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Theoretical Parametric Study of Wrap-Around Heat Pipe (WAHP) in Air
Conditioning Systems
Article · December 2018
DOI: 10.1142/S2010132519500044
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Mridul Sarkar
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International Journal of Air-Conditioning and Refrigeration
World Scientific Publishing Company
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air
conditioning systems
Mridul Sarkar
Integrated Environmental Solutions India Pvt. Ltd.
Pune-411021, India.
mridul.sarkar@iesve.com; mridul.rns@gmail.com
Warp around heat pipes (WAHP) belong to a special class of recuperative heat exchangers that transfer
heat from inlet to outlet locations via thermal gradient, without using any energy. In the present work,
effects of various mechanical parameters on the performance of a WAHP dehumidifier system that are
based on the underlying principles of heat and mass conservation are presented primarily from a
theoretical point of view. A simplified methodology pertaining to wet cooling coils is applied here for
defining the case of moisture condensation during precooling process at WAHP evaporator. Inlet air
temperature, inlet humidity ratio, air mass flow rate, dehumidifier outlet temperature and effectiveness
are the main operational parameters considered in this study. On the other hand, comparative
performance study of the WAHP system is done through other set of thermodynamic parameters like
the supply air temperature, supply humidity ratio, specific coil load and recovered enthalpy. The subtle
variations in these factors against the operational parameters not only help in stipulating functional
characteristics of the WAHP, but also allow HVAC designers to make informed decisions for system
design and performance without relying entirely on manufacturer’s equipment data.
Keywords: Wrap-around heat pipe (WAHP), dehumidification, humidity, coil load, recovered
enthalpy, effectiveness
higher than many conductors of comparable
dimensions4-5.
Performance investigations of heat pipe heat
exchangers (HPHX) and WAHP applied in HVAC
systems for heat recovery are important topics of
research. El-Baky et al. performed experimental
investigation6 on the effect of return to fresh air mass
flow ratios and fresh air temperatures on the
effectiveness of HPHX system. Experimental study on
a 2-Row copper HPHX7 charged with R-134a
refrigerant by Yau et al. is aimed towards the
investigation of the influence of evaporator inlet
temperatures and face velocity on heat pipe
performance. From the results, they concluded that the
sensible effectiveness of HPHX actually decreased as
the evaporator face velocity is increased. However, in
the temperature range considered for the study, the
sensible effectiveness stayed almost constant. Noie-
1. Introduction
Due to global rise in energy prices and demand, it
becomes very important that the energy sources be used
and managed in an efficient and prudent way. Almost,
10-30% of annual energy consumption in building
sector is due to air conditioning equipment1. In recent
years, serious strides are taken in the field of energy
recovery for cooling and dehumidification applications,
which is a major requirement from HVAC systems
particularly for hot, humid and temperate climates. The
usage of heat pipes in air conditioning equipment for
air-to-air heat recovery and efficient dehumidification
is becoming more popular in recent time due to its ease
of integration, less maintenance and no supplementary
energy requirement for operation2-3. In fact, thermal
conductivity of heat pipes is reported to be several times
1
2
Mridul Sarkar
Baghban et al. presented theoretical and experimental
investigations of a methanol-based HPHX system8 for
hospital surgery rooms. Yau showed the impact of heat
pipes on the energy efficiency of dehumidification
systems9 through transient simulation model of an
HVAC system installed with two 8-row HPHX for an
operating theater in tropical climate of Malaysia.
Ahmadzadehtalatapeh investigated the performance of
an air conditioning system with a HPHX10 and verified
that it met the comfort criteria recommended by
ASHRAE through TRNSYS simulation.
Experimental study of an air handling unit with 7looed WAHP11 by Jouhara et al. is aimed towards the
investigation of the effect of heat loads and face
velocities on the overall resistance of the heat pipe
loops. They also concluded that the overall
effectiveness of WAHP decreases as the face velocity
increases. Ezzuddin et al. presented an experimental
investigation of WAHP charged with R-134a
refrigerant12 and two-pass evaporator and condenser
sections to characterize the thermal performance of the
system in terms of overall thermal resistance.
Many researchers have also evaluated the economic
potential of heat pipes for building air conditioning.
Jouhara conducted a detailed study on the energy
performance13 of WAHP and reported an annual saving
of 134 MWh for a ventilation system supplying 3m3/s
of outdoor air. Zhang et al. presented simulation
results14 showing the energy conservation potential of
heat pipes for dedicated outdoor air handling units
serving office buildings in Hong Kong.
From the literature review, it is quite evident that
the application of heat pipes for air conditioning and
building HVAC services is an active area of research
and development. Despite all of these, lack of
simplified methodologies for analyzing the
performance of heat pipes forces designers and
engineers to depend on various manufacturer selection
software and catalogs. The present work is aimed
towards bridging this knowledge gap. The primary twofold objective of the present work is outlined as follows:
• Establishing basic formulations for defining
psychrometric process through a WAHP enhanced
Fig. 1. Schematic of heat pipe systems used in HVAC: (a) Wrap-Around Heat Pipe (WAHP), (b) Heat Pipe Heat Exchanger (HPHX).
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
dehumidifier system, including the limiting case of
moisture condensation during precooling.
• Depicting theoretical variation of characteristic
parameters of a WAHP against the operating
parameters like inlet air temperature, inlet humidity
ratio, dehumidifier coil outlet temperature, air mass
flow rate and WAHP effectiveness.
WAHP 
t4  t3
t1  t3
3
(1)
Energy balance across the evaporator and condenser in
terms of air enthalpy is expressed as:
2. Basic Heat Pipe systems
A heat pipe system does not utilize any mechanical
component or consume electricity to transfer energy
from one point to another. Heat pipes used for air
conditioning applications are closed loop systems,
where a difference in density and temperature between
the two phases of refrigerant fluid drives its movement
inside the tubes and creates a pulsating effect. The
working fluid evaporates by absorbing heat at one point
and rejects heat at the other by condensing back to
liquid as per Ref.2. Figure 1 shows the two basic
configurations of heat pipes used prevalently in air
conditioning systems. In wrap-around heat pipe
(WAHP) system, front and rear sides of the
dehumidifier coil are covered by the evaporator and
condenser sections, respectively. The evaporator
section precools the incoming air before the
dehumidifier coil cools it further. The cooled and
dehumidified air is subsequently reheated as it passes
through the condenser section and supplied to the space.
In heat pipe heat exchanger (HPHX) system, the supply
and exhaust streams pass through the evaporator and
condenser sections, respectively, which allows air-toair heat recovery between the two streams. The
connecting tubes enable transport of the refrigerant
fluid between the evaporator and condenser sections of
the heat pipe system during the whole cycle. The
operating temperature range of WAHP and HPHX for
air conditioning systems depends upon the required
supply conditions for intended space application and
refrigerant used in heat pipes. Literature sources [Ref.
6, 8] suggest 15-550C to be appropriate temperature
range for heat pipes in air conditioning applications.
m  q1  q2   m  q4  q3 
If recovered heat at the evaporator is entirely sensible,
then the effectiveness is also defined by:
WAHP 
The sensible effectiveness of WAHP from fig.1 is
given by:
t1  t2
t1  t3
(3)
which gives:
t2  t1  WAHP   t1  t3 
(4)
The evaporator exit temperature from Eq. (4) is
compared with the dew point temperature (DPT) at inlet
(point 1) to check whether condensation occurs at the
evaporator. The DPT can be expressed in terms of
humidity ratio and absolute pressure as per Ref.15:
tadp 
  B  kT0  
 B  kT0 2  4 A  AT0 2  BT0 
2A
 T0
(5)
Where,
 C plv 
A  

