The calculation of the heat exchange conditions of the human body is a complex task.
However, this is the basis of the indoor thermal comfort designing. In the frame of this paper
starting from the basic equation of heat balance of the human body we will overview the
possibilities for the calculation and modelling of convective and radiant heat exchange

Bakó Biro, Zsolt

Bánhidi, László

English

Periodica Polytechnica (Budapest University of Technology and Economics)

PERIODICA POLYTECHNICA SER. MECH. ENG. VOL. 44, NO. 2, PP. 185–193(2000)DESIGN AND CALCULATION POSSIBILITIES FOR THE HEATEXCHANGE CONDITIONS OF THE HUMAN BODYLászló BÁNHIDI and Zsolt BAKÓ BIRODepartment of Building Service EngineeringBudapest University of Technology and EconomicsH–1521 Budapest, HungaryPhone: (36-1) 463 2636Received: April 5, 2000AbstractThe calculation of the heat exchange conditions of the human body is a complex task. However, thisis the basis of the indoor thermal comfort designing. In the frame of this paper starting from the basicequation of heat balance of the human body we will overview the possibilities for the calculation andmodelling of convective and radiant heat exchange.Keywords: thermal comfort, heat balance, heat exchange.1. IntroductionThe modern indoors design methods are based on the heat exchange conditions ofthe human body. The ideal situation is when the heat production (metabolism) andheat output of the human body are balanced. In the beginning of the last centurythe physiologists defined the heat generation of the human body – depending on theactivity. The ultimate methods for the calculation of heat exchange of the humanbody, however, were developed only 30-40 years ago. Several tasks could only besolved with the help of special thermal modelling methods (thermal manikin) aswell as experiments on the human body in many cases.In the following we are going to review the designing modelling and calcula-tion possibilities of the heat exchange conditions of the human body.2. Heat Balance of the Human BodyThe calculation of the heat exchange of the human body can be executed withthe help of the so-called heat-balance equation, as studies have proved that thesubjective heat sensation is pleasant and the work concentration ability is optimalif the heat generated in the human body and the heat dissipated in various waysare in balance. According to this the generally applied heat-balance equation is asfollowsH − Ed − Esw − Ere − L = K = R + C, (1)186 L. BÁNHIDI and ZS. B. BIROwhere H = the internal heat production in the human bodyEd = the heat loss by water vapour diffusion through the skinEsw = the heat loss by evaporation of sweat from surface of the skinEre = the latent respiration heat lossL = the dry respiration heat lossK = the heat transfer from the skin to the outer surface of the clothedbody (conduction through the clothing)R = the heat loss by radiation from the outer surface of the clothedbodyC = the heat loss by convection from the outer surface of the clothedbodyThe doubleEq. (1) expresses that the internal heat productionH minus theheat loss by evaporation from the skin(Ed + Esw) and by respiration (Ere + L)is equal to the heat conducted through the clothing (K ) and dissipated at the outersurface of the clothing by radiation and convection(R + C). It is assumed that theevaporation corresponding toEsw and Ed takes place at (or underneath) the skinsurface.In the following section first the internal heat production of the human bodywill be discussed in more detail.3. Internal Heat Production of the Human BodyAn oxidation (burning) process happens in the human body, and the energy trans-formed in the course of this evolves partly in the form of internal body heat andpartly used for mechanical (muscle) work and active output in a physical sense.For this burning the human body needs to take on oxygen, the degree of whichwill determine the intensity of the work. The oxygen consumption of an adulthuman body in stationary position is the so-called basic metabolism 0.25 l/min (4.210−6m3/s). The heat evolving as a result of the burning of this is 88 W.The oxygen consumption is multiplied in case of mechanical work comparedto stationary position. In case of an average person it can be 12 times as much asthe stationary position for a short time, which is 3 l/min (0.051 · 10−3 m3/s) thatequals 1060 W.According to BÁLINT [1] and WINSLOW and HARRINGTON[2] the efficiencyof the so-called efficient work in the course of metabolism is 20%, therefore thehuman body works on a higher degree of efficiency than an average steam machine(14%). Beside this, metabolism is carried out on a constant level of heat, on 37±0.5◦C. This is the fundamental difference between simple burning – the temperatureof which is not constant – and metabolism.There are only approximate data available as