Research on the Human Thermal Model with a Poly-segmentedHand

Ding Li,1 Sang Minjing,2 Lei Yanpeng,1,2 and Yuan Xiugan2

1Bioengineering Department, Beihang University, Beijing, 100083, China2School of Aeronautic Science and Engineering, Beihang University, Beijing, 100083, China

A more integral human thermal model was built by combining the humanthermal cylindrical model and the manual poly-segment thermal model. Finite elementmethods (FEM) was used to define the body thermal model. It was in good agreementwith the experimental results. The results show: the experimental results are consistentwith the calculated value, when suitable blood flux is taken into consideration. Theblood flux is in a certain range when the manual temperature is stable. Blood flux isthe major factor in the manual temperature field. Body temperature and intake arterytemperature have little effect on the hand temperature. © 2008 Wiley Periodicals, Inc.Heat Trans Asian Res, 37(2): 94–100, 2008; Published online in Wiley InterScience(www.interscience.wiley.com). DOI 10.1002/htj.20187

Key words: human thermal model, hand, temperature field

1. Introduction

As international space stations are set up, the duration and frequency of extravehicular activity(EVA) will increase. The environmental space temperatures the astronaut encounters become moreand more vicious (–140 to 160 °C). But there is no satisfactory method to protect the hands of theastronaut. Therefore, it is necessary to further study the temperature of hands and fingers [1, 2].

The present study of temperature of hands and fingers depends on the hypothesis, which saysthat there is a fixed relationship between the temperature fields of the body and hand. Therefore, thehand is studied as an independent part and is irrelevant when it comes to the changes of bodytemperature fields [2, 3]. However, when the hand is simplified as a multilayer cylindrical element[4], it is difficult to study the temperature fields of hand and fingers precisely. In this paper, both handand body models were combined to study their relationship. The analytical results were substantiatedthrough experiments.

Nomenclature

B.: blood perfusion rate, Kg⋅m–3⋅s–1

© 2008 Wiley Periodicals, Inc.

Heat Transfer—Asian Research, 37 (2), 2008

Contract grant sponsor: National Youthful Nature Science Fund (50406008), Excellent Teacher honored by Ministry ofEducation (The computer simulation of outside spaceship and the efficiency analysis of man-machine).

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Cb: blood specific heat, J⋅kg–1⋅K–1

Cp: tissues specific heat, J⋅kg–1⋅K–1

D: curving surface

n: normal vector

qc: the heat exchange between skin and environment, W⋅m–2

qe: the vaporization heat of skin, W⋅m–2

qeb: the breath heat exchange (limit to head and trunk), W⋅m–3

qm: volumetric metabolic heat generation rate, W⋅m–3

qr: the radiant heat exchange between skin and environment, W⋅m–2

t: time, s

T: tissue temperature, K

Tai: arterial blood temperature of segment i, K

Tb: arterial blood temperature, K

x, y: coordinate of point, m

Γ: curving line

α: the convection heat transfer factor, W⋅m–2⋅K–1

λ: thermal conductivity, W⋅m–1⋅K–1

ρ: tissue density, kg⋅m–3

2. Hand and Body Model

Using multilayer cylindrical elements to define anatomy parameters, the whole body issubdivided into 15 cylindrical segments: the head, neck, trunk, upper arms, forearms, hands, thighs,calves, and feet. Moreover, the hand is subdivided into 15 sections: palm, thumb, index, middle finger,ring finger, and little finger. The fingers are divided into upper, middle and lower sections, except thethumb which has two sections.

As the three-dimensional body model is extremely complex, it is hard to create a precisethree-dimensional numerical study of the human body. For the thermal fields of hands, the majorthermal diversification happens on the diameter and radius of the fingers, not the inner section [2, 3].Thus, under the usual hypothesis [2, 4], in this paper, the body and fingers are assumed to be cylindricalwith every section divided into four layers: core, muscle, fat, and skin, whereas the palm is arectangular slab. Table 1 1ists the physiological data and thermal parameters of the hand. In the model,it is assumed that the thermal parameters of tissue do not change with space coordinate. The body’sthermal equation is expressed by Ref. 5.

ρCp ∂T

∂t = λ

∂2T

∂x2 + ∂2T

∂y2

+ qm + qed + B

.Cb(Tb − T) (1)

where ρ is the tissue density, Cp is the tissue specific heat, T is the tissue temperature, λ is the tissueheat conduction coefficient, qm is the metabolic heat generation rate, qed is the breath heat exchange(only include head and trunk sections), and B

. is the blood flux rate. Subscripts b and p represent blood

and tissue. x, y, and z represent the space coordinate. The boundary condition is

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λ ∂T

∂n = qc + qe + qr (2)

where

qc = α(Ts − Ta) (3)

qe = 0.0031(ps − pv) (4)

qr = εσXs(Ts4 − Tr

4) (5)

qc is the convection heat transfer between the skin and surroundings. α is the convection heat transferfactor. Subscript s represents skin and subscript a represents surroundings. qe is evaporation heattransfer between the skin and surroundings. ps is saturated evaporation pressure on the skin and pv isthe vapor pressure in the air current. The radiation heat transfer between the skin and surroundings isqr. The black body radiation function of the hand is ε. The Stefan–Boltzmann number is σ. Theradiation heat transfer coefficient is X. For temperatures, Ts is the temperature of hand skin and Tr isthe temperature of radiation. The velocity of air flow could be ignored. The initial condition is

T|t=0 = ϕ(x, y) (6)

where ϕ(x, y) is the initial temperature field of the human body, the neutral thermal fields. Theinitialization thermal field is neutral. With FEM, Eq. (1) is transformed into the integral equation (4)

J = ∫∫D

λ2

∂T

∂x

2

+

∂T

∂y

2 − qmT − qebT − B

.CbTbT +

B.Cb

2 T2 + ρCp

∂T

∂t T

dxdy

+ x hc

12

T2 − TfT + hr

12

T2 − TVaT + qeT

ds

(7)

The bend surface can be divided into triangular or quadrangle cells. But it is hard to obtainthe result directly. Commonly we can transform it into an equilateral triangle and square cells innatural coordinates before computing.