 2R 
P 
  
k  ln  t   ln 

  
 P0 
B
3. Basic underlying equations
(2)
l0  C plvT0
R
Based on the comparison between evaporator exit
temperature and the inlet dew point temperature, two
4
Mridul Sarkar
different cases can be shown as per the proceeding
subsections.
The unit for temperature in Eq. (10) is Kelvin. Hence,
here ‘T’ implies T0+t. The saturation humidity ratio
corresponding to this temperature is given by:
3.1.1. Case 1: No condensation
If the temperature at evaporator exit (t2) is greater
than or equal to the inlet DPT, moisture condensation
does not occur at the evaporator and unsaturated air
passes through the coil. So in case 1:
t2  DPT1
(6)
In this case, the absolute humidity at point 2 will be:
2  1
(7)
On a psychrometric chart, the cooling-dehumidification
process through the coil can be simply depicted by a
straight line from the coil inlet to outlet conditions that
intersects the saturation curve at coil ADP (apparatus
dew point) on extending further16. In terms of the ADP
and coil bypass factor (BF), coil outlet temperature is:
t3  tadp  1  BF   t2  BF
(8)
adp 
  PTadp
Pt  PTadp
(11)
Humidity ratio at the coil exit is obtained by
substituting the value of ωadp into Eq. (9). It should be
noted that the relative humidity of air at coil exit can not
exceed 100%. If air reaches the saturation condition inbetween coil inlet and exit temperatures, it follows the
100% RH curve on a psychrometric chart for rest of the
process. In that case, ω3 will be simply equal to
saturation humidity ratio corresponding to the coil exit
temperature. Since, heat addition to the air stream at
condenser is entirely sensible, humidity ratio remains
unchanged after leaving the condenser:
4  3
However, due to an increase in temperature through the
condenser, relative humidity of the supply air reduces.
The condenser exit (supply) temperature is obtained by:
Similarly the absolute humidity ratio at coil exit is:
3  adp  1  BF   1  BF
(9)
Since, ADP condition corresponds to the lowest
saturation limit of air passing through the coil, the vapor
pressure at this temperature (tadp) is determined from
the modified Clausius-Clapeyron equation17-18 as:
PTadp
 C plv  