regards the average workingability. According to these the working ability of an average young man is – incase of regular working−1 l/min (17· 10−6m3/s), which equals a power of 350 W.Deducting the degree of basic metabolism of 88 W we get the result of 262 W.HEAT EXCHANGE CONDITIONS 187According to FANGER[3] the so-called metabolic heat generated in the courseof the oxidation process in the human body comprises two parts: the outside me-chanic labour (W ) and the inside heat demand (H ).In this case the outside mechanic labour considered as the heat necessaryfor the mechanical work carried out by the person is also assured by the oxidationprocess of the human body.W is positive if the energy needed for the physical work has to be covered bythe valueM (e.g.: climbing a stair) butW is negative when we are descending ona slope.Therefore the metabolic heat can be divided into two parts:M = H + W [W]. (2)According to this the work efficiency can be expressed from the following equation:η = WM. (3)Putting back this into the equation:H = M(1 − η) [W]. (4)Or expressing it for one unit of body surface:HFDu= MFDu(1 − η) [W/m2].FDu is the so-called Dubois surface of the body, which considers the most importantindividual ‘metric’ characteristics and can be defined on the basis of the followingcorrelation:FDu = 0.203G0.425L0.725 [m2] (5)where: G is the weight of the individual (kg),L is the height of the individual (m).Eventually, it is important to mention that for the numerical definition of theheat equivalent value of the different labours the unit of ‘met’ is applied in theinternational practice, and 1 met= 58 W/m2.The design data to be considered have been processed in a tabular form.4. Conditions for Thermal ComfortThe next question is: which conditions are necessary for the optimal thermal com-fort. By the theory there are three basic conditions for it. The first conditionnecessary for thermal comfort for a person under long exposure to a given envi-ronment is the existence of a heat balance, a condition which is naturally far from188 L. BÁNHIDI and ZS. B. BIROsufficient. Man’s thermoregulatory system is quite effective and will therefore cre-ate heat balance within wide limits of the environmental variables, even if comfortdoes not exist.With the establishment of a double heat balance an equation of the followingform can be obtained (only the main variables have been taken into consideration):f(HFDu, Icl, ta, tmrt , pa, v, ts,EswFDu)= 0, (6)whereHFDu= internal heat production per unit bodysurface area (FDu = DuBois area) W/m2Icl = thermal resistance of the clothing m2K/Wta = air temperature ◦Ctmrt = mean radiant temperature ◦Cpa = pressure of water vapour in ambient air Pav = relative air velocity m/sts = mean skin temperature ◦CEswFDu= heat loss per unit body surface area byevaporation of sweat secretion W/m2For a given activity level, the skin temperature,ts, and the sweat secretion,Esw, are seen to be the only physiological variables influencing the heat balance inEq. (6). The sensation of the thermal comfort has been related to the magnitude ofthese two variables. Experiments involving a group of subjects at different activitylevels have been performed to determine mean values of skin temperature and sweatsecretion, as functions of the activity level, for persons in thermal comfort. Theresults have the following form:ts = f(HFDu), (7)Esw = FDu = f(HFDu). (8)Eqs. (7) and (8) are presented as the second and third basic conditions for thermalcomfort.The quantitative evaluation ofEqs. (7) and (8) and the theoretical founda-tion for relating the sensation of thermal comfort with skin temperature and sweatsecretion are set out in the second part of this chapter.By substituting conditions (7) and (8) in (6), the desired comfort equationtakes the following form:f(HFDu, Icl, ta, tmrt , pa, v,)= 0. (9)HEAT EXCHANGE CONDITIONS 189Using the comfortEq. (1), it is possible for any activity level (H/FDu) and anyclothing (Icl) to calculate all combinations of air temperature (ta), mean radianttemperature (tmrt ), air humidity (pa) and relative air velocity (v) which will createoptimal thermal comfort.We have to mention that the exact calculation of the heat transmission throughthe clothing on the outer surface of the skin is almost impossible. The several layersof clothing on the human body, the air layers randomly formed between these layers,the change of these when the person is moving and air speed are all such aspectsthat do not make the direct and exact calculation possible. Therefore, the so calledthermal manikins have been developed, which model the different temperatures onthe surface of the human body with the help of electric heating. From the changesof the heating performance and the summarisation of the results of certain parts ofthe skin surface the dry heat emission can be