Abstract—This paper describes the design of a thermal comfort controller for indoor thermal environment regulation. In this controller, Predicted Mean Vote (PMV) is adopted as the control objective and six variables are taken into consideration. Meanwhile, a kind of direct neural network (NN) control is designed, and a thermal space model for Variable-Air-Volume (VAV) application is developed. Based on the computer simulation, it is seen that this thermal comfort controller can maintain the indoor comfort level within the desired range under both heating / cooling modes. Furthermore, by combining the energy saving strategy with the VAV application, it also shows the potential for energy saving in future.

I. INTRODUCTION

RESENTLY, in tropic and sub tropic regions, heating, ventilating and air conditioning (HVAC) system has

become a common commodity and is wildly used in the residential buildings and industrial applications. In China, the consumption of energy by HVAC constitutes 15% of the domestic energy consumption, but most of the HVAC systems still adopt the temperature / humidity controllers which are cheap but can not achieve both the highest comfort level and energy saving at the same time. Facing ever increasing pressure of energy saving, it is necessary to design a kind of HVAC controller with higher efficiency and comfort level.

To overcome this problem, a new concept of thermal comfort control has been proposed during the past decades. Some indices, such as “Standard Effective Temperature” (SET) [1] and “Predicted Mean Vote” (PMV) [2], have been set up to evaluate the indoor thermal comfort. PMV is proposed by Fanger in 1970, used to predict the mean thermal sensation vote on a standard scale for a large group of persons. Currently it has been widely used and adopted by ISO 7730 standard [3]. Meanwhile, some thermal comfort sensing systems [4] and controllers have been designed. MacArther [5] and Scheatzle etc [6] developed a kind of comfort index regulators (CIR) [7], which were dependent on PMV, took 0 (neutral) as the default reference input, and the

Manuscript received February 18, 2005. This work was supported in part by a grant (Grant No. UIM/122) from Innovation and Technology Commission of Hong Kong and Aoyagi (H.K.) Ltd.

Jian Liang is with the Department of Automation and Computer-Aided Engineering, the Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China (corresponding author to provide phone: 852-3163-4237; fax: 852-2603-6002; e-mail: jliang@acae.cuhk.edu.hk).

Ruxu Du is with the Department of Automation and Computer-Aided Engineering, the Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China (e-mail: rdu@acae.cuhk.edu.hk).

occupant as a supervisory controller by adjusting the reference value. Federspiel developed another kind of user-adaptable comfort controller (UACC) [7], in which the thermal sensation model was based on a simplified PMV-like index, and the model parameters could be tuned by learning the specific occupant’s thermal sensation.

In this paper, we describe the design of a thermal comfort controller based on neural network control. This controller aims at providing the highest comfort level for specific user by learning the user’s comfort zone, and optimizing the system operation to achieve energy saving. PMV is adopted as the control objective, in which six variables are taken into consideration. Then a thermal space model for VAV application is developed. To overcome the nonlinear feature of PMV calculation and provide better control performance, a kind of direct NN controller is designed and investigated. To minimize the energy consumption further, energy saving strategy and VAV application are combined and analyzed. The simulation results confirm the controller design and potential application for energy saving in HVAC systems.

II. DESIGN OF THE THERMAL COMFORT CONTROLLER

The mentioned comfort controllers above are still based on the conventional on-off control or PI / PID control, and the energy saving hasn’t been taken into consideration yet. In this paper, we propose a new kind of a thermal comfort controller based on neural network control, which is similar to CIR but with more powerful functions. The system structure is shown in Fig. 1. It consists of several major components: learning of the user’s comfort zone, minimum-power control strategy, direct NN controller, thermal sensation model and HVAC

system. Compared to the previous comfort controllers, the major

contribution of this controller can be summarized as follows: 1) Comfort zone is set by learning the user’s input

Thermal Comfort Control Based on Neural Network for HVAC Application

Jian Liang and Ruxu Du

P

Fig. 1. Block diagram of the intelligent comfort control system.

Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

TB2.5

0-7803-9354-6/05/$20.00 ©2005 IEEE 819

command to meet the comfort preference of specific user.

2) Direct NN controller based on back-propagation algorithm is designed to overcome the nonlinear feature of PMV calculation and enhance control performance.

3) Minimum-power control strategy is designed by combining an energy saving strategy and VAV control to improve the indoor air quality and system efficiency.

