the water flow.
b. Determine and plot on psychrometric coordinates the air outlet state as the spray dryer
effectiveness is varied between 0 and 1.0.
c. Draw some conclusions from your results.
4.11 An evaporative condenser with an effectiveness of 0.7 operates with 20,000 L/s of air at a
condition of 30/20 (dry bulb/wet bulb).
a. Determine the condenser capacity and the amount of water evaporated for a
condensing temperature of 25 C.
b. For the capacity found in part a, determine and plot the condensing temperature over
the range of effectiveness of 0.2 to 0.9.
c. Draw some conclusions from your results.
4.19
4.12 An evaporative condenser is to be designed for an air conditioner that rejects 200 kW. The
design conditions are 35/28 (dry bulb/wet bulb) and the design effectiveness is 0.7. The
evaporative condenser is to be compared to a dry condenser with the same effectiveness.
a. Determine the condensing temperatures and air flow rates for the evaporative and dry
condensers at design conditions.
b. At the design air flow rates, determine the condensing temperatures for the two units
over an range of ambient temperature and humidity representative of operation.
c. Draw some conclusions from your results.
4.13 A commercial building application has an outdoor air requirement of 5,000 L/s. In summer
time the average conditions are 30 C dry bulb, and 20 C F wet bulb for 2000 hours per
year. In winter the average conditions are -10 C and 80 % RH for 1000 hours. The zone is
maintained at 24 C and 40 % RH in summer and 22 C and 20 % in winter. The air
conditioner has a COP of 3.4 and electrical costs are $ 0.11/kWh, and heating costs are $
0.035/kWh. Determine the seasonal energy savings for
a. An enthalpy exchanger with a heat transfer effectiveness of 0.7 and a mass transfer
effectiveness of 0.65
b. A sensible heat exchanger with an effectiveness of 0.7.
c. Plot the processes for both exchangers and for both seasons on psychrometric
coordinates.
d. Draw some conclusions from your results.
4.14 An exchanger is considered for a commercial building operation in Washington D.C. to
recover exhaust heat in the air-conditioning season. The indoor conditions are 22 C and 45
% RH, the average summer ambient conditions are 30 C and 60 % RH, and the flow rate is
2,000 L/s. There are 1900 hours of operation for the unit. A sensible heat exchanger
would cost $ 7000, and an enthalpy exchanger would cost $ 8000. Both would have an
effectiveness of 0.7. Determine whether either exchanger is cost effective and, if so, which
one is the more cost effective. The cooling system has a COP of 3 and electrical costs are
$0.085/kWh.
4.20