3. Test Method

3.1 Experiment principle

For a simplified human thermal model, one needs to validate the model. An experiment, inwhich hands were cold and body was moderate, was designed. (This is similar to the EVA space low-temperature environment).

Three barrels of different sizes are used to produce the artificial environment, with the smallerplaced inside each bigger barrel progressively. The low-temperature environment is created by fillingthe smallest barrel with cold gas (Fig. 1). As thermal protection for the smallest barrel, a 60-mm-thick

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piece of absorbent cotton is placed between the smallest barrel and the medium sized barrel. Then inorder to decrease the heat transfer between the smallest barrel and the external environment, thetemperature of the gas between the largest barrel and the medium sized barrel is maintained at a levelsimilar to that inside the smallest barrel. The thermocouples are applied to measure the temperatureat different points of the hand in the test. To provide the comparative data for the calculation, thethermocouples are plastered to the middle of each finger segment, the back side of the tips of thumb,index, middle fingers, and the middle and the back of palm. It was proved that the thermocouples didnot affect the hand temperature field.

3.2 Experiment methods and experimenter

The experimenters were six males and two females who were healthy with no big wounds inthe skin. Their hands were all in good function. The experiment procedures were:

(1) The air temperature in the smallest barrel was fixed at 10 °C by controlling a small blastof icy wind, which was not faster than 0.02 m/s, blowing through it.

(2) The thermocouples were plastered to different parts of the experimenter at the environmenttemperature (15 °C) before the test.

(3) The experimenter sat still until the temperature was stable, and all the test points weremeasured. The experimenter put his hand in the smallest barrel and flux.

(4) The skin temperatures were measured every 2 seconds until they were stable (the time is60 to 120 minutes).

4. Results and Discussion

In Table 1, the human heat conduction coefficient was small, and a great portion of the heatwas transferred by blood flux. Therefore, the influence of the body upon the hand was displayedthrough blood flux and blood temperature.

Fig. 1. Experimental installation.

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4.1 Blood temperature

Figure 2 shows the influence of different arterial temperature and the temperature of thefingertip, e.g., the temperature of the middle finger tip, when the hand was put in still air which was0 °C, and the surrounding temperature was 25 °C. Curve 1 was the change of intake artery bloodtemperature in root finger over time; the temperature was calculated from the human model. Curve2 shows when the intake artery blood temperature in root finger was 30 °C. Curve 3 was thetemperature change of the finger tip when the intake artery blood temperature conditions were thesame as Curve 1. Curve 4 was the temperature change of the finger tip when the intake artery bloodtemperature conditions were the same as Curve 2. The difference between Curve 3 and Curve 4 wasso small that the blood temperature affects the finger tip temperature minimally. That was mainlybecause the blood flux was so small at a low temperature. Furthermore, there was a celerity heattransfer between the finger tip and surroundings. Therefore, the blood heat temperature difference didnot have a large influence on the temperature field of the finger tip.

Table 1. Parameters Used in the Numerical Computations [3]

Fig. 2. The influence of the temperature between the intake artery blood and finger tip.

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4.2 Blood flux

Based upon the limitations of the experimental conditions and technique, each blood fluxchange could not be registered. Thus, the blood flux changed with the hand temperature during thecalculations. First, the blood flux increased several times 2 to 7 minutes before the rise of the fingertemperature. In the same way, the blood flux has dropped several times 2 to 7 minutes before thefinger temperature decrease. The results prove that the experiment was identical to the calculationand the difference was less than 1 °C (the temperature changes of the different parts of the middlefinger of the A experimenter were shown in Figs. 3 and 4, in which the line shows the experimentalresults and the dashes were the calculated results). The blood flux focused was 2 to 3 times the basiclow rate (2 times: 5 people, 2.5 times: 1 person, 3 times: 1 person).

For the thermal capacity and thermal resistance, the temperature changes lag behind those ofthe blood flux nearly 2 to 7 minutes, which is consistent with the report of Shitzer and colleagues [3].Comparison with the results shows the calculation model is correct.

Fig. 3. The middle finger root’s temperature of A.

Fig. 4. The middle finger tip’s temperature of A.

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5. Conclusions

The study shows that the blood rate is the primary cause of the temperature fields of the hand.The directional change of the results of the experiment is identical with that of the calculation whensuitable blood flux is considered during calculations. Moreover, the stable temperatures of both arein an affirmatory range. Such a body temperature model is creditable and has great significance in theimprovement of heat preservation of EVA spacesuit gloves.

Literature Cited

1. Abramov LP. The experiment in operation & improving the Orlan type space suits [J]. ActaAstronautica 1995;36:1–12.

2. Ding Li. The study of thermal protection of EVA space glove. Beihang University doctoralpaper, 2000.

3. Shitzer A, Stroschein LA, Vital P. Numerical analysis of an extremity in a cold environmentincluding countercurrent arterio-venous heat exchange. J Biomech Eng 1997;119:179–186.

4. Wee-Hee S, Sam T, Harvey C, Satish N. Determination of human thermal experimentaluncertainty. SAE:2001-01-2270.

5. Jing L, Cuncheng W. Biology heat transfer. Science Press; 1997.

"F F F"

Originally published in J Eng Thermophys 19(2), 2006, 106–108.Translated by Ding Li, Bioengineering Department, Beihang University, Beijing, 100083, China.

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