III. MODELS OF THE THERMAL COMFORT CONTROLLER

A. Thermal Sensation Model In this thermal comfort controller, PMV is adopted as the

control object to evaluate the indoor comfort level. The thermal sensation model based on Fanger’s PMV formula can be used to calculate the PMV value as follows [2]:

)}(])273()273[(10

96.3)34(0014.0)867.5(0173.0]15.58)[(42.0])(000699.0

733.5[05.3){()3033.0028.0(

448

036.0

aclcmrtcl

a

M

TThfclTTfcl

TMPaM

WMPaWMWMePMV

−×−+−+××

−−−−−−−−−−−

−−×+= −

(1)

where

)}(])273()273[(

1096.3{155.0)(028.07.3544

8

aclcmrtcl

clcl

TThfclTTfcl

IWMT

−×−+−+×

×−−−= −

(2)

≤+

≥+−=

airaclair

airaclaclc

VTTforV

VTTforTTh

1.12)(38.21.12

1.12)(38.2)(38.225.0

25.025.0 (3)

In the above equations, M is metabolism (W/m2); W is external work (W/m2); Pa is partial water vapor pressure (Pa), which is related to relative humidity; fcl is ratio of clothed body surface area to nude body surface area; Tcl is surface temperature of clothing; Icl is thermal resistance of clothing (clo); hc is convectional heat transfer coefficient (W/m2·K).

In the calculation, six variables are involved: the user’s activity level and clo-value, indoor air temperature, mean radiant temperature, relative air velocity and humidity. Furthermore, the seven point psycho-physical ASHRAE scale is used to measure the thermal comfort level as: -3 (cold), -2 (cool), -1 (slightly cool), 0 (neutral), +1 (slightly warm), +2 (warm), +3 (hot). To guarantee a comfort indoor climate, ISO recommends to maintain PMV at 0 with a tolerance of 0.5.

Since the above PMV calculation is nonlinear and complicated, the iterative calculation is necessary. This is a problem for real time control, particularly if the iterative solution is not unique [7], [8]. To solve the problem, many researchers proposed some simplified calculation models [7] –[11]. In this paper, the computer calculation model proposed by D. Int-Hout [9] is adopted for simulation. If high real time performance is required, the PMV-like index proposed by Federspiel [7] or neural network model can also be adopted.

B. HVAC and Thermal Space Model To evaluate the indoor thermal environment, some lumped

parameter models of single-zone HVAC systems have been

proposed [12]–[15], but none of them considered all the necessary factors in a VAV HVAC system for comfort control and indoor air quality control. In this paper, a complete HVAC and thermal space model for VAV application is derived by enhancing Betzaida [14] and Federspiel’s models [12], as shown in Fig. 2. In the model, four environmental-dependant variables for PMV calculation are involved, and the VAV control and ambient disturbance are also considered.

This model consists of several major components: variable-frequency compressor, heat exchanger, variable speed fan, connecting ductwork, damper and mix air components. Some assumptions are made as follows: (i) The wall temperature is equal to the mean radiant temperature, i.e. Tmrt = Tw; (ii) The indoor air relative velocity is proportional to the supply air flow rate, i.e. Vair = kfmix; (iii) The humidity mass ratio is proportional to the vapor pressure, i.e. W = Kwvp;(iv) The heat transfer coefficients are the sum of a natural convective heat transfer coefficient and a forced convective heat transfer coefficients [12], [16], i.e. h = hc+hvV

2/3; (v) Time delay is negligible.

The mathematical model is derived from the energy conservation and mass balance in different system components, and the sensible and latent heat exchange are both considered. In the air flow mixer, the return air and the fresh air are missed perfectly, and hence, the equation can be given as:

aomix Tr

rT

rT

11 −+= (4)

aomixaomix p

rr

pr

pWr

rW

rW

1111 −+=−+= (5)

In the heat exchanger, for the supply air, the equation is given as:

]0.0,)(min[')()( shehehesmixwvfgmixsmixpmixshep pTphQppKHfTTCfTVC −++−+−=•

ρρρ (6)

)(]0.0,)(min['smix

he

mixwvshe

hefg

heswv pp

Vf

KpTpVH

hpK −+−=• (7)

where is the Lewis relation, which is derived as =HfgKwv/Cp

in this model; hhe' is heat transfer coefficient on the surface of heat exchanger, which is derived as hhe'=hheVair'

