Sensitivity Numerical Analysis of Human Body Exergy Balance under an Unsteady-State Thermal Environment
—Behavioral Adaptation Induced by Undesirable Cold Storage by Building Envelope in Winter ()
Received 23 February 2016; accepted 28 May 2016; published 31 May 2016
1. Introduction
It is as important to strive for comfort and energy saving with regard to a resident’s thermal adaptation (software) as it is to optimize the environmental system of a building (hardware), because energy use by building equipment is influenced considerably by the turning on/off the air-conditioning/heating units and the clothing of the residents [1] .
The adaptive comfort temperature in an adaptive model is predicted on the basis of the outside air temperature [2] [3] . Since, exergy is calculated by considering the outside air temperature as the environmental temperature [1] , it can be surmised that there is a certain relationship between adaptation and exergy.
Behavioral adaptation (the cycle from sensation to behavior [4] ) in an unsteady-state thermal environment is influenced both by long-term and short-termvariations. Therefore, it is considered that thermal adaptation reflects the unsteady state. The consideration of the pattern of the unsteady-state human body exergy balance can help in the design of environmental systems of buildings, which is to provide both thermal comfort and desirable adaptations that decrease consumption of fossil fuels. It can also clarify, to some extent, the mechanisms of physiological adaptation.
Therefore, in this research, we performed a sensitivity analysis that focused on the relationships between thermal adaptations and the pattern of the human body exergy balance. Using numerical analysis, we investigated the human body exergy balance under an unsteady-state thermal environment surrounding the human body in the course of individuals moving indoors after having been outside for a while in winter.
2. Application of Exergy to the Built Environmental System
In terms of the energy (i.e., electricity and heat) and matter (i.e., air and water) flowing in and out of an architectural environmental space, it is inevitable that the natural phenomenon of diffusion occurs. Therefore, although the “quantities” of these energies and matters are conserved, their “qualities” are consumed. Thus, when evaluating the function of an architectural environmental system, we consider it important to use the concept of exergy, because this can evaluate explicitly the “diffusing capacity” of energy and matter [5] .
According to natural rhythms, such as the annual and daily fluctuations of external air temperature and humidity, exergy is repeatedly generated and quenched. The concept of exergy can quantify the ability of energy and matter to disperse within an outdoor environment and it can clarify the relationship between “resources” and the “environment”. In addition, exergy can be used to quantify the consumption of energy and matter penetrating a “system” while diffusing, according to the spatial variation of temperature and relative humidity with time. Thus, it can be claimed that the merit of an evaluation of exergy is the evaluation of process for the effective use of resources.
3. Application of Exergy to the Human Body System
Oshida, a pioneer of exergy research, has claimed that thermal comfort might relate more to the speed of energy flowing in and out of the human body than to the temperature of the surrounding environment. Furthermore, there could be a strong relationship between thermal comfort and the speed of exergy flowing in and out of the human body rather than the speed of the energy flow [6] . Hence, to complement the conventional index for the evaluation of thermal comfort based on the human body “energy” balance, we focus on a new evaluation index based on the human body “exergy” balance. Because the diffusion of energy and matter, i.e., natural deterioration, occurs randomly in an architectural environmental space and in the human body, it must be expected that thermal sensations such as “hot” and “cold” correspond to the human body exergy balance.
3.1. Steady-State Valuation Using Steady-State Models
Saito and Shukuya were the first to find a relationship between thermal comfort and the exergy balance. They found that the smallest exergy-consumption rate appears at approximately 23˚C, which corresponds roughly to the neutral condition [7] . They also found that greater exergy consumption burdens the human body [8] . It has also become clear that there is an optimal combination of indoor thermal environmental elements, such as air temperature and mean radiant temperature, that provide the lowest possible human body exergy consumption rate in both winter [9] and summer [10] . A series of research projects on the relationship between the human body exergy balance and thermal comfort revealed that the minimal exergy consumption provides thermal comfort [11] . Asada developed software to calculate the human body exergy balance [12] . Simone et al. analyzed the relationship between human body exergy consumption rates and subjectively assessed thermal sensations [13] . Schweiker compared the predicted mean vote approach, adaptive comfort model, and a calculation of the human body exergy consumption rate [14] . Ala-Juuselaand Shukuya used the human body exergy analysis to evaluate the case of office workers in typical and extreme weather conditions in Finland [15] . Dovjak et al. analyzed thermal exergy flows through the building envelope jointly with the human body exergy balance in four typical climates (temperate, cold, hot/dry, and hot/humid) [16] .