determined. [4]5. Heat Balance and Comfort EquationSubstituting all the heat loss terms derived above into the double heat balanceEq. (1)and dividing byFDu givesMFDu(1 − η) − 0.35[1.92ts − 25.3 − pa] − EswFDu − 0.0023MFDu(44− pa)−0.0014 MFDu(34− ta) = ts − tcl0.18Icl(10)= 3.4 · 10−8 fcl[(tcl + 273)4 − (tmrt + 273)4] + fclhc(tcl − ta).Substituting the expressions forts andEsw in the double heat balanceEq. (10)MFDu(1 − η) − 0.35[43− 0.061 MFDu(1 − η) − pa] − 0.42[MFDu(1 − η) − 50]−0.0023 MFDu(44− pa) − 0.0014 MFDu (34− ta) =35.7 − 0.032 MFDu(1 − η) − tcl0.18Icl(11)= 3.4 · 10−8 fcl[(tcl + 273)4 − (tmrt + 273)4] + fclhc(tcl − ta).Solving the left part of the doubleEq. (11) gives the following expression fortcl :tcl = 35.7 − 0.32 MFDu(1 − η) − 0.18Icl{MFDu(1 − η)−0.35[43− 0.061· MFDu(1 − η) − pa]− 0.42[MFDu(1 − η) − 50](12)−0.0023 MFDu(44− pa) − 0.0014· MFDu (34− ta)}◦C.190 L. BÁNHIDI and ZS. B. BIROSetting the left side of doubleEq. (11) equal to the right side gives:MFDu(1 − η) − 0.35[43− 0.061· MFDu(1 − η) − pa]− 0.42[MFDu(1 − η) − 50]−0.0023 MFDu(44− pa) − 0.0014· MFDu(34− ta) (13)= 3.4 · 10−8 fcl[(tcl + 273)4 − (tmrt + 273)4] + fclhc(tcl − ta).Eq. (13) is the desired general comfort equation, in whichtcl is given byEq. (12)The comfort equation contains the following variables:Icl, fcl, M/ADu, η, v, v, ta, pa, tmrtA function of the A function of the Environmentaltype of clothing type of activity variablesIcl and fcl are functions of the type of clothing (values for different clothing en-sembles are shown in tabies).M/FDu, η, and partiallyv, are functions of the typeof activity ta, pa , tmrt and partiallyv, are thermal environmental variables.The comfort equation being obtained by inserting in the heat balance equationthe comfort expressions found for skin temperature and sweat rate, satisfaction ofthe comfort equation therefore means at the same time satisfaction of the threebasic comfort conditions. Satisfaction of the comfort equation is thus a necessarycondition for optimal thermal comfort.Using the comfortEq. (13) it is possible, for any type of clothing (clo) and anytype of activity (W/m2), to calculate all reasonable combinations of air temperature(◦C), air humidity, mean radiant temperature (◦C), and relative velocity (m/s) whichwill create optimal thermal comfort for persons under steady state conditions.Comfort DiagramsThe comfort equation is quite complex, since the involved heat transfer processes arerelatively complicated. Solution by hand would be laborious as multiple iterationis necessary. It has, therefore, been solved by digital computer, for all relevantcombinations of the variables, and 9 diagrams for direct practical application havebeen prepared. Since the diagrams, and not the equation itself, should be used inpractice, it was not necessary – at the expense of accuracy – to simplify the comfortequation in order to make hand calculations easier.The curves in the figures represent comfort lines, i.e. lines through points(conditions) which satisfy the comfort equation and thus will provide optimal ther-mal comfort. In all the figures the mechanical efficiencyη is set equal to zero,covering the great majority of practical applications.The comfort diagrams are well known and they could be found in the differentliteratures [3], [5], [6], [7].HEAT EXCHANGE CONDITIONS 191Fig. 1. Operation of the main ventilation system6. PMV-PPD ValueFanger developed the above calculation approach by working out a theory and apractical method, on the basis of which an expected sense of heat as regards to a givenpoint in space can be determined with the help of the available parameters. Theseare the so called PMV, the Predicted Mean Vote value and the PPD value, whichstands for the proportional probability of disadvantageous sense of heat PredictedPercentage of Dissatisfied. The knowledge of the theoretical development of thesetwo indicators is indispensable.In the course of the development of PMV Fanger started from the basic equa-tion of heat balance and the scale of subjective psychophysical sense of heat byASHRAE [8].Assuming an environment of discomfortable conditions the thermostatic mech-anism of the body changes the average value of skin temperature, starts sweatingif necessary in order to maintain the thermo-balance of the body. This thermalload is the physiological accelerator of the thermostatic mechanism, therefore theassumption that the degree of the load determines the sense of heat at the same timeis justified. In a simplified form it can be expressed with the following equation:Y = f(HFDu· L), (14)where Y is the expected sense of heatL is the thermo-load on the bodyH/FDu is the thermal-load on 1 m2Functionality can be verified only if the votes of sense of heat and the equa-tion of heat balance have been compared with an appropriate number of field orlaboratory experiments.In respect of comparing the data Fanger considered the experiments of Nevinsand McNall partly, as regards four levels of activities for those cases where the192 L. BÁNHIDI and ZS. B. BIROvalues of air and mean radiation temperature were the same and the relative degreeof humidity was 50%. The resultingY value is the so called PMV value.With the application of the measurements on people and these correlationstabular values were worked out first, then Fanger developed a diagram, which canbe seen inFig. 