2/3Ahe; Qhe is the thermal power from the heat exchanger, which is derived

Fig. 2. HVAC and thermal space model

820

as: )(' 3/2

sheheairhehe TTAVhQ −= (8) For the heat exchanger, the governing equation is derived

as:

inshehesheheairhehehe QpTphTTAVhTC +−−−−=•

]0.0,)(min[')(' 3/2 (9) In the thermal space, the governing equations can be given

as: )()( as

a

mixaas

a

mixa pp

Vf

pWWVf

W −=−=•• (10)

wloadaswvfgmixaspmixaap QQppKHfTTCfTVC ++−+−=•

)()( ρρρ (11)

where Qw includes the thermal power from the side walls, the roof, the floor and the side windows for simplification, and can be derived as: )( awwww TTAhQ −= (12) where hw is heat transfer coefficient on the surface of side walls, which is derived as hw = hc+hvVair

2/3. In the side walls, the equation describing the heat

transfer process can be derived as:

)()( owwoawwwww TTAhTTAhTC −−−−=•

(13) Based on the above equations, the state-space model for

the HVAC and thermal space can be derived as follows:

−

−−++−

−−−+−

+−−−−

−+++−+−

−+−+−−++−−+

=

•

•

•

•

•

•

)(

])11[(]0.0,)(min['

)()()(

]0.0,)(min[')('

)]([)()()(

]0,)(min[')('])11[(])11[(

3/2

3/2

3/23/2

3/2

3/23/2

asa

mix

saohe

mixshe

wvhefg

heairhe

oww

woaw

w

wairvc

he

inshe

he

heairheshe

he

heairhe

awwap

airvc

ap

loadas

ap

wvfgmixas

a

mix

hep

sheheairheshe

hep

heairhesao

hep

wvfgmixsao

he

mix

a

s

w

he

a

s

ppVf

ppr

rp

rVf

pTpKVH

AVh

TTCAh

TTC

AVhh

CQ

pTpC

AVhTT

CAVh

TTAVCVhh

VCQ

ppVC

KHfTT

Vf

VCpTpAVh

TTVC

AVhpp

rr

prVC

KHfTT

rr

TrV

f

p

p

T

T

T

Tρρ

ρρ

(14) Since the thermal space model is developed for VAV

application, three control inputs are provided in this HVAC system as u = [Qin, fmix, r]: heating / cooling capacity Qin is controlled by the variable-frequency compressor; variable-air-volume is controlled by the variable-speed fan to adjust indoor air flow rate fmix; system-to-fresh-air volumetric flow-rate ratio r is controller by return air damper. Three kinds of disturbances are also taken into consideration in the system design as d = [Qload, To, po]: variation of indoor cooling / heating load Qload, ambient temperature To and humidity RHo(po).

When the HVAC system works in cooling mode, water vapor condensation may occur in the heat exchanger, which means that the corresponding term min[p(The)–ps, 0.0] is nonzero. Therefore, the above model is nonlinear. But in the heating mode, no water vapor condenses, so it means min[p(The)–ps, 0.0]. Furthermore, if the controlled parameters fmix and r are only adjusted discontinuously at some specific moment, they can be regarded as constant within the running period. Therefore, the above model can be simplified and

linearized as:

inhe

load

o

o

he

mix

w

wo

ap

hep

wvfgmix

he

mix

a

s

w

he

a

s

a

mix

a

mix

he

mix

he

mix

w

wo

w

wairvc

w

wairvc

he

heairhe

he

heairhe

ap

wvfgmix

ap

wvfgmix

ap

wairvc

ap

wairvc

a

mix

a

mix

hep

wvfgmix

hep

wvfgmix

hep

heairhe

he

mix

hep

heairhe

he

mix

a

s

w

he

a

s

QC

Q

P

T

rVf

CAh

VC

VrC

KHf

rVf

P

P

TT

T

T

Vf

Vf

rVfr

Vf

CAh

CAVhh

CAVhh

CAVh

CAVh

VC

KHf

VC

KHf

VCAVhh

VCAVhh

Vf

Vf

VrC

KHfr

VC

KHf

VCAVh

rVfr

VCAVh

Vf

p

p

T

T

T

T

++

−

−−

−+−+

−

−++

−−

−−

−−−

=

•

•

•

•

•

•

000

100

000

00

00000

100

0

0000

)1(0000

00)(

0)(

0

000'

0'

)(0

)(

)1(0

')1('

3/23/2

3/23/2

3/23/2

3/23/2

ρ

ρρ

ρρ

(15)

IV. DIRECT NN CONTROLLER

For the comfort controller, to overcome the nonlinear feature of PMV calculation, time delay and system uncertainty, some advanced control algorithms have been proposed, such as fuzzy adaptive control by A. I. Dounis [15] and Francesco Calvino [17], optimal comfort control by MacArthur [18], and minimum-power comfort control by Federspiel [12]. In this paper, a kind of direct NN controller is designed based on back-propagation algorithm, as shown in Fig. 3. Compared to the common used indirect NN controller, the identification model of the plant is not necessary, and hence, it is easy to implement in practice and has been applied in the hydronic heating systems for temperature control by A. Kanarachos etc [13].