3.2. Unsteady-State Valuation Using Steady-State Models
Saito and Shukuya were the first to conduct a numerical analysis to investigate how the transition between thermal environments, i.e., from outdoors into indoors, affects the human body exergy balance [17] . Tokunaga and others have performed unsteady-state human-body analyses using a steady state model for cases in the summer [18] and winter [19] . There were differences in body-core and skin-layer temperatures, which cannot be disregarded, between a subject’s actual value and the computed value when a human moves to the indoors from the outdoors.
3.3. Unsteady-State Valuation Using Unsteady-State Models
The original calculation model, i.e., the famous 2-node model, was not really an unsteady-state model because the one-hour periods for the calculation of the body-core and skin-layer temperature were assumed in between the time steps representing the actual unsteady-state condition [20] - [22] . Therefore, Shukuya reviewed the entire calculation procedure for the body-core and skin-layer temperature and modified the calculation method to perform under unsteady-state conditions [23] . Using the modified method, Schweiker et al. explored the relationship between the human-body exergy consumption rate and the subjective assessment of the thermal environment represented by thermal sensations and extended the investigation to thermal acceptability votes [24] .
4. Positioning of the Current Paper
The originality of this paper and its differences from previous research are as follows. First, we preformed the unsteady-state sensitivity analysis using an unsteady-state model. Few studies have used this approach so that further analysis is necessary. Second, we set a unique case-study situation, i.e., “undesirable cold storage by the building envelope in winter”, described in Section 5.1. Third, we set a “step transition” in the numerical analysis in contrast to the “ramp transition” used in previous research [24] . Fourth, we reflected the “behavioral adaptation” using a calculation condition described in Section 5.4. Fifth, we tried to clarify the mechanisms of “physiological adaptation” from the exergetic viewpoint, i.e., we investigated each term of the human body exergy balance equation thoroughly, as described in Section 6.
5. Numerical Analysis
5.1. Situation of Case Study
Spaces such as school lecture rooms and office conference rooms tend to be used for short periods on an intermittent basis, and the periods when they may remain unheated (e.g., during holidays or overnight) can be comparatively long. Furthermore, “undesirable cold storage in winter” can arise because a building envelope can be cooled by external air brought in via a ventilation system, even when thermal insulation of the building envelope is installed, particularly in the case of a building envelope that has a comparatively large heat capacity, e.g., concrete.
The feeling of “cold”, which cool radiation (shortage of warm radiant exergy) from the interior surfaces of a building envelope can cause when a person walks into a room, could induce the behavioral adaptation in the occupants of presetting the air-conditioner/heating temperature to be relatively high. It is thought that the period during which the stored coldness within a building envelope becomes warm, after the heating is started, requires a large amount of exergy and that during this period the thermal comfort is comparatively low.
5.2. Human Body System and Exergy Balance Equation
The exergy balance equation is derived from energy and entropy together with the environmental temperature. Exergy balance equation for the system can be set up in a general form as follows:
(1)
Figure 1 shows the human body system. The human body exergy balance equation is also derived by combining the following three elements: a human body energy balance equation, a human body entropy balance equation, and the environmental temperature (outdoor air temperature). The human body exergy balance equation is expressed as follows [1] :
(2)
5.3. Calculation Method
The temperatures of the core, shell, and clothing under “steady-state” conditions are determined by the two-node model (human body energy balance model), which was originally developed by Gagge et al. [20] - [22] . The body-core and skin-layer temperatures under “unsteady-state” conditions can be calculated using a modified method based on the two-node model. This method enables us to conduct unsteady-state human-body exergy analyses [23] . In the modified method, the two-node thermal “energy” balance equations for the calculation of the human-body core, skin-layer, and clothing surface temperatures are numerically solved using the explicit finite-difference method (forward differencing). We set the calculation interval to 1 minute to stabilize the calculation in this study since such calculations become unstable when the time interval is equal to or greater than 2 minutes. The detailed procedure is described in [23] [24] .