T


 adp  R  
 P0  


T
0






 l0  C plv  T0   1
1 
exp 

 
R

  T0 Tadp 
(10)
t4  t3  WAHP   t1  t3 
(12)
3.1.2. Case 2: With Condensation
If the evaporator exit temperature calculated from
Eq. (4) is lower than the inlet DPT, condensation of
water vapor occurs during precooling. Since heat
absorbed at the evaporator is not entirely sensible in this
case, the effectiveness given by Eq. (3) is not valid.
From conservation of energy, heat released at the
condenser section is expressed in terms of air enthalpy
difference by:
Qc  ma  q4  q3 
(13)
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
Since, humidity ratio at the condenser inlet and exit are
unknown and heat transfer to air at condenser side is
entirely sensible, Eq. (13) can be written as:
(14)
Qc  ma  c pm   t4  t3 
The term cpm is the specific heat of moist air and can be
approximated within the limits of workable accuracy by
a constant value ~ 1.02 kJ/kg-K for a wide range of
humidity ratios encountered in air conditioning
systems. Using Eq. (2), (13) and (14):
q2  q1  c pm   t4  t3 

q1  c pa  t1  1  l0  c pv  t1
NTUWAHP
1  NTUWAHP

UAWAHP
 Re  Rc  2 Re
NTU e
2
(19)
From Eq. (17) and (19):
NTU e 
2WAHP
1  WAHP
(20)
(16)
BFe  exp   NTU e 
qe 
q2  BFe  q1
1  BFe
(22)
The saturation enthalpy (qe) determined above could
also be approximated by a quadratic equation in terms
of the evaporator effective surface temperature (te)
reported in literature as per Ref. 21-22 as:
(18)
qe  a  te 2  b  te  c
The above equation is based on the assumption that the
heat pipe has infinite thermal mass because the vapor
(23)
Typical values of the coefficients a, b, and c for wet
coils at different barometric pressures by considering a
Table 1 Regression coefficients of saturation enthalpy function
Coefficients of trend line function:
Coefficient of
determination (R2)
qe  a  te 2  b  te  c
Pt (kPa)
(21)
Analogous to cooling coils, enthalpy of wet surface of
the evaporator is given by:
(17)
Overall resistance of the WAHP is given in terms of
external resistances at the evaporator and condenser by:
1
NTUWAHP 
As with cooling coils, bypass factor of the evaporator
section can be similarly defined in terms of NTU as:
The effectiveness of a WAHP with equal flow rates
through its evaporator and condenser sections is written
in terms of the number of heat transfer units (NTU)19- 20
as:
WAHP 
inside has almost a uniform temperature throughout its
length and its overall thermal resistance is due to
external fluid flow at the evaporator and condenser
sections3, 5. In terms of NTU on evaporator side, the
overall NTU of WAHP module is give by:
(15)
where, the inlet enthalpy (q1) is given by:
5
a
b
c
108.386
0.0774
0.1988
19.484
0.9998
106
0.0793
0.1797
19.895
0.9998
101.325
0.0838
0.1036
21.24
0.9998
100
0.0849
0.1004
21.383
0.9998
99
0.0859
0.0838
21.677
0.9998
6
Mridul Sarkar
saturation temperature band of 4-25oC is shown in Ref.
21. The same theory can be applied here for wet
evaporator surface of the heat pipe. However, taking the
operational parameters of the WAHP into account,
these regression coefficients are modified for a
relatively wider dew point band of 10-35oC. Table 1
shows typical values of the coefficients at different
atmospheric pressures encountered in air conditioning
problems. The logical solution of Eq. (23) is given by:
te 
b  b2  4  a  (c  qe )
(24)
2a
By determining qe from Eq. (15), (16) and (22) and
substituting into Eq. (24), the value of te is obtained.
Temperature of air at the evaporator exit is given by:
t2  BFe  t1  (1  BFe )  te
(25)
and the corresponding humidity ratio is:
2  BFe  1  1  BFe   e
The humidity ratio (ωe) at the evaporator surface is
determined by replacing Tadp with Te in Eq. (10) and
(11). From above, it is clear that moisture condensation
occurs during precooling if effective temperature of the
evaporator is lower than the DPT of air at WAHP inlet.
The psychrometric condition at evaporator exit is
determined by applying Eq. (25) and (26), which
require evaporator BF and saturated conditions
corresponding to the effective evaporator surface
temperature. This is analogous to the methodology for
determining exit conditions through a cooling coil using
the coil BF and ADP conditions.
Now air that enters the dehumidifier coil is at near
saturated condition (t2 and ω2). Similar to case 1, air will
exit the coil (required coil outlet temperature t3 and
corresponding humidity ω3) at saturated state, if the line
that is joining coil inlet and coil ADP conditions
intersects the 100% RH curve (saturation) in between.
Eq. (27) and (28), given below shows the saturation
vapor pressure and relative humidity (RH)
corresponding to the coil exit temperature (t3),
respectively:
(26)
Fig. 2. Parametric variation with evaporator inlet temperatures at coil outlet temperature: 12oC, coil bypass factor: 0.1, inlet humidity ratio:
0.018 kg/kg-DA of: (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load.
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
7
Fig. 3. Psychrometric plots at different inlet temperatures - (a) Evaporator inlet temperature: 41oC, inlet humidity ratio: 0.018 kg/kg-DA,
dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. (b) Evaporator inlet temperature: 29oC,
inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4.
with each of the operating parameters while holding all
the remaining parameters constant.
 C plv  



