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International Journal of Air-Conditioning and Refrigeration

World Scientific Publishing Company

1

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

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

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-

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 7-

looed 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 two-

fold 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 3

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.

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-to-

air 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.

3. Basic underlying equations

The sensible effectiveness of WAHP from fig.1 is

given by:

Energy balance across the evaporator and condenser in

terms of air enthalpy is expressed as:

If recovered heat at the evaporator is entirely sensible,

then the effectiveness is also defined by:

which gives:

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:

Where,

Based on the comparison between evaporator exit

temperature and the inlet dew point temperature, two

(1)

(3)

(4)

43

13

WAHP

tt

tt

1 2 4 3

m q q m q q

(2)

12

13

WAHP

tt

tt

2 1 1 3WAHP

t t t t

22

0 0 0 0

0adp

tB kT B kT 4A AT BT T

2A

(5)

plv

t

0

0 plv 0

C

A2R

P

k ln ln

P

l C T

BR

4 Mridul Sarkar

different cases can be shown as per the proceeding

subsections.

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:

In this case, the absolute humidity at point 2 will be:

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:

Similarly the absolute humidity ratio at coil exit is:

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:

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:

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 in-

between 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:

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:

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:

(6)

(7)

(8)

(13)

21

t DPT

21

32

1

adp

t t BF t BF

31

1

adp BF BF

(9)

(10)

adp

adp

ad T

tT

p

P

PP

(11)

43

4 3 1 3WAHP

t t t t

(12)

43ca

Q m q q

plv

adp

C

R

00

0 plv 0

a

dp

dp

0a

T

T

PPT

l C T 11

exp

R T T

Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 5

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:

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):

where, the inlet enthalpy (q1) is given by:

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:

Overall resistance of the WAHP is given in terms of

external resistances at the evaporator and condenser by:

The above equation is based on the assumption that the

heat pipe has infinite thermal mass because the vapor

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:

From Eq. (17) and (19):

As with cooling coils, bypass factor of the evaporator

section can be similarly defined in terms of NTU as:

Analogous to cooling coils, enthalpy of wet surface of

the evaporator is given by:

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:

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

Pt (kPa)

Coefficients of trend line function:

Coefficient of

determination (R2)

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

(15)

(16)

(17)

(18)

43c a pm

Q m c t t

(14)

2 1 4 3pm

q q c t t

1 1 1 0 1pa pv

q c t l c t

1

WAHP WAHP

WAHP

NTU

NTU

12

e c e

WAHP

R R R

UA

2e

WAHP NTU

NTU

(19)

2

1WAHP

WAHP

e

NTU

(20)

exp

ee

BF NTU

(21)

21

1e

ee

q BF q

qBF

(22)

2

e e e

q a t b t c

(23)

2

e e e

q a t b t c

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:

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:

and the corresponding humidity ratio is:

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:

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.

24 ( )

2

e

e

b b a c q

ta

(24)

21

(1 )

e e e

t BF t BF t

(25)

(26)

2 e 1 e e

BF 1 BF

Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 7

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

with each of the operating parameters while holding all

the remaining parameters constant.

4.1. Inlet temperature

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

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.

(27)

(28)

plv

3

C

R

00

0 plv 0

3

T

03

T

PPT

l C T 11

exp

R T T

3

t

33

T3

P

R 1

P0H 0%

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

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:

Where, x is expressed in terms of the ratio of air mass

flow rate to the reference air mass flow rate as:

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.

r

r

11

ef

ef

WAHP

WAHP

WAHP

x

x

0.534

ref

a

a

m

xm

10 Mridul Sarkar

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.

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.

Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 11

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:

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 cooling-

dehumidification 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

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.

0

exp

a

X

BF m

(29)

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 13

• 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 heat-

exchanger 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:

The number of heat transfer units (NTU) for the heat

pipe shown in the equation above is given by:

Where,

The overall thermal resistance of WAHP is given

by:

The resistance at condenser side in terms of

corresponding NTU is given by:

Overall NTU of the WAHP is written in terms of the

condenser side NTU as:

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:

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:

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:

1

WAHP WAHP

WAHP

NTU

NTU

min

WAHP

WAHP

UA

NTU C

(A-1)

12

e c c

WAHP

R R R

UA

(A-3)

min

1

cc

RNTU C

(A-4)

2c

WAHP NTU

NTU

(A-5)

0.33

Re Pr

m

c

cc

f

hD

Nu a

k

(A-6)

0.466

ca

hm

(A-7)

0.466

ref ref

ca

ca

hm

hm

(A-8)

min ec

C C C

(A-2)

14 Mridul Sarkar

Similarly in terms of the overall thermal conductance

from ε-NTU relation:

From Eq. (A-8) and (A-9):

d) Expressing the effectiveness in terms of the reference

effectiveness and flow ratio:

By applying Eq.(A-5) and (A-10):

Where,

Hence, the effectiveness of WAHP in terms of its

reference performance can be written as:

Eq. (A-12) derived above should be applied on a case-

by-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

effectiveness and manufacturer’s documented

effectiveness is lower than ±5%.