5.4. Fixed Conditions
The fixed conditions of the experiment are shown in Table 1. The calculation considered a period of 240 minutes, which assumed a transfer (e.g., commute to school or work) of 0 - 60 minutes in the outdoor environment and a period of 60 - 240 minutes within the indoor space (room). The metabolic rate and the amount of clothing were set to reflect the outdoor transit period and the period indoors.
5.5. Comparative Conditions
Four Cases are shown in Table 2 for comparison. In Case 1 and Case 2, both the room air temperature and the mean radiant temperature (MRT) were 10˚C. These values represent the ambient temperatures when heating was inactive. It was assumed that the occupants removed a coat (outside clothing) after entering the room space in Case 1, while they kept wearing the coat in Case 2. Both Case 3 and Case 4 considered a room air temperature of 20˚C and an MRT of 15˚C and 20˚C, respectively. The temperatures in both cases represent the activation of convective heating immediately after the occupants entered a room that has not been in use for a long period of time. Case 3 represents a building envelope that has a comparatively large heat capacity, whereas Case 4 represents a room where wood paneling was installed on the interior surfaces of a building envelope with a comparatively large heat capacity (such as concrete), or a wooden construction where the building envelope has a comparatively small heat capacity.
6. Results and Discussion
6.1. Body Temperature
The temperatures of the core, shell, and clothing are shown in Figures 2-4, respectively. During the time of the outdoor transfer, all four cases changed at the same rate in response to the external environment. In the indoor period in Figure 2, the core temperature in Case 1, Case 2, and Case 3 dropped, whereas that in Case 4 remained almost stable. In the indoor period in Figure 3, the shell temperature in Case 1, Case 2, and Case 3 dropped, whereas that in Case 4 rose gradually. It is considered in Case 4 that the shell temperature that dropped during
the outdoor transfer period started to recover during the indoor period. In the indoor period in Figure 4, the clothing temperature in Case 3, Case 1, and Case 2 dropped slightly, whereas that in Case 4 rose slightly.
6.2. Physiological Adaptation
The shell ratio and blood flow rate are shown in Figure 5 and Figure 6, respectively. During the indoor period in Case 1, Case 2, and Case 3, the shell ratio increased gently (Figure 5) and the blood flow rate decreased (Figure 6). Conversely, in Case 4, the shell ratio became smaller and the blood flow rate increased. It is thought that the physiological adaptation that increased the shell ratio and decreased the blood flow rate in Case 1, Case
2, and Case 3, prevented superfluous heat (warm exergy) release. However, in Case 4, it is thought that a moderate rate of heat release (discarding of entropy) occurred.
6.3. Exergy Balance
6.3.1. Input
The warm exergy production rate by the metabolism is shown in Figure 7. The fall from 8 to 6 W/m2 immediately after entering the room is influenced by the calculation condition, whereby the metabolic rate alters instantaneously (outdoor 1.5 met ® indoor 1.0 met). In Case 1, the exergy production rate by the metabolism increased rapidly after about 80 minutes. This was because shivering started to prevent the core temperature from falling rapidly and thus, the warm exergy production increased. A warm radiant exergy input rate is shown in Figure 8, which during the period in the room, decreased in the order Case 4 > Case 3 > Case 2 = Case 1, according to calculation conditions (Table 2, MRT).
6.3.2. Consumed
The exergy consumption rate of a human body is shown in Figure 9. The exergy consumed is a part of exergy inputted to the human body (Figure 7 and Figure 8). During the time in the room, the decreasing order of exergy consumption was Case 1 > Case 2 > Case 3 > Case 4. It is confirmed that behavioral adaptations such as activating the air-conditioning/heating switch (Case 3 and Case 4) and wearing clothes (Case 2) decrease the rate of exergy consumption within the human body. The comparatively small value of Case 4 suggests that thermal comfort and desirable behavioral adaptation, which decreases the consumption of fossil fuels, could be achieved by installing wooden cladding in rooms that has not been in use for a long period of time, the building envelope has a comparatively large heat capacity, or in wooden structures where the building envelope has a comparatively
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Figure 7. Warm exergy production rate by metabolism [W/m2].