 T3   R  
PT  P0   

3
 T0 



 l0  C plv  T0   1 1 
exp 
    
R
  T0 T3 

RH 3 
3  Pt
 100%
PT    3 
3
4.1. Inlet temperature
(27)
(28)
The RH from Eq. (28) will be equal to 100% in case
condensation occurs during precooling.
4. Parametric variation
This section presents a comparative performance
study of WAHP based dehumidifier systems by
defining the effects of various operating parameters on
key performance parameters like WAHP supply
humidity, supply temperature, recovered enthalpy and
dehumidifier coil load. The proceeding subsections
depict the variation in these performance parameters
Inlet air temperature affects the supply condition,
coil load and recovered heat through a WAHP system.
For a WAHP operating at a particular effectiveness,
increasing the evaporator inlet temperature leads to an
increase in the coil inlet temperature. Due to this, a
lower coil ADP is required for cooling and
dehumidifying air to a fixed coil outlet temperature
thereby increasing the dehumidifier coil load and may
result in reduction of supply humidity ratio, when air
exiting the dehumidifier is not 100% saturated.
Although, the recovered energy increases with an
increase in inlet temperature through the evaporator, it
leads to reheating of air to a higher temperature through
the condenser. With WAHP operating at higher
effectiveness, the precooling and reheating can be
increased through the evaporator and condenser,
respectively at a fixed inlet condition and coil outlet
temperature. This leads to an increase in recovered
energy and supply temperature, but reduces the net
dehumidifier coil load. It should be noted that moisture
8
Mridul Sarkar
condensation occurs at the evaporator, if difference
between the inlet air DBT and effective evaporator
temperature exceeds the entering air dew point
depression (DPD). Now this scenario arises either when
the effectiveness of WAHP is higher, which enables the
evaporator to precool air below its DPT or when the air
temperature entering the WAHP itself is lower, which
results in comparatively lower DPD. Figure 2 shows
variations of thermodynamic parameters of the WAHP
system with the evaporator inlet temperatures at varying
sensible effectiveness and typical psychrometric
processes through a WAHP system at different inlet
temperatures are depicted in Figure 3.
4.2. Inlet humidity ratio
Contrary to inlet temperature, an increase in inlet
humidity ratio does not affect the condenser outlet
temperature or recovered heat as long as dehumidifier
coil has enough capacity to cool and dehumidify air up
to the required level. However, both the condenser
outlet temperature and recovered heat will increase with
the operating effectiveness of WAHP. As the humidity
ratio rises, DPT also increases. This leads to a sharp
decrement in the DPD. As the DPD reduces, the net
sensible load ratio (SLR) of the coil also decreases. As
a result, dehumidification efficiency of the
dehumidifier coil increases. Water vapor in moist air
will condense off at the evaporator, if its effective
temperature is low enough to precool the air below its
inlet DPT. With an increment in the inlet humidity ratio,
the supply DPT also increases until further reduction in
DPD causes moisture condensation during precooling
and fully saturated air exits the dehumidifier coil.
Beyond this point, a further increase in inlet humidity
ratio does not change the supply humidity ratio and
remains constant at the saturated humidity ratio
corresponding to the coil outlet temperature. For a fixed
coil outlet temperature, increasing the inlet humidity
ratio directly affects the net coil load. In this case,
predominant portion of the coil load will be the latent
part. Due to elevated air moisture content entering the
dehumidifier, net coil load increases and more energy is
expended for dehumidification. However, operating a
WAHP at a higher effectiveness results in greater
temperature differential across the evaporator thereby
reducing net coil loads. Figure 4 shows the variation of
different parameters of a WAHP system with inlet
humidity ratios and Figure 5 depicts psychrometric
plots at different inlet humidity ratios.
4.3. Coil outlet temperature
DPT of the supply air through a wrap-around
dehumidifier heat pipe can be controlled by modulating
the coil outlet temperature. This is done by either
Fig. 4. Parametric variation with inlet humidity ratios at coil outlet temperature: 12oC, coil bypass factor: 0.1, evaporator inlet
temperature: 35oC of: (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load.
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
9
Fig. 5. Psychrometric plots at different inlet humidity ratios - (a) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA,
dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. (b) Evaporator inlet temperature: 35oC, inlet
humidity ratio: 0.012 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4.
controlling the opening and closing of chilled water
valve to vary the water flow rate through the coil or
bypassing air around the coil by using face and bypass
dampers (FBD). At fixed inlet humidity ratio and
temperature, air exits the condenser at a slightly
elevated temperature on increasing the coil outlet
temperature. This results in marginal reduction of
recovered heat, since the maximum theoretical heat
transfer reduces with an increase in coil outlet
temperature. However, to achieve a lower coil outlet
temperature, the coil ADP needs to be reduced that not
only increases the latent load ratio and net coil load, but
also results in reduction of supply humidity ratio. In
addition to this, increased dehumidification load at a
lower coil outlet temperature leads to saturation of air
leaving the coil. Operating a WAHP at a higher
effectiveness leads to increased precooling and
reheating through evaporator and condenser. As a
result, recovered enthalpy and condenser exit
temperature increases, but reduction in dehumidifier
coil load is observed. Figure 6 and 7 shows the
parametric variation and psychrometric plots at
different coil outlet temperatures, respectively.
4.4. Air mass flow rate
Air mass flow rates drastically affect the
performance of heat pipes. The face velocity through a
WAHP dehumidifier increases as the airflow rate is
increased. Due to this, higher fraction of air bypasses
the WAHP and dehumidifier coil leading to reduction
in the contact time with heat pipe and coil surfaces.
Hence, as airflow rate is increased, sensible
effectiveness of the WAHP and contact factor (1 - BF)
of the dehumidifier coil decreases. The effectiveness of
a WAHP at any airflow rate in terms of a reference
airflow rate and effectiveness is given by:
WAHP 
x  WAHP
r ef
1   x  1  WAHP
r ef
Where, x is expressed in terms of the ratio of air mass
flow rate to the reference air mass flow rate as:
 m
x a
 ma
 ref




