Ciência/Science

88 Engenharia Térmica (Thermal Engineering), Vol. 10 • No. 01 - 02 • June and December 2011 • p. 88-95

SECOND LAW OF THERMODYNAMICS AND HUMAN BODY

C. E. K. Madya,

M. S. Ferreiraa,

J. I. Yanagiharaa,

P. H. N Saldivab,

and S. Oliveira Juniora

a Escola Politécnica da Universidade de São

Paulo

Departamento de Engenharia Mecânica

Av. Prof. Mello Moraes 2231

CP. 05508-900, São Paulo, SP, Brasil

cekm@usp.br

soj@usp.br bFaculdade de Medicina da Universiddade de

São Paulo

Departamento de Patologia

Av. Dr. Arnaldo 445

CP. 01246-903, São Paulo, SP, Brasil

ABSTRACT

Exergy analysis was applied to assess the energy conversion processes that take place in the human body, aiming at developing correlations of the destroyed exergy and exergy efficiency with the constants of the thermoregulatory system of a human model. Moreover the main concern of the present work was obtaining the exergy behavior of a healthy person. The analysis was applied to a model composed of 15 cylinders with elliptical cross section representing: head, neck, trunk, arms, forearms, hands, thighs, legs, and feet. For each cylinder a combination of the following tissues was considered: skin, fat, muscle, bone, brain, viscera, lung, and heart. From this model it was possible to obtain the energy and exergy transfer to the environment associated with radiation, convection, vaporization and respiration. It was also possible to calculate the energy and exergy variation of the body over time. Results indicate that the energy transfer to the environment is one order of magnitude larger than the exergy transfer and both have different trends. Simulations were carried out for different constants of the thermoregulatory system, and the results that gave the thermal response close to experimental responses of the human body, are in a point near to the minimum exergy destruction and maximum exergy efficiency. Keywords: Human Body; Exergy Destruction; Exergy efficiency

NOMENCLATURE B exergy rate/flow rate, W B body exergy, J c specific heat, J/kgK cp specific heat at constant pressure, J/kgK H enthalpy flow rate, W hlv enthalpy of vaporization, J/kg M metabolism, W m mass flow rate, kg/s P pressure, Pa Q heat transfer rate, W R gas constant, J/kgK S entropy rate and flow rate, W/K s specific entropy, J/kgK slv entropy of vaporization, J/kgK T temperature, K t time, s U internal energy, J W power, W

Greek symbols η Exergy efficiency φ relative humidity

ω blood perfusion, m3/m3s

Subscripts and superscripts 0 reference a environment air ar arterial blood bl blood c convective cl clothing dest destroyed e evaporative ex expired hy hypothalamus in inflow M metabolic out outflow r radiative res respiration sk skin ve venous blood w water vapor INTRODUCTION

The comprehensive study of human body

behavior requires the use of the Second Law of

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Thermodynamics in order to assess the quality of the energy conversion processes that take place in human body.

One of the first authors that tried to describe life as a function of the physical quantity entropy was Schrödinger (1945). Prigogine and Wiame (1946) proposed a principle that a biological organism tends to progress to a state of minimum entropy production (minimum entropy production principle).

Several authors performed experimental studies attempting to confirm the minimum entropy principle. Stoward (1962) studied the entropy production in bacterial culture. Zotin and Zotina (1967) examined different organism (from trout eggs to organism). Balmer (1982) studied the fish Nothobranchius guentheri, a species that lives in interment rivers of the East Africa and has the life cycle of 12 months. They all based the idea that most of entropy production is related to metabolism. Other authors, such as Aoki (1987, 1989, 1990, 1991), Rahman (2007), Silva and Annamalai (2008, 2009) analyzed the entropy generation over the lifespan and their results confirmed the minimum entropy principle. Mady et al. (2012a) obtained that not only the entropy production decreases over time, but also the exergy efficiency decreases as a function of lifespan.

Batato et al. (1990) performed the exergy analysis and found that, although the energy losses to the environment are considerable, the exergy losses are negligible. Mady et al. (2012b) proposed a model to calculate the human body exergy metabolism which takes into account the consumption of nutrients (carbohydrates, lipids and proteins). Both authors obtained that in basal conditions the metabolism in energy and exergy basis have similar magnitudes.

Prek (2005, 2006), Prek and Butala (2010) aiming to obtain the relation between exergy consumption with thermal comfort conditions proposed a two node model of human body, where it was obtained that only a combination of environmental conditions ensures minimum destroyed exergy. Mady et al. (2012a) obtained that the human body destroy less exergy and is more efficient in higher temperatures and lower relative humidities.

