Thermodynamic Analysis of Human Heat and Mass Transfer and Their Impact on Thermal Comfort
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International Journal of Heat and Mass Transfer 48 (2005) 731–739 www.elsevier.com/locate/ijhmt Thermodynamic analysis of human heat and mass transfer and their impact on thermal comfort Matjaz Prek * Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia Received 26 April 2004 Available online 6 November 2004 Abstract In this paper a thermodynamic analysis of human heat and mass transfer based on the 2nd law of thermodynamics in presented. For modelling purposes the two-node human thermal model was used. This model was improved in order to establish the exergy consumption within the human body as a consequence of heat and mass transfer and/or conver- sion. It is shown that the human bodyÕs exergy consumption in relation to selected human parameters exhibit a minimal value at certain combinations of environmental parameters. The expected thermal sensation, determined by the PMV* value, shows that there is a correlation between exergy consumption and thermal sensation. Thus, our analysis repre- sents an improvement in human thermal modelling and gives even more information about the environmental impact on expected human thermal sensation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Exergy; Human body; Heat transfer; Mass transfer; Thermal comfort 1. Introduction more than 30 years. These models range from simple one-dimensional, steady-state simulations to complex, Human body acts as a heat engine and thermody- transient finite element models [1–5]. The main similarity namically could be considered as an open system. The of most models is the application of energy balance to a energy and mass for the human bodyÕs vital processes simulated human body (based on the 1st law of thermo- are taken from external sources (food, liquids) and then dynamics) and the use of energy exchange mechanisms. exchanged with the environment. These exchange mech- The models differ mainly in the physiological response anisms are of great importance, since they define the models and in the criteria used to predict thermal sensa- thermal sensation, i.e. thermal comfort. Therefore, the tion [6,7]. pathway of energy, mass, and the transformations asso- In this paper a different approach is presented, ciated with their generation leading to an exchange with namely an analysis based on the 2nd law of thermody- the environment should be considered. Thermal models namics. Every energy transfer and conversion is accom- of the human body and its interaction with the sur- panied by an exergy transfer and conversion. Energy is rounding thermal environment have been available for conservative in its transfer and conversion process (1st law of thermodynamics: nothing disappears), while exergy is known to be non-conservative due to the * Tel.: +386 1 4771 312; fax: +386 1 2518 567. irreversibility of its transfer process (2nd law of thermo- E-mail address: [email protected] dynamics: everything disperses). As a result, exergy 0017-9310/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2004.09.006 732 M. Prek / International Journal of Heat and Mass Transfer 48 (2005) 731–739 Nomenclature A area (m2) Subscripts c specific heat (J/kgK) a air ex exergy (J/kg) bbody E exergy load (J) bl blood f correction factor for clothing surface area (–) c convective h enthalpy (J/kg) ch chemical he latent heat of evaporisation (J/kg) cl clothing K thermal conductivity (W/mK) cr body core m mass (kg) diff diffusive m_ mass flow rate (kg/s) Du DuBois M metabolism (W/m2) e evaporative p pressure (Pa) in input Q heat load (J/kg) out output R gas constant (J/kgK) r radiative 2 Rcl clothing thermal resistance (m K/W) res respirative s entropy (J/kgK) rsw requested sweating S heat storage (J/kg) s saturated state t time (s) sk skin T temperature (°C, K) th thermal W specific work (J/kg) w water, water vapour x humidity ratio (–) 0 reference state Greek symbols a relative mass of the skin u percent relative humidity transfer has rules of its own which are different from and to identify the magnitude and mechanisms of those those of energy transfer. Exergy is only conserved, or irreversibilities. in balance, for a reversible process, but is partly con- An example is considered to verify the presented mod- sumed in an irreversible process. For a real process the el and it is shown that there is a correlation between the exergy input always exceeds the exergy output; this exergy consumption within the human body and the ex- unbalance is due to irreversibilities and represents exergy pected level of thermal comfort. Furthermore, the exist- destruction or exergy consumption. There are corre- ing methods for comfort assessment could be improved sponding entropy flows associated with heat and mass and expanded with the inclusion of exergy