0.534
10
Mridul Sarkar
Fig. 6. Parametric variation with coil outlet temperatures at evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, coil
bypass factor: 0.1 of (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load.
A detailed derivation of the correlations for sensible
effectiveness of WAHP and HPHX in terms of the
reference effectiveness and corresponding airflow rates
are presented in Appendix A and B, respectively. With
respect to the reference airflow rate, the effectiveness of
a WAHP decreases as the airflow ratio exceeds 1 and
vice-versa. Due to this, higher energy recovery and
higher condenser outlet temperature are expected by a
WAHP operated at a higher effectiveness or reduced
airflow rate. As airflow rate increases, distribution
energy from fans also increases due to an increase in
pressure drop through the WAHP dehumidifier unit,
which indirectly affects dehumidifier coil loads.
However, in this paper only the explicit effect of air
flow rate on the coil bypass factor and WAHP
effectiveness are considered. The pressure drop across
Fig. 7. Psychrometric plots at different coil outlet temperatures - (a) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA,
dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. (b) Evaporator inlet temperature: 35oC, inlet
humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 11oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4.
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
a WAHP module depends primarily on its geometrical
configuration (fin dimensions, number of heat pipe
rows, tube diameter and fin spacing) and flow rate of air
stream passing through it [Ref. 4].
As per literature study [Ref. 21, 23] the bypass
factor of a coil can be expressed entirely as a function
of air mass flow rate by:
 X 
BF  exp   0 
 ma 
(29)
The term X0 shown in Eq. (29) above is derived from a
reference air mass flow rate and the coil bypass factor
corresponding to this reference air mass flow rate. For
a given configuration, the coil BF increases with an
increment in the face velocity and must be operated at a
lower ADP to supply at the required DPT. As a result,
the specific coil load actually increases with an increase
in air mass flow rate. As the ADP or effective
temperature of the coil is reduced, air gradually moves
towards the saturated condition during the coolingdehumidification process and exits the coil at 100% RH.
On the other hand, as heat recovery increases with a
reduction in airflow ratio, more precooling occurs at the
evaporator that reduces air DPD. This allows it to reach
the saturated condition even at a relatively higher coil
ADP. Based on the above arguments, the variations in
11
the thermodynamic parameters of a WAHP with air
mass flow rate ratios are shown in Figure 8. Typical
psychrometric plots of the processes through a WAHP
enhanced dehumidifier at a reference airflow rate and at
reduced airflow rate is depicted in Figure 9.
5. Conclusions
The present work showed the variation of
characteristic factors of a WAHP enhanced
dehumidifier system with operational parameters. Basic
mathematical formulations are derived here for
theoretically deducing the operational characteristics of
WAHP system including the limiting case of moisture
condensation at the evaporator. The operating
effectiveness of a WAHP system played a pivotal role
in the variation of system supply temperature,
recovered enthalpy and dehumidifier coil load. Even
though, a fixed effectiveness is assumed while deriving
the variation of characteristic parameters with operating
parameters, this operating effectiveness is shown to be
inversely correlated with external air flow rates at the
condenser and evaporator sections. Based on the
variation trends in supply conditions, coil load and
recovered energy by applying these formulations, it can
be concluded that the specific dehumidifier coil load is
directly dependent on the inlet air temperature, inlet
humidity ratio and air mass flow rate and tends to
increase with an increment in each of these operating
Fig. 8. Parametric variation with air mass flow rate ratio at evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, reference
coil bypass factor: 0.1, dehumidifier coil outlet temperature: 12oC. of: (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c)
Recovered enthalpy, (d) Coil load.
12
Mridul Sarkar
parameters. However, the same coil specific load
showed a decreasing trend with an increase in coil outlet
temperature and operating effectiveness of WAHP. The
WAHP supply temperature and recovered enthalpy,
increased as the WAHP is operated at a higher