This direct NN controller is a MISO system, which has two inputs and one output: e is the error between the PMV set value and feedback value, •

e is the error derivative; and u is the output to control the HVAC system. A two-layer NN without hidden layer is adopted in this controller. The input in the output layer can be calculated as:

131211 wewewI ++=•

(16) where w11 and w12 are the weights, and w13 is the bias term. In this neural network, Unipolar Sigmoid function is adopted as the activation function, and hence, the output in the output layer can be calculated as:

)exp(11

2Iu

−+= (17)

Since u has been constrained within [0, 1], it is not necessary to set the output limitation for this controller. To adapt the weights, back-propagation law is adopted, which is

•e

Fig. 3. Design of the direct NN controller.

821

based on the gradient decent method and can be given as:

ijijij w

uu

PMVPMV

EwE

w∂∂

∂∂

∂∂−=

∂∂−=∆ ηη (18)

where E is the error function, which is defined as E=(PMV_SV-PMV)2/2 here. Meanwhile, according to the thermal comfort concept, it is obvious that PMV/ u is always negative / positive when the system works in cooling / heating modes. Therefore, (18) can be rewritten as:

ij

ij wu

PMVE

w∂∂

∂∂

±=∆ *η (19)

where “+” is used in cooling mode and “–” is used in heating mode. * is the learning coefficient, which should be set properly for good transient performance and stability. Then, the weight update can be given as: euuPMVSVPMVww )1()_(*

1111 −−= η (20)

•

−−= euuPMVSVPMVww )1()_(*1212 η (21)

)1()_(*1313 uuPMVSVPMVww −−= η (22)

Based on the above equations, the implementation procedure of this direct NN controller in each time step can be given as follows: 1) Acquire the input signals, and calculate the node input I

and output u in the output layer based on (16) and (17); 2) Update the weights in the output layer based on (20), (21)

and (22); 3) Calculate the node output u based on the new weights,

and finally update the output control signal.

V. SIMULATION AND DISCUSSIONS

A. Simulation Settings Using the dynamic models above, a number of computer

simulations were carried out to study the system performance under various conditions and control strategies. In the simulation, both heating and cooling modes, CAV and VAV applications are all taken into consideration. First of all, we analyze the comfort level under temperature controller, and compare it to the comfort controller; then we evaluate the control performance of the direct NN controller under

ambient disturbance and cooling load disturbance; based on these, the system performance under VAV control and energy saving strategy are investigated. In the simulation, the settings of major parameters in heating / cooling modes are listed in Table I.

Based on the simulation settings, when the HVAC system works in heating mode under CAV control, the system model in (15) can be rewritten as:

in

load

o

o

a

s

w

he

a

s

a

s

w

he

a

s

Q

Q

P

T

PP

TT

TT

p

p

T

T

T

T

++

−−

−−

−−−−

=

•

•

•

•

•

•

000

005-3.3333e00

00000.0680000004-3.1875e000

005-1.1149e0001.03180.0680

0.00360.003600000.20400.27200000

00004-5.4650e0004-2.2775e00000.013600.0136

0.05500.05500.004100.00770.00363.09554.127400.34172040.06137.0

(23)

B. System Performance under Thermal Comfort Control To investigate the thermal comfort concept, we compare

the comfort level under the conventional temperature control and comfort control first. In the simulation, the HVAC system works in the cooling / heating modes, and both kinds of controllers are based on PI control: for the temperature control, the reference input is 23oC (cooling) and 25oC(heating) respectively; for the comfort control, the reference input is 0. The simulation is performed in 24 hours under CAV control with ambient temperature and humidity disturbance, which is simplified as a sinusoidal function with period of 24h. The results are shown in Fig. 4.