Albuquerque Neto et al. (2010) and Mady et al. (2012c) applied the exergy analysis to runners in treadmill during an exercise test.

The purpose of the present work is to apply the exergy analysis, previously indicated in Mady et al. (2012a) and Mady et al. (2012b) on the thermal model developed by Ferreira and Yanagihara (2009). It was made a comparison of the energy and exergy rates and flow rates to environment as a function of relative humidity, air temperature and mean radiant

temperature. Furthermore, the exergy analysis was made to investigate the experimental constants of the thermoregulatory system. The aim was to obtain a response for a set of specific anatomic parameters that is close to experimental results (based on the concept of minimum destroyed exergy and maximum exergy efficiency).

MODEL DESCRIPTION

Figure 1 indicates a model with a schematic representation of the human body, where it is indicated the heat transfer rate and enthalpy flow rates associated with radiation (Qr), convection (Qc), vaporization (He), respiration (Hex-Ha), food intake, food wastes, water intake and urine. The model was previous demonstrated in Mady et al. (2012b). The term QM is the heat released to the body caused by the cellular metabolism. In this figure the human body is divided in two control volumes, CV1 and CV2. The first one represents the thermal system and respiratory system and the second the cellular metabolism.

According to Rahman (2007) in a period of one day the mass input (food, liquids and inspired gases) is equivalent to the mass output (food wastes, urine, expired gases and vaporization). In shorter periods of time this may not be verified. In this article, for the sake of the simplicity, the variation of body mass due to food and water intake, wastes and accumulation is neglected.

The Energy and Exergy Analysis is applied in the control volume shown in Fig. 1, with given environment and reference conditions such as temperature (T0 = Ta), pressure (P0 = Pa) and relative humidity (Φ0 = Φa). Thus, a general equation of the exergy balance:

destk k

0koutin BW

TT1QBB

dtdB

−−⎟⎟⎠

⎞⎜⎜⎝

⎛−+−= ∑∑∑

(1)

The energy (M) and exergy (BM) metabolism for

the whole body are part of the total internal energy (dU/dt) and exergy (dB/dt) variation of the body over time:

ΔTdtdUM

dtdU

+−= (2)

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−=+−=

ΔT0

ΔTM

ΔTM dt

dSTdtdUB

dtdB

dtd BB

(3)

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90 Engenharia Térmica (Thermal Engineering), Vol. 10 • No. 01 - 02 • June and December 2011 • p. 88-95

Figure 1. Schematic representation of the human body, with the intake of food, water and inspired air; and output of food, urine, expired air, vaporization trough skin and heat release due to radiation and convection.

In Eqs. (2) and (3), U is the internal energy of the body, B is the exergy of the body; dU/dt│ΔT and dB/dt│ΔT are the internal energy and the exergy variation of the body due to a variation in environmental conditions, respectively. This last term is related to the variation of the internal energy and entropy variation of the body over time, as in Eq. (3). In Eqs. (2) and (3) there is an assumption that the variation of the volume of the body is neglected. The energy and exergy variation of the body over time due to transient conditions is considered only in CV1.

The energy and exergy balance for CV1, and the exergy intake of this control volume are:

( )resercMΔT

ΔHHQQQdtdU

+++−=

(4)

( )ΔT

resercQCV1dest dt

dΔBBBBBBM

B−+++−=

(5)

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

b

0MQ T

T1QBM

(6)

In Eq. (4) the energy intake QM is the heat

released to CV1 caused by the metabolism. The terms Qc, Qr are the heat transfer rates to the environment associated with convection and radiation, He and ΔHres are the enthalpy flow rate related to vaporization and respiration. In Eq. (5) the exergy intake is BQM, indicated by Eq. (6). Where, BQM is the exergy transferred to CV1 caused by the exergy metabolism, T0 is the environment/reference temperature and Tb the body temperature. The exergy rate and flow rates Bc, Br, Be and ΔBres (Bex - Ba) are the exergy rates and flow rates associated with convection, radiation, vaporization and respiration, previously determined in Mady et al. (2012a).

The cellular metabolism is a representation of the human cells. In this control volume (CV2) the reactions of oxidation of the energy substrates, also called metabolism, take place. The energy and exergy balance for CV2 are:

prodreacM HHQ −=

(7)

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−=

b

0Mprodreac

CV2dest T

T1QBBB (8)

In Eqs. (7) and (8), Hreac is the enthalpy of the

reactants (carbohydrates, lipids, amino acids and oxygen), Hprod is the enthalpy of the products (urea, liquid water and carbon dioxide), Breac is the exergy content of the reactants and Bprod is the exergy content of the products.