effectiveness. The supply temperature also showed
considerable increment as inlet air temperature is
increased. The inlet humidity ratio does not affect the
recovered enthalpy or supply temperature, but directly
influenced the net coil load. The supply DPT and
humidity ratio depended explicitly on the required coil
outlet temperature, inlet dew point depression (DPD)
and coil ADP, but indirectly affected by the WAHP
effectiveness and coil bypass factor during operation. If
condensation occurs during precooling, the supply DPT
will be equal to the coil outlet temperature. These
simple conclusions aided in defining the performance
characteristics of the WAHP system in terms of each
operational parameter in consideration and allowed
making informed decision regarding system design and
control.
Appendix A.
WAHP effectiveness in terms of
reference effectiveness and mass
flow ratio
Sensible effectiveness is identified as the main
characteristics to define the performance of heat pipes.
Researchers have assumed infinite thermal mass for a
heat pipe because the vapor inside it has almost a
uniform temperature throughout its length3. Hence, the
effectiveness of heat pipes prominently depends upon
the external flow conditions that affect the transport of
heat in and out of evaporator and condenser sections,
respectively5,11. So, in this paper, the overall heat
transfer efficiency of heat pipe is assumed to vary only
with external airflow rates, without considering the
influence of other thermodynamic parameters like heat
load and operating temperature.
Several assumptions are made here to simplify the
methodology of deriving theoretical correlation for
sensible effectiveness at any airflow rate in terms of the
reference effectiveness and corresponding airflow rate
ratio:
Fig. 9. Psychrometric plots at different air mass flow rate ratio - (a) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA,
dehumidifier coil outlet temperature: 12oC, reference coil BF: 0.1, reference sensible effectiveness of WAHP: 0.4, air mass flow rate to
reference air mass flow rate ratio: 1, (b) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet
temperature: 12oC, reference coil BF: 0.1, reference sensible effectiveness of WAHP: 0.4, air mass flow rate to reference air mass flow rate
ratio: 0.6.
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
• Steady state analysis.
• Density and heat transfer coefficient of air are
assumed to be constant throughout the process.
• Thermal resistances of the heat pipe tube and wick
are neglected. Fouling resistance is also neglected.
• Internal resistance due to pulsating flow of
refrigerant is considerably lower than the external
resistance and hence neglected here.
• The fins are assumed to be 100% efficient. The face
velocities over evaporator and condenser are
determined by the fin height and width.
• Geometrical configurations of evaporator and
condenser sections are assumed to be identical.
• The analysis is simplified by considering the
condenser and evaporator sections as single circular
tubes.
The whole procedure can be simplified and
categorized into following steps:
a) Simplifying the external resistance by heatexchanger ε-NTU relation:
For a heat exchanger with equal mass flow rates at the
hot and cold ends, the net effectiveness in terms of NTU
is shown in section 3.1 as:
WAHP 
NTUWAHP
1  NTUWAHP
The number of heat transfer units (NTU) for the heat
pipe shown in the equation above is given by:
NTUWAHP 
UAWAHP
(A-1)
Cmin
Where,
Cmin  Ce  Cc
(A-2)
The overall thermal resistance of WAHP is given
by:
1
UAWAHP
 Re  Rc  2 Rc
13
(A-3)
The resistance at condenser side in terms of
corresponding NTU is given by:
Rc 
1
NTU c  Cmin
(A-4)
Overall NTU of the WAHP is written in terms of the
condenser side NTU as:
NTUWAHP 
NTU c
2
(A-5)
b) Expressing the heat transfer coefficient as a function
of flow rate for WAHP:
The Nusselt number for flows over circular tubes as per
Hilpert correlation19 is given by:
Nuc 
hc D
 a  Rec m  Pr 0.33
kf
(A-6)
For typical heat pipes, the hydraulic diameter of the
exposed tube does not exceed 0.5 inch and the face
velocities prescribed by manufacturers for enhanced
dehumidification does not exceed 500 fpm24. In this
range, the external Reynold’s number remains below
4000, for which, m and a takes the value 0.466 and
0.683, respectively19. Hence, for flow around heat pipe
tubes:
hc  ma 0.466
(A-7)
c) Expressing the ratio of NTU as a function of airflow
rate ratio:
In terms of the reference airflow rate, the ratio of heat
transfer coefficients can be written as:
 m
hc
 a
hc
 ma
ref
 ref