Based on the simulation results, it is seen that by using the conventional temperature control, the PMV values fluctuate between –0.5~0.5 under ambient disturbance. To achieve high comfort level, it is necessary to adopt the thermal comfort controller: although indoor temperature will vary slightly, PMV can always remain at the desired value and

TABLE ITHE SETTINGS OF MAJOR SIMULATION PARAMETERS

Simulation Parameter Settings (Cooling)

Settings (Heating)

Dimension of thermal space 5m × 5m × 3m 5m × 5m × 3m Clo-value 0.6 1.3Activity level (Metabolic rate) 1.0Met (W/m2) 1.0Met (W/m2)Cooling / heating load QLoad 0.8KW –1.6KW HVAC capacity -8KW 12KW Desired minimum fresh air flow rate (for VAV)

150m3/h (0.042 m3/s)

150m3/h(0.042 m3/s)

Air flow rate fmix (for CAV) 980 m3/h (0.272 m3/s)

980 m3/h (0.272 m3/s)

Mixed air ratio r (for CAV) 4 4 Outdoor temperature range To 25oC~33oC 4oC~12oCOutdoor Humidity range RHo 65%~85% 45%~65%

0 5 10 15 20

15

20

25

30

Tem

pera

ture

(o C)

0 5 10 15 20

-1

-0.5

0

0.5

Time (hour)

PM

V

Thermal comfort control (cooling)Thermal comfort control (heating)

Temperature control (cooling, 23oC)

Temperature control (heating, 25oC)

Thermal comfort control (cooling) Thermal comfort control (heating)

Temperature control (cooling, 23oC)

Temperature control (heating, 25oC)

Fig. 4. System performance under thermal comfort control and conventional temperature control.

822

show potential for energy saving.

C. System Performance under Direct NN Control To overcome the nonlinear feature of PMV calculation and

provide better performance, the thermal comfort controller is designed based on direct NN control. To analyze the controller performance, we compared it to a well-tuned PI controller with integral anti-windup as follows: ]11[

sTKu

ic += (24)

where Kc = –2.0, Ti = 118. When the control output reaches the limitation, the integral action is cut off.

The simulation is performed in cooling mode within 120 minutes under setpoint variation and cooling load disturbance respectively: the former occurs at 30 and 60 minutes, changes from 0 to 0.5, and then back to 0; the later occurs at 90 minutes and changes from 800W to 1600W. The simulation results of PMV and control signal are shown in Fig. 5.

From the simulation results, it is seen that the direct NN controller has the similar control performance as the well-tuned PI controller with integral anti-windup, and can reach the setpoint in a short time with small overshoot. In the simulation, its learning coefficient is set as * = 0.315, which is critical in the design and has to be set properly with respect to the practical process, or the system performance will be

bad, such as unstable or slow response. Compared to the PI control, this direct NN controller exhibits some advantages: (i) There is only one adjustable parameter, learning coefficient, and hence, it is easier to implement and fine tune in practice; (ii) The control signal is very smooth and provide

good control performance. Based on the direct NN control, the thermal comfort

controller can be used to regulate the indoor thermal environment efficiently. When it works in cooling / heating modes under ambient disturbance, by letting PMV = 0, the dynamic responses of the temperature and humidity in the thermal space are shown in Fig. 6 and Fig. 7.

D. System Performance under VAV Control The above simulations are based on the CAV control. To

enhance indoor air quality and the HVAC performance further, a minimum-power control strategy is designed based on VAV control. By adjusting the air flow rate fmix, mixed air ratio r, and the PMV value according to the user’s comfort zone, energy saving can be obtained. The implementation procedure in cooling mode can be described as follows: 1) At start up, HVAC operates at QuickCool Mode: fmix is

set at the high level, and PMV value is maintained at the lower limit of comfort zone;

2) Then HVAC operates at Comfort Mode: fmix is set at medium level and PMV value is changed and maintained at the highest comfort level during a HoldTime;

3) Beyond this period (such as at night), HVAC operates at Energy Saving Mode: fmix is set at the low level and r is set at the high level, the cooling power decreases and PMV value increases at a rate till it approaches to the limit of comfort zone.

Under this strategy, simulation is performed during 12 hours as shown in Fig. 8, and compared to the CAV control. The user’s comfort zone is assumed between -0.5~0.5, and

0 20 40 60 80 100 120-0.2

0

0.2

0.4

0.6

0.8

Time (minute)

PM

V

0 20 40 60 80 100 120

0

0.2

0.4

0.6

0.8

1

Time (minute)

Con

trol

sig

nal

Direct NN controlPI control (anti-w indup)

Direct NN controlPI control (anti-w indup)

Fig. 5. System performance under direct NN control and PI control.