The metabolisms in energy and exergy basis are:

prodreac HHM −= (9)

prodreacM BBB −= (10) Equations (7) to (10) indicate that from the

energy balance the condition QM=M is satisfied, but BM differ from BQM.

For the whole body as a control volume, the energy and exergy balance are:

( )resercΔT

ΔHHQQMdtdU

+++−=

(11)

( )resercMbodydest ΔBBBB

dtdBB

ΔT

+++−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−=

B (12)

Equations (11) and (12) are for basal conditions,

so W=0. Note that Eq. (5) takes into account only the thermal part of metabolism. Eq. (12) is similar to the analysis proposed by Batato et al. (1990). The

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difference between these two approaches is that all the exergy released to the body in CV2 is neglected if Eq. (4) is used as the metabolic exergy as indicated in Mady et al. (2012c). Although, for the energy balance, in steady state conditions Eq. (4) is equal to Eq. (11), because M=QM.

The exergy efficiency can be calculated as:

ΔTM

destdest

dtdB

B1dt

dB1η

BB+−

−=−= (13)

If the body temperature is constant, than

dB/dt│ΔT becomes zero in Eq. (13). HUMAN THERMAL MODEL

The human thermal model developed by Ferreira and Yanagihara (2009) is composed of the thermoregulatory and passive system. The first is related to physiological responses to changes in thermal environment or activity level: vasodilatation or constriction, shivering and sweating. The second includes heat conduction inside the body, heat transfer by convection because of the flowing blood and heat and mass transfer between the body and the environment.

As presented by Ferreira and Yanagihara (2009), the global data of the anatomic model used are: height 1.76 m, weight 67 kg, surface 1.8 m2 and volume of 0.0627 m3. The human body was divided into 15 cylinders representing the head, neck, trunk, arms, forearms, hands, thighs, legs and feet which represent a model with realistic dimensions. Each cylinder has a combination of some of these tissues: skin, fat, muscle, bone, brain, viscera, lung and heart. With exception of the head and trunk, that have composition as function of the cross section, all cylinders have composition independent of the cross section.

The heat conduction equation with constant density and specific heat and internal heat generation (metabolism) is solved for each tissue. The numerical solution is achieved using a coordinate transformation which transforms an elliptical cylinder in Cartesian space in a parallelepiped in the new coordinate system. To calculate the heat transfer between tissues and blood it was necessary to divide vessels in two classes the small ones (that can be treated as part of continuum) and the big ones. The model is similar to the one proposed by Pennes (1948) with the difference that the arterial blood temperature depends on the position inside the tissue and it is not equal to the body core temperature. The big vessels can be modeled as proposed by Wissler (1985), using two reservoirs, one of arterial blood and other of venous blood, with exception of the trunk

that is modeled with only one reservoir. From this model it is possible to obtain heat and mass transfer to the environment through skin due to radiation, convection and evaporation, as well as mass flow rates due to respiration (difference of temperature and humidity of inspired and expired air). It is also possible to obtain the transitory response of body due to a variation on environment conditions (temperature dependence with time). A representation of the model is indicated in Figures 2 and 3.

Figure 2. Human thermal model with the circulatory system. Obtained in Mady et al. (2012a).

Figure 3. Representation of each segment with the circulatory system. Obtained in Ferreira and

Yanagihara. (2012b).

In Ferreira and Yanagihara (2009) model of thermoregulatory system comprises the mechanism of vasodilatation and constriction, shivering and sweating. For the vasomotor mechanism (variation of blood flow to the skin) the equation used was proposed by Savage and Brengelmann (1996):

)T(Tk)T(TkΔω sk,0sk2hy,0hy1sk −+−= (14)

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where in Eq. (14), Δωsk (m3/(m3.s)) is the skin blood perfusion rate variation (814x10-6 ≤ Δωsk ≤3345 m3/(m3.s)), k1 and k2 are constants whose values are 1810x10-6 and 181x10-6

m3/(m3.s) respectively, Thy and Thy,0 (K) are the hypothalamus temperature and reference temperature (brain temperature in the model - ), Tsk and Tsk,0 (K) are the skin temperature and reference temperature.