0.466
(A-8)
14
Mridul Sarkar
Similarly in terms of the overall thermal conductance
from ε-NTU relation:
effectiveness and manufacturer’s
effectiveness is lower than ±5%.
Appendix B.
NTU c  Cmin
h
 c
 NTU c  Cmin ref hc
Effectiveness of HPHX in terms of
the reference effectiveness and
mass flow ratios
(A-9)
ref
From Eq. (A-8) and (A-9):
 m
NTU c
 a
 NTU c ref  maref




0.466
 maref

 ma

  m
 a
  ma
  ref




0.534
(A-10)
d) Expressing the effectiveness in terms of the reference
effectiveness and flow ratio:
By applying Eq.(A-5) and (A-10):
 2

2WAHP
 x   WAHP 
1  WAHP
 1  WAHP ref
documented
Unlike WAHP, the airflow rates through the
condenser and evaporator in a HPHX system vary
freely. Hence, effectiveness of HPHX at any supply
flow rate not only depends on the supply flow rate but
also on the condenser to evaporator flow rate ratio too.
With all the assumption made earlier, the whole
derivation can be simplified into following steps:
a) Simplifying the external resistances at the
evaporator and condenser by heat-exchanger ε-NTU
relation:
The effectiveness of HPHX from Fig. 1(b) is given by:
(A-11)
 HX 
C T  T 
Ce T1  T2 
 c 4 3
Cmin T1  T3  Cmin T1  T3 
(B-1)
The effectiveness of a counter flow heat exchanger as
reported in literature19-20 is given by:
Where,
 m
x a
 ma
 ref




0.534
 HX 
Hence, the effectiveness of WAHP in terms of its
reference performance can be written as:
WAHP 
1  exp  NTU HX  1  Cr 
1  Cr  exp  NTU HX  1  Cr 
The net heat capacity ratio Cr in Eq. (B-2) is defined as:
Cr 
x  WAHP
r ef
1   x  1  WAHP
(A-12)
r ef
Eq. (A-12) derived above should be applied on a caseby-case basis for every unique constructional
configuration of WAHP. The accuracy of the derived
equation is tested against the manufacturer’s data
obtained from selection software25 for two different
WAHP configurations.
Figure A1 shows the
comparison of results at mass flow rate ratios over a
wide range around the reference ratio (equal to 1). The
results show that the error between estimated
(B-2)
Cmin
Cmax
(B-3)
Defining a new parameter ‘r’ as:
r
Condenser mass flow rate mc

Evaporator mass flow rate me
(B-4)
From Eq. (B-3) and (B-4), one can deduce:

Cmin  mc  c pa 


 if mc  me
Cr  r




(B-5)
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
Cmin  me  c pa 



 if me  mc
1
 Cr 


r

(B-6)
and in this case:
Considering the first case, when Cr = r, Eq. (B-2) can
be written as:
 HX 
1  exp  NTU HX   1  r 
1  r  exp  NTU HX   1  r 
(B-7)
NTU HX 
 1  r   HX 
1
 ln 
1  r   1   HX 
(B-8)
1
 Re  Rc
1
 1
r 



 NTU c NTU e 
where:
Re 
(B-13)
(B-9)
he  me 


hc  mc 
Rc 
(B-12)
Cc
b) Expressing the evaporator to heat pipe NTU ratio as
a function of the condenser to evaporator air mass flow
ratio:
Since the evaporator and condenser sections are
assumed to have identical geometrical configuration:
In terms of the net resistance:
UAHX
UA HX
From Eq. (B-4) and (B-9)-(B-12):
NTU HX 
which gives:
NTU HX 
15
1
NTU c  Cc
(B-10)
1
NTU e  Ce
(B-11)
0.466
(B-14)
The ratio of heat transfer coefficients shown above is
due to Eq. (A-7) applicable for external flows over
circular tubes of heat pipes.
Hence:
Fig. A-1. Comparison of effectiveness for two different WAHP configurations: (a) Qref = 9.5 m3/s, heat pipe dim.: 6 rows, 10 fpi, 0.5 inch OD,
fin dim. 2540 x 1580 mm2, Refrigerant: R-410a, Evaporator inlet: 42oC, 35% RH, Condenser inlet: 12oC, 95% RH. (b) Qref = 3 m3/s, heat pipe
dim.: 6 rows, 10 fpi, 0.5’ OD, fin dim. 762 x 1260 mm2, Refrigerant: R-410a, Evaporator inlet: 42oC, 35% RH, Condenser inlet: 12oC, 95% RH.
.
16
Mridul Sarkar
NTU e  me 


NTU c  mc 
0.534
1
 
r
0.534
(B-15)
NTU HX
NTU HX
ref
And from Eq. (B-13) and (B-15):
 1  r 0.466 
NTU e
  0.534 
NTU HX  r

(B-16)

1  r 0.466
r 0.534
(B-17)

 HX



1 r
 1 

  1  r   HX 
  1   HX 
ref

1  rref 0.466
(B-18)
rref 0.534








z


  r 


(B-21)
z  x
1  r    ref
1  r ref 
Reiterating the steps shown above for the case when
r >1 and:
me  mc
As shown earlier in Eq. (A-10) for WAHP, similar
expression can be written for evaporator of HPHX as:
 m
NTU e
 e
NTU e
 me
ref
 ref
(B-20)
where, the exponent ‘z’ is a function of mass flow ratio
and is given by:
At a reference condenser to evaporator flow ratio,
Eq.(B-17) takes the form as:
 ref 





Eliminating the LHS of the above equation by
substituting corresponding variables from Eq. (B-13),
(B-15), (B-16) and (B-19), the effectiveness of HPHX
in terms of its reference performance can be written as:
In conclusion, the evaporator to heat pipe NTU ratio is
shown to be a direct function of the condenser to
evaporator air mass flow rate ratio.
c) Expressing effectiveness in terms of the reference
performance and condenser to evaporator air mass
flow ratio:
Defining the evaporator to heat pipe NTU ratio as
parameter ‘γ’, Eq.(B-16) can be rewritten as:
 1  r   HX 
1
 ln 
1  r   1   HX 