analysis. flows; combining the energy and entropy balance brings about exergy balance [8–10]. One of the objectives of the presented research is to calculate entropy generation or 2. Human thermal model exergy destruction (based on the Gouy–Stodola theo- rem). The calculation of exergy destruction is usually For analytical purposes, the chosen human thermal based on second law analysis, either from the rate of ex- model must fulfil some basic conditions. For optimal ergy destruction within the relevant control volume, or thermal comfort three basic conditions must be fulfilled: from the unbalanced rate of exergy input within the con- heat balance must exist, and skin temperature and sweat trol volume [11]. rate must be within the comfort range. The human body In the case of the human body, exergy is consumed as produces heat, exchanges heat with the environment, a consequence of heat and mass transfer and/or conver- and loses heat by diffusion and evaporation of body liq- sion. These processes are dependent on the human ther- uids. During normal rest and exercise these processes re- moregulatory system and on the state of the sult in an average vital organ temperature of around environment. Therefore, the human body generates spe- 37°C. The bodyÕs temperature control system tries to cific mechanisms of irreversibilities. The purpose of the maintain these temperatures even when thermal distur- presented study is to introduce an approach to calculate bances occur. The human thermoregulatory system is the rate of exergy destruction within the human body quite effective and creates heat balance within wide lim- M. Prek / International Journal of Heat and Mass Transfer 48 (2005) 731–739 733 its of the environmental variables (air temperature, sents the body core and the outer cylinder represents the mean radiant temperature, air humidity, and relative skin layer. The core is the compartment with a regulated air velocity). For a given activity level (metabolism), skin and defined temperature, while the skin is a buffer be- temperature and sweat rate are seen to be the major tween the core and environment whose temperature is physiological variables influencing heat balance. defined by heat and mass exchanges with the core and The model used as a starting point is comprised of a with the environment. The core and skin compartments physiological part based on the Gagge two-node model exchange energy passively through direct contact and [2] and a physical model describing the heat and mass through the thermoregulatory controlled peripheral transfer properties of clothing. The physiological model blood flow. Metabolic heat production at the core is re- contains a number of control functions for physiological leased to the environment by two paths. The predomi- processes, as well as the heat transfer properties of the nant pathway is the transfer of heat to the skin by human body. Core, skin, and mean body temperatures blood flow and heat conduction, followed by release are used as inputs for several set-point-defined feedback from the skin to the environment by convection, radia- loops controlling effector responses [12,13]. The effector tion, and evaporation. The minor pathway is the direct responses together with metabolic heat production result release of heat (and mass) to the environment through in a certain heat loss or gain, which then affects the body respiration. Therefore, two heat balance equations for resulting in a new body temperature (i.e. feedback). The the body core and the skin layer can be built up. The relation between effectors and the resulting body temper- transient energy balance states that the rate of heat stor- ature is affected by environmental parameters (heat and age equals the net rate of heat gain minus heat loss. This mass transfer properties) and heat production level thermal model is described by two coupled heat balance (activity). equations for the two compartments: Thermal regulation by the human body is mainly ÀÁ S ¼ M À W À Q À Q À Q ð1Þ achieved by regulating blood flow [14]. The body regu- cr c;res e;res cr!sk lates blood distribution by vasoconstriction and vasodil- S ¼ Q ÀðQ þ Q þ Q Þð2Þ atation in order to control skin temperature and to sk cr!sk c r e increase or decrease heat loss to the environment. Dur- The rate of heat storage in the body equals the rate of ing work, blood carries the extra heat produced to increase in internal energy. The rate of storage can be the body surface where higher skin temperature in- written separately for each compartment in terms of creases heat loss through convection and radiation. the thermal capacity and the rate of change of tempera- During cold stress, vasoconstriction shunts blood flow ture as: from arteries to veins at deeper layers. Veins and arteries 1 dT cr are paired and veins carry heat from the arteries back Scr ¼ ðÞÁ1 À a m Á cb Á Á ð3Þ ADu dt to the core.