The equation proposed by Nadel et al. (1971) calculates the evaporation of sweat:

)10

TTexp(

)T(Tk

)T(Tk sk,0isk,

sk,0sk4

hy,0hy3ie,

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−

+−=H

(15)

where in Eq. (15), He,i (W/m2) is the evaporation of sweat in segment i, k3 and k4 are constants whose values are 197 and 23 W/(m2K).

Similarly to the Equation proposed by Gordon et al. (1976) it is possible to calculate shivering by:

ΔQk)T(Tk)T(TkM 7sk,0sk6hy,0hy5sh +−+−=

(16)

Where in Eq. (16), Msh (W) is the change in the metabolism due to shivering (0 ≤ Msh ≤ 429W), k5, k6 and k7 are constants whose values are 250W/K, 40W/K and 0.06, and ΔQ (W) is the difference between heat lost through skin in any instant and in thermal neutrality. ENERGY AND EXERGY METABOLISM

As indicated by Mady et al. (2012b) the energy and exergy metabolism can be calculated from the enthalpy and exergy variation of three reactions of oxidation: carbohydrates, lipids and amino acids (represented by glucose, palmitic acid and an amino acid with mean composition). Therefore, it is possible to obtain an equation of the metabolism in energy and exergy basis as a function of nutrients consumption or carbon dioxide production and oxygen consumption as in Mady et al. (2012b) ENERGY AND EXERGY TRANSFER TO ENVIRONMENT

The energy and exergy analysis proposed in the present work is based on a previous study by Mady et al (2012a). The heat transfer rate and mass flow rates to the environment were obtained from a procedure described in Ferreira and Yanagihara (2009).

The exergy associated with radiation and convection are:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

skrr T

rT1QB (17)

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

sk

acc T

T1QB (18)

In Eq. (17) and (18), Tsk is the skin temperature

(K), Tr is the mean radiant temperature (K) and Ta is the air temperature (K).

The exergy flow rate due to vaporization through skin is determined by:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

w,0

skw,0wwlv0lvwe P

PlnTRmsThmB (19)

The first term in Eq. (19) is related to the

vaporization of the sweat on the skin and the second term is related to the difference in the concentration of saturated vapor near the skin and concentration of the vapor in the environment. In this equation, mw is the mass rate of sweat evaporated, hlv and slv are the enthalpy and entropy of vaporization of the water, respectively; Pw,sk is the water vapor pressure at skin temperature and Pw,0 is the water vapor pressure at reference temperature.

The exergy variation of the body associated with respiration can be calculated according to:

∑⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=i

i,0

exi,0iexi,

0

ex00exip,exi,

resres

PP

lnTRy

TTlnTTTcy

mΔB (20)

In Eq. (20), mres is the pulmonary ventilation, yi,ex

is the mass fraction of the gas i (oxygen, carbon dioxide, nitrogen, water vapor) in the expired air, cp,i is the specific heat, Tex is the expired air temperature, Pi,ex is the expired partial pressure of the gas i and Pi,0 is the partial pressure of the gas i, in the environment. TRANSIENT ANALYSIS

The temporal variation of exergy due to a variation in environment temperature over time (dB/dt│ΔT) is indicated by Eq. (3). The first term is the temporal variation of the internal energy and can be calculated from Eq. (11). The second term is the temporal variation of the body entropy and can be calculated for each element (j= hand, arm, forearm, etc) according to:

∑∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+==

j

jti,jbl,

j

jelement,

ΔT dtdS

dtdS

dtdS

dtdS

(21)

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎞⎜⎜⎝

⎛

=+

+

kve,

1kve,bljve,

kar,

1kar,bljar,

jbl,

TT

lncm

TT

lncm

dtd

dtdS

(22)

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⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑ +

i k,ti

1k,tititi

jti,

i

iii T

Tlncm

dtd

dtdS

(23)

In Eq. (21), for each cylinder j, the term dSbl,j/dt is the temporal variation of entropy in the blood compartment indicated in Eq. (22) and dSti,j/dt is the temporal variation of the entropy in the tissues indicated in Eq. (23) (the blood in the small vessels is already considered in the tissues). In Eq. (22), the subscript ar indicates arterial blood reservoir and ve indicates venous blood reservoir. Tar,k, Tar,k+1, Tve,k and Tve,k+1 are the temperatures of the reservoir of the component j at instant k and k+1 and cbl is the specific heat of the blood. In Eq. (23), i represents the tissue (skin, fat, muscle, etc), Tti,k, Tti,k+1 are the temperatures of the tissue i at instants k and k+1,respectively, and cti is the specific heat of the tissue.