 1  rref   HX
1
ref
 ln 
 1   HX ref
1  rref

The effectiveness at any supply flow rate can be
expressed in terms of the reference effectiveness as:
0.534
x
(B-19)
 HX
Taking the ratio of heat pipe NTU from Eq. (B-8) into
account, one can write:








1
 
1 


r

 1 
y



  1   HX  

 
r    1
  1   HX  
r
 
 

ref 
 

(B-22)
Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems
17
Fig. B-1. Comparison of effectiveness for HPHX configuration 1: Qe-ref = 9.5 m3/s, rref = 0.999, heat pipe dim: 6 rows, 10 fpi, 0.5 inch OD, fin
dim: 2540 x 1580 mm2, Refrigerant: R-410a, evaporator inlet: 42oC, 35% RH, condenser inlet: 24oC, 50% RH at (a) constant condenser side
airflow rate and variable evaporator side air flow rates, (b) constant evaporator side airflow rate and variable condenser side airflow rates
Fig. B-2. Comparison of effectiveness for HPHX configuration 2: Qe-ref = 3.0 m3/s, rref = 0.999, heat pipe dim: 6 rows, 10 fpi, 0.5 inch OD, fin
dim: 762 x 2025 mm2, Refrigerant: R-410a, evaporator inlet: 42oC, 35% RH, condenser inlet: 24oC, 50% RH at (a) constant condenser side air
flow rate and variable evaporator side airflow rates, (b) constant evaporator side air flow rate and variable condenser side airflow rates
Where the exponent ‘y’ is:
 1
1  
r
ref
y  x 


 1
1 
r ref

and evaporator to heat pipe NTU ratio ‘λ’ for this case
is given by:

NTU e
 1  r 0.466
NTU HX
(B-23)
Figures B-1 and B-2 show the comparison of results
from the derived correlation and manufacture’s
performance data25 for two different configurations of
HPHX. It should be noted that both Eq. (B-21) and (B22) can’t be defined for equal reference flow rates at
condenser and evaporator sections (i.e. flow ratio equal
to 1). Hence, for mathematically approximating the
results, a reference condenser to evaporator flow ratio
of 0.999 is applied here to derive the sensible
effectiveness at different evaporator and condenser
flow rates. The data are plotted for two different
scenarios: first scenario, where condenser flow rate is
kept constant and second scenario, where evaporator
flow rate is kept constant. Comparison of results shows
that the error between the two data does not exceed
±5%, which affirms the validity of the derived
correlations.
18
Mridul Sarkar
Nomenclature
Symbols
A
BF
C
Surface area (m2)
Bypass factor
Heat capacity rate (kW/K)
cpa
Specific heat capacity of dry air (1.006 kJ/kg-K)
cpm
Specific heat capacity of moist air (1.02 kJ/ kg-K)
cpv
D
DPT
h
Specific heat capacity of vapor (1.86 kJ/kg-K)
Hydraulic diameter (m)
Dew point temperature (oC)
Convective heat transfer coefficient (W/m2-K)
kf
Thermal conductivity of fluid (W/m-K)
l0
NTU
Specific latent heat of vaporization of water at 273
(2501 kJ/kg)
Air mass flow rate (kg/s)
Number of heat transfer units
Nuc
P
Pr
Nusselt number
Saturation vapor pressure (kPa)
Prandtl number
Pt
Q
Ambient pressure (kPa)
Volume flow rate
Heat transfer rate (kW)
Specific enthalpy of air (kJ/kg)
m
Q
q
qe
R
Specific saturation enthalpy of air at effective
surface temperature of evaporator (kJ/kg)
Gas constant for water vapor (0.4618 kJ/kg-K)
Rc
External thermal resistance at condenser (K/W)
Re
External thermal resistance at evaporator (K/W)
Rec
RH
r
t
te
U
Reynold’s number
Relative humidity
Condenser to evaporator mass flow ratio
Air temperature (oC)
Effective surface temperature of evaporator (oC)
Overall heat transfer coefficient (W/m2-K)
Greek symbols
α
ε

Ratio of molecular mass of water vapor and dry air
(0.622)
Effectiveness of WAHP
Humidity ratio (kg moisture/kg DA)
Subscripts
0
1
2
Reference state (273.15 K)
Evaporator inlet
Evaporator outlet / dehumidifier coil inlet
3
4
a
adp
c
e
HX
min.
ref
WAHP
Dehumidifier coil outlet / condenser inlet
Condenser outlet
Of air
Apparatus Dew Point
At condenser
At evaporator
Heat pipe heat exchanger
Minimum
Reference performance
Wrap-around heat pipe
Acknowledgments
The author acknowledges no conflict of interest. This
research did not receive any specific grant from funding
agencies in the public, commercial, or not-for-profit
sectors.
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