0 20 40 60 80 100 1205

10

15

20

25

30

35

Time (minute)

Tem

pera

ture

(o C)

0 20 40 60 80 100 12040

50

60

70

80

90

100

Time (minute)

Hum

idity

(%

)

Supply air humidity

Indoor air humidity

Supply air temperature

Indoor air temperatureHeat exchanger temperature

Wall temperature

Fig. 6. Cooling response under thermal comfort control.

0 20 40 60 80 100 120

10

20

30

40

50

60

70

80

90

100

Time (minute)

Tem

pera

ture

(o C)

0 20 40 60 80 100 1200

10

20

30

40

50

60

Time (minute)

Hum

idity

(%

)

Supply air temperature

Indoor air temperature

Heat exchanger temperature

Wall temperature

Supply air humidity

Indoor air humidity

Fig. 7. Heating response under thermal comfort control.

0 5 10

-0.4

-0.2

0

0.2

0.4

0.6

Time (hour)

PM

V

0 5 100

5

10

15

20

25

30

Time (hour)

Coo

ling

Pow

er (

KW

h)

VAV control

CAV controlVAV control

CAV control

Fig. 8. System performance under VAV control and CAV control.

823

VAV control is applied to change fmix and r to maintain the required fresh air fo = 150m3/s.

It is seen that within 12 hours, cooling power consumed by VAV and CAV systems are 25.93KWh and 28.93KWh respectively, and hence, 3KWh cooling power can be saved.

VI. CONCLUSION

This paper presents a thermal comfort controller for HVAC application, and validates it by simulation. Compared to the conventional HVAC controllers, three factors play important roles in the design: the thermal comfort control, the direct NN control, and the VAV control based on minimum-power strategy. By using this controller, high comfort level and energy saving can be obtained at the same time, but it should also be mentioned that there still exist some limitations in practice. For example, two personal-dependent variables, activity level and the clo-value, are involved in the PMV calculation, but they can not be measured by using the sensors directly, and hence, they can only be set as a constant with respect to the season. Therefore, much work is still required to improve the controller performance. If the sensor technique could be improved and cost could be reduced further, the proposed thermal comfort controller would have a great potential in the future of HVAC application.

APPENDIX

Nomenclature Ahe Surface area of the heat exchanger (m2)Aw Surface area of the walls, windows, etc. (m2)Che Heat capacity of the heat exchanger (J/oC) Cp Constant pressure specific heat of air (J/kg·oC) Cw Heat capacity of the side walls (J/oC) fmix Mixed air Volumetric flow rate (m3/s)fo Fresh air Volumetric flow rate (m3/s)Hfg Enthalpy of water vapor (J/kg)ho Outdoor heat transfer coefficient (W/m2·oC) hw Heat transfer coefficient in the side walls (W/m2·oC) Lewis relation Air density (kg/m3)

P(T) Saturated Vapor pressure at temperature T (Pa) Ps Vapor pressure near heat exchanger (Pa) Pmix Vapor pressure of water in mixed air (Pa) Qhe Thermal power from the heat exchanger (W) Qin Heat input provided by air conditioning system (W) Qload Cooling load in the room (W) Qw Thermal power from the wall (W) r System-to-fresh-air volumetric flow-rate ratio (fmix/fo)RHa Relative air humidity in thermal space RHo Relative air humidity outdoor Ta Temperature in thermal space (oC) The Temperature in the heat exchanger surface (oC) Tmix Mix Air temperature (oC) Tmrt Radiant air temperature indoor (oC) To Outdoor ambient temperature (oC)

Ts Supply air from the heat exchanger (oC) Tw Indoor wall temperature (oC) Vair Relative air velocity indoor (m/s) V'air Relative air velocity in the heat exchanger (m/s) Vhe Effective heat exchanger volume (m3)Vs Effective thermal space volume (m3)Wa Humidity mass ratio in thermal space Wmix Humidity mass ratio of mixed air Wo Outdoor humidity mass ratio Ws Humidity mass ratio of the supply air

REFERENCES

[1] A.P. Gagge, J.A.J. Stolwijk and Y. Nishi, “An effective temperature scale based on a simple model of human physiological regulatory response,” ASHRAE Trans., vol. 77, part 1, pp. 247–262, 1971.

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