RESULTS AND DISCUSSION

Results in Fig. 4(a) and (b) indicate the

contribution of the energy and exergy rates and flow rates to the environment as a function of relative humidity and operative temperature. The former is one order of magnitude higher than the later. Moreover, the energy transfer to environment is equal to metabolism (and has the same trend), but, the exergy transfer has a different trend indicating a first difference in applying the exergy analysis: the quality of the energy conversion process that takes place in the human body. The exergy transfer to environment is larger for lower relative humidities and higher temperatures, whereas the energy transfer is higher for lower temperatures and relative humidities.

Figure 4. (a) Energy - Eenv - and (b) exergy - Benv - transfer rate to the environment as a function of relative humidity (�) and operative temperature (To).

Therefore, the exergy analysis can be a powerful tool in adjusting the constants of Eq. (14) to (16), which are usually determined from experimental results (whose values are hard to find and are specific to a person) or from methods to adjust these constants to the specific anatomic characteristics of the model. Figures 5 to 7 indicate the exergy destruction and exergy efficiency as function of the thermoregulatory system constants.

In Fig. 5, for a temperature of 30oC, the constants of vasomotor mechanism do not affect significantly the total of exergy destruction. Although it is clear that the constants used in the model of Ferreira and Yanagihara (2009) (marked by a black arrow), which leads to a thermal response close to experiments, are close to the minimum of exergy destruction and maximum of exergy efficiency.

Figure 5. Exergy destruction and exergy efficiency as a function of constants k1 (a) and k2 (b).

In Fig. 6 the effects of the constants in total

exergy destruction are small, but the model constants values are at the minimum of exergy destruction and maximum of exergy efficiency in Fig. 6(a) and close to this result in Fig. 6(b). So, as before, the model constants (which give results close to experimental results) lead to the minimum exergy destruction and maximum exergy efficiency (or close to).

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Figure 6. Exergy destruction and exergy efficiency as a function of constants k3 (a) and k4 (b).

Finally, the increase in the metabolism own to

shivering has different effect on exergy analysis and it is more evident. The environment temperature chosen was 20oC (lower to thermal neutrality to cause the shivering). In Fig. 7 (a-c) the model constants are near the minimum of exergy destruction, but also the minimum of exergy efficiency. This is an expected result because an increasing in metabolism comes with an increasing of exergy destruction which decreases the exergy efficiency.

Figure 7. Exergy destruction and exergy efficiency as a function of constants k5 (a), k6 (b) and k7 (c). CONCLUSIONS

In this work a thermal model was used to analyze the exergy behavior of the body. From the range analyzed it is possible to conclude that the energy contribution of heat rate and mass flow rates is relevant, although the exergy rates are almost negligible. These are function of the environmental conditions, but with different slopes, indicating that the exergy analysis can add quality information in the analysis of the human body. Moreover fhe exergy analysis can be used as a tool to determine the constants of the thermoregulatory system for specific anatomic condition. Points around minimum destroyed exergy and maximum exergy efficiency are the ones that lead to thermal response close to experiments in subjects; even though the effect is not always elevated the method indicates the point of best parameter to choose. ACKNOWLEDGEMENTS The first author acknowledges FAPESP (São Paulo Research Foundation) for the PhD grant 09/17578-0. REFERENCES

Albuquerque Neto, C., Pellegrini, L. F., Ferreira, M. S., Oliveira Jr, S. and Yanagihara, J. I., 2010, Exergy Analysis of Human Respiration Under

Ciência/Science Mady et al. Second Law of Thermodynamics …

Engenharia Térmica (Thermal Engineering), Vol. 10 • No. 01 - 02 • June and December 2011 • p. 88-95 95

Physical Activity, International Journal of Thermodynamics, Vol. 13, No. 3, pp. 105-109.

Aoki, I., 1987, Entropy balance of white-tailed deer during a winter night, Bulletin of Mathematical Biology, Vol. 49, No. 3, pp. 321-327

Aoki, I., 1989, Entropy Flow and Entropy Production in the Human Body in Basal Conditions, Journal of Theoretical Biology, Vol. 141, No. 1, pp. 11-21.

Aoki, I., 1990a, Effects of Exercise and Chills on Entropy Production in Human Body, Journal of Theoretical Biology, Vol. 145, No. 3, pp. 421-428.