Appendix B. Effectiveness of HPHX in terms of

the reference effectiveness and

mass flow ratios

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:

The effectiveness of a counter flow heat exchanger as

reported in literature19-20 is given by:

The net heat capacity ratio Cr in Eq. (B-2) is defined as:

Defining a new parameter ‘r’ as:

From Eq. (B-3) and (B-4), one can deduce:

min

min ref

cc

cc

ref

NTU C h

NTU C h

(A-9)

0.466 0.534

ref

ref ref

a

c a a

c a a a

ref

m

NTU m m

NTU m m m

(A-10)

11

22

WAHP WAHP

WAHP WAHP ref

x

(A-11)

0.534

ref

a

a

m

xm

r

r

11

ef

ef

WAHP

WAHP

WAHP

x

x

(A-12)

43

12

min 1 3 min 1 3

HX c

eC T T

C T T

C T T C T T

(B-1)

1 exp 1

1 exp 1

HX

HX r

r HX r

NTU C

C NTU C

(B-2)

min

max

rC

CC

(B-3)

c

e

m

Condenser mass flow rate

rEvaporator mass flow rate m

(B-4)

min c pa

ce

r

C m c if m m

Cr

(B-5)

Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 15

Considering the first case, when Cr = r, Eq. (B-2) can

be written as:

which gives:

In terms of the net resistance:

where:

and in this case:

From Eq. (B-4) and (B-9)-(B-12):

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:

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.

.

min e pa

ec

r

C m c

if m m

1

Cr

(B-6)

HX

HX

HX

1 exp NTU 1 r

1 r exp NTU 1 r

(B-7)

1

1ln

11

HX

HX

HX r

NTU r

(B-8)

1ec

HX

RR

UA

(B-9)

1

ccc

RNTU C

1

eee

RNTU C

(B-10)

(B-11)

HX

HX c

UA

NTU C

(B-12)

1

1

HX

ce

NTU r

NTU NTU

(B-13)

0.466

ee

cc

hm

hm

(B-14)

16 Mridul Sarkar

And from Eq. (B-13) and (B-15):

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:

At a reference condenser to evaporator flow ratio,

Eq.(B-17) takes the form as:

As shown earlier in Eq. (A-10) for WAHP, similar

expression can be written for evaporator of HPHX as:

Taking the ratio of heat pipe NTU from Eq. (B-8) into

account, one can write:

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:

where, the exponent ‘z’ is a function of mass flow ratio

and is given by:

Reiterating the steps shown above for the case when

r >1 and:

The effectiveness at any supply flow rate can be

expressed in terms of the reference effectiveness as:

0.534 0.534

1

ee

cc

NTU m

NTU m r

(B-15)

0.466

e0.534

HX

NTU 1r

NTU r

(B-16)

0.466

0.534

1r

r

(B-17)

0.466

ref

ref 0.534

ref

1r

r

(B-18)

ref ref

0.534

ee

ee

NTU m x

NTU m

(B-19)

ref ref

ref

HX

HX

HX

HX

HX

HX ref

ref

1r

1ln

1 r 1

NTU

NTU 1r

1ln 1

1r

(B-20)

1

1

1

1

HX

HX

HX ref

z

r

rr

(B-21)

1

1

ref

ref

r

xr

z

ec

m m

HX

HX

HX

ref

y

1

1r

1

11

r

1r

(B-22)

Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 17

Where the exponent ‘y’ is:

and evaporator to heat pipe NTU ratio ‘λ’ for this case

is given by:

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 (B-

22) 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.

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

ref

ref

1

1r

yx 1

1r

10.466

e

HX

NTU r

NTU

(B-23)

18 Mridul Sarkar

Nomenclature

Symbols

A Surface area (m2)

BF Bypass factor

C 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 Specific heat capacity of vapor (1.86 kJ/kg-K)

D Hydraulic diameter (m)

DPT Dew point temperature (oC)

h Convective heat transfer coefficient (W/m2-K)

kf Thermal conductivity of fluid (W/m-K)

l0 Specific latent heat of vaporization of water at 273

(2501 kJ/kg)

Air mass flow rate (kg/s)

NTU Number of heat transfer units

Nuc Nusselt number

P Saturation vapor pressure (kPa)

Pr Prandtl number

Pt Ambient pressure (kPa)

Q Volume flow rate

Heat transfer rate (kW)

q Specific enthalpy of air (kJ/kg)

qe Specific saturation enthalpy of air at effective

surface temperature of evaporator (kJ/kg)

R 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 Reynold’s number

RH Relative humidity

r Condenser to evaporator mass flow ratio

t Air temperature (oC)

te Effective surface temperature of evaporator (oC)

U Overall heat transfer coefficient (W/m2-K)

Greek symbols

α Ratio of molecular mass of water vapor and dry air

(0.622)

ε Effectiveness of WAHP

Humidity ratio (kg moisture/kg DA)

Subscripts

0 Reference state (273.15 K)

1 Evaporator inlet

2 Evaporator outlet / dehumidifier coil inlet

3 Dehumidifier coil outlet / condenser inlet

4 Condenser outlet

a Of air

adp Apparatus Dew Point

c At condenser

e At evaporator

HX Heat pipe heat exchanger

min. Minimum

ref Reference performance

WAHP 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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