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Figure 8. Warm radiant exergy input rate [W/m2].
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Figure 9. Human body exergy consumption rate [W/m2].
small heat capacity. The human body exergy consumption rate (Figure 9) is the sum of the exergy consumption between the core and the shell, and between the shell and the clothing. Hence, a greater temperature difference across the core, shell, and clothing means greater exergy consumption within the human body. Even though the shell temperature in Case 2 was higher than that in Case 3 (Figure 3), the rate of exergy consumption by the human body in Case 2 was larger (Figure 9). The reason for this could be that the clothing temperature in Case 2 was lower than that in Case 3 (Figure 4).
6.3.3. Stored
The rate of accumulation of warm exergy in the core is shown in Figure 10. This value was negative (i.e., decreasing) in all cases immediately after entering the room. It is considered that the change in the rate of warm exergy accumulation from increasing to decreasing is due to insufficient production of warm exergy. This is something that is influenced by the change in the metabolic rate, when moving indoors from outside (outdoor 1.5 met ® indoor 1.0 met), in the calculation condition.
The warm exergy accumulation rate in the shell is shown in Figure 11. The rate increased in all cases immediately after entering the room. It is thought that the clothing temperature also rose because the ambient temperature of the room was higher than that in the outdoor temperature; hence, the rate of warm exergy flow from the shell to the clothing fell.
The rate of exergy accumulation in the core and shell recovered toward zero as the duration of the period in the room increased. It is thought that the complex interaction of the warm exergy production by shivering (Fig- ure 7), lifting of the shell ratio (Figure 5), and reduction of the blood flow rate (Figure 6) constitutes the physiological adaptation necessary for maintaining the constant core temperature, which is an important aspect in living organisms.
6.3.4. Output
The rate of warm radiant exergy output is shown in Figure 12. The decreasing order of Case 4 > Case 3 > Case 1 > Case 2 corresponds to the order of clothing temperature (Figure 4).
The rate of warm convective exergy output is shown in Figure 13. Unlike Figure 12, the decreasing order is Case 1 > Case 4 > Case 2 > Case 1, which corresponds to the decreasing order of the temperature difference between the clothing (Figure 4) and indoor air (Table 2).
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Figure 10. Warm exergy accumulation rate in the core [W/m2].
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Figure 11. Warm exergy accumulation rate in the shell [W/m2].
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Figure 12. Warm radiant exergy output rate [W/m2].
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Figure 13. Warm convective exergy output rate [W/m2].
7. Conclusions
We performed an unsteady-state sensitivity analysis by using the unsteady-state two-node model, focusing on the relationships between behavioral adaptations and the pattern of the human body exergy balance. Using numerical analysis, we investigated the variation of thermal environment surrounding the human body when individuals moved indoors after having been outside in winter.
1) This study confirmed that behavioral adaptations such as wearing clothing and activating an air-condi- tioning/heating unit could cause the rate of exergy consumption within a human body to decrease.
2) The mechanisms of “physiological adaptation” were clarified from the exergetic viewpoint to some extent. It was thought that the complex interaction of the warm exergy production by shivering, lifting of the shell ratio, and reduction of the blood flow rate constituted the physiological adaptation necessary for maintaining the constant core temperature, which was an important aspect in living organisms.
3) In the case of intermittent use room, it was suggested that greater thermal comfort and desirable behavioral adaptations, which decreased the consumption of fossil fuels, could be achieved for rooms used infrequently if interior wooden cladding was used in constructions with building envelopes that had a comparatively large heat capacity, or in cases of wooden constructions in which the building envelope heat capacity was comparatively small.
8. Future Work
The question of whether the human body exergy balance could be used to indicate the thermal comfort provided by passive strategies should be investigated in future work. If this could be developed as an adequate indicator, passive design might become more accepted in many buildings. To facilitate such research, future studies should consider the use of meteorological data, obtained at 1-minute intervals, for performing quantitative investigations of the exergy resulting from adaptations (physiological and behavioral) that may arise from daily (day and night) or seasonal (spring, summer, autumn, and winter) rhythms.
Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 25289200.