Aoki, I., 1991, Entropy Principle for Human Development, Growth and Aging, Journal of Theoretical Biology, Vol. 150, No. 2, pp. 215-223.

Balmer, R. T., 1982, Entropy and Aging in Biological Systems, Chemical Engineering Communications, Vol. 17, No. 1, pp. 171-181.

Batato, M., Borel, L., Deriaz, O. and Jequier, E., 1990, Analyse Exergétique Théorique et Expérimentale du Corps Humain, Entropie, Vol. 26, No. 153/154, pp. 120-130.

Coratassa, S., Aon, M.A., Iglesias, A.A., Lloyd, D., 2002, An Introduction to Metabolic and Cellular Engineering, World Scientific Pub Co Inc.

Ferreira, M.S. and Yanagihara, J.I., 2009a, A Transient Three-Dimensional Heat Transfer Model of the Human Body, International Communications in Heat and Mass Transfer, Vol. 36, No. 7, pp. 718–724.

Gordon, R.G., Roemer, R.B. and Horvath, S.M., 1976, A Mathematical Model of the Human Temperature Regulatory System — Transient Cold Exposure Response, IEEE Transactions on Biomedical Engineering, Vol. 23, No. 6, pp. 434–444.

Mady C.E.K., Ferreira M.S., Yanagihara J.I., Saldiva P.H.N., Oliveira Jr S., 2012a, Modeling the exergy behavior of human body, Energy, accepted manuscript, DOI: 10.1016/j.energy.2012.02.064

Mady, C.E.K. and Oliveira Jr, S., 2012b, Human body exergy metabolism, in: 25th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems, Perugia, Italy, pp. 160-1-160-13.

Mady, C. E. K., Albuquerque-Neto, C., Fernandes, T. L., Hernandez, A.J., Saldiva P. H. N., Yanagihara J. I. and Oliveira Jr S., 2012c, Exergy Based Indicators for Cardiopulmonary Exercise Test Evaluation, in: 25th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems, Perugia, Italy.

Nadel, E. R., Bullard, R. W. and Stolwijk, J. A. J., 1971, Importance of Skin Temperature in the Regulation of Sweating, Journal of Applied Physiology, Vol. 31, No. 1, pp. 80–87.

Pennes, H. H., 1948, Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm, Journal of Applied Physiology, Vol. 1, No. 2, pp. 93–122.

Prek, M., 2005, Thermodynamic Analysis of Human Heat and Mass Transfer and Their Impact on Thermal Comfort, International Journal of Heat and Mass Transfer, Vol. 48, pp. 731-739.

Prek, M., 2006, Thermodynamical Analysis of Human Thermal Comfort, Energy, Vol. 31, No. 5, pp. 732-743.

Prek, M. and Butala, V., 2010, Principles of Exergy Analysis of Human Heat and Mass Exchange with the Indoor Environment, International Journal of Heat and Mass Transfer, Vol. 48, pp. 731-739.

Prigogine. I. and Wiame. J., 1946, Biologic et Thermodynamique des Phenomenes Irreversibles, Experimentia, Vol. 2, No. 11, pp. 451-453.

Rahman, M. A., 2007, A Novel Method for Estimating Entropy Generation Rate in Human Body, Thermal Science, Vol. 11, No. 1, pp. 75-92.

Savage, M. V. and Bregelmann, G.L., 1996, Control of Skin Blood Flow in the Neutral Zone of Human Body Temperature Regulation, Journal of Applied Physiology, Vol. 80, No. 4, pp. 1249–1257.

Schördinger, E., 1944, What is life? The Physical Aspects of Living Cell, Ed. Cambridge University Press, Cambridge, UK.

Silva, C. and Annamalai, K., 2008, Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level, Entropy, Vol. 10, No. 2, pp. 100-123.

Silva, C. and Annamalai, K., 2009, Entropy Generation and Human Aging: Lifespan Entropy and Effect of Diet Composition and Caloric Restriction Diets, Journal of Thermodynamics, Vol. 2009, pp. 1-10.

Stoward. P. J., 1962, Thermodynamics of Biological Growth, Nature, Vol. 194, No. 4832, pp. 977-978.

Wissler, E. H, 1985, Mathematical Simulation of Human Thermal Behavior Using Hole Body Models, in Heat Transfer in Medicine and Biology, Analysis and Applications, Ed. Plenum Press.

Zotin, A.I. and Zotina, R.S., 1967, Thermodynamics Aspects of Developmental Biology, Journal of Theoretical Biology, Vol. 17, No. 1, pp. 57-75.