1. This figure is the basis of the practical evaluation of the thermo-environment according to Fanger. The PMV value of the diagram is symmetricaland has a minimum level. This minimum is 5% according to Fanger implying thatthe best result is that we can get when forming a microclimate in respect of thesense of heat if 95% of those who are there have a pleasant sense of heat.7. The Possibilities for the Practical Application of the Calculation Method inHungaryFor the practical application of the calculation method Fanger developed the so-called comfort diagrams, which – as we have mentioned – can be found in numerousHungarian and foreign publications [3] [5] [6] [7]. However, when applying thecalculation method the following aspects have to be considered usually:a.) The factor of dissatisfaction of 5% is considered. As the admissible PPD valueis economy-dependent the demands of the given country (or contractor) haveto be respected at all times. This however necessitates the calculation of thePMV value.b.) The design theory of Fanger assumes that the sense of heat is independentof age, sex and ethnical characteristics. This is often disputed, numerousexperiments – domestic ones, too [9] [10] [11] – have tried to define moreaccurate values.c.) The theory also provides an explanation for the method of calculation if theparameters of the microclimate are different in the various parts of the givenspace. These are the so-called local aspects of discomfort, two of whichare draft and asymmetric radiation. However, a separate article should bedevoted to the elaboration of this subject, although there are plenty of foreignand domestic experiments and publications e.g. [12], 13], [14] available inthis respect.ConclusionThe subjective sense of heat of a person in an interior, his/her working and concen-trating ability are primarily determined by the heat exchange conditions of his/herbody. The so- called thermo-balance equation and the PMV-PPD method are suit-able for the calculation of this. The paper has overviewed the theoretical design ofthe calculation method and the possibilities for practical application. Our work andresults in Hungary on this special field could be perceptible from the mentionedpapers too.HEAT EXCHANGE CONDITIONS 193References[1] BÁLINT , P.: Orvosi élettan, Medicina (1975).[2] WINSLOW, C. E. – HARRINGTON, L. P.: Temperature and Human Life, Princeton Univ. Press(1949).[3] FANGER, P. O.: Thermal Comfort. Robert E. Krieger Publ. Co., Malabar, Florida (1982).[4] BÁNHIDI , L. : Using a Thermal Manikin.Building Research and Practice. Journal of CIB.1988/1. pp. 14–17 (1988).[5] BÁNHIDI , L. : Zárt terek h̋oérzeti méretezése, M̋uszaki Könyvkiadó, Budapest (1976).[6] BÁNHIDI , L. : Radiant Heating Systems (Design and Application), Pergamon Press, Lon-don(1991).[7] BÁNHIDI , L. : Ember, épület, energia, Akadémiai Kiadó, Budapest(1994).[8] ASHRAE . Standard 55-81: Thermal Environmental Conditions for Human OccupancyASHRAE, New York (1981).[9] BÁNHIDI , L. – BESENYŐ, J. – KINTSES, G. : About Local Discomfort Effects Caused byAsymmetric Radiation Occurring During Winter in Dwelling Houses.CLIMA 2000, Copen-hagen (1985).[10] BÁNHIDI , L. : Thermal Comfort Studies at Hungary, Proc. ICHES’91, Tokyo (1991).[11] BÁNHIDI , L. – YOSHIDA, J. A. – POLINSZKY, T. – KINTSES, G. – HACHISU, H. –IMAI , H. O. – SATO, K. – NONAKA , M.: A Study on Termal Environment for PhysicallyHandicapped Persons, Results from Japanese – Hungarian Experiment in 1990, PergamonPress,J. Thermal. Bid. 18 No. 5/6, London (1993).[12] FANGER, P. O. – BÁNHIDI , L. – OLESEN, B. – LANGKILDE , G. : Comfort Limits for HeatedCeilings. Ashrae trans (1980).[13] BÁNHIDI , L. – BISCHOF, W. : Zur physiologischen Adaption des Thermal Manikin,Z. gesamtHyg. Heft. 12(1989).[14] BÁNHIDI , L. – MAGYAR, T. : Selection of Ventilation Systems of Optimal Applicabilityto Closed Spaces from the Aspects of Energetic and Thermal Comfort.Indoor Air QualityVentilation and Energy Conservation in Buildings Conf. Montreal, Canada, Proc. Vol. 2 (1995).

Design and Calculation Possibilities for the Heat Exchange Conditions of the Human Body

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Design and Calculation Possibilities for the Heat Exchange Conditions of the Human Body

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