Numerical simulation of human thermal comfort in indoor environment TIBERIU SPIRCU 1, IULIA MARIA CÂRSTEA 2, ION CARSTEA 3 1, 2 University of Medicine and Pharmacy "Carol Davila, Bucharest ROMANIA E_mail:spircut@yahoo.com 3 University of Craiova, Craiova ROMANIA E_mail: ion_crst@yahoo.com Abstract: The thermal comfort is a great demand of the human occupants in indoor environment. Numerical analysis of the complex system human body environment is important for clinicians that can predict the thermal response of the whole system to the environment factors. With the advanced computers new algorithms and programs must be developed and the paper is directed to this trend. Keywords: - Thermal comfort; Simulation; Finite element method. 1 Introduction The human body and surrounding environment represent a complex system because of the interaction of the heat transfer process with the physiological processes in the tissue. The two components are analyzed independently although they are coupled naturally. From the analyst s viewpoint they have different structures and different models of the behaviours. For simplicity, they are analyzed independently but with the new technologies in the computer architectures the whole system can be analyzed as a single system. The thermal comfort is defined as the condition of mind that expresses satisfaction with the thermal environment [1]. The thermal comfort of a person depends upon the environmental conditions, the insulation and evaporative resistance provided by his/her clothing system, the activity of the person, and the duration of the exposure [2]. Thermal comfort is associated with neutral whole body thermal sensations. The thermal sensation depends on body temperature and the body temperature depends on: thermal balance, the effects of the environmental factors (air s temperature and velocity, relative humidity, mean radiant temperature), and personal factors (metabolism and clothing). Comfort seems to occur when body temperatures are maintained with the minimum physiological regulatory effort. In the human body there are various biomechanical reactions due to the eaten foods and inhaled oxygen. The rate of energy generation within an organism is defined as the rate of transformation of chemical energy into heat and mechanical work by aerobic and anaerobic metabolic activities. These activities are the sum of the biochemical processes by which food is broken down into simpler compounds with the exchange of energy. Thermal energy resulted from these reactions must be regulatory transferred to the environment in order to maintain vital body functions and thermal comfort. It is necessary a sensation of the thermal neutrality generated by the actual combination of temperature and the body s core temperature. The human body can be separated in two interacting systems: an active system and a passive system [3]. The active system is an automatic control system which is responsible for the maintenance of the human body s temperature at a certain level. The active system predicts regulatory responses such as shivering, vasomotion, and sweating. The passive system simulates heat transfer in human body and its external environment. A mathematical model of the body s temperature based on the physics laws as the heat transfer and thermodynamic can help the specialists to predict the thermal behaviour of the entire human body or a part of it. Computer-aided analysis of the human thermal comfort gives more information about the interaction of the human body and environmental factors, and the impact on some environmental factors on an expected human thermal sensation [3]. Typically in the models used for analysis of the thermal comfort, there are more parameters that are included in one of the following classes: Indoor climatic parameters Human thermal system parameters In the first class the following parameters are important: Air temperature Mean radiant temperature ISSN: 1790-2769 65 ISBN: 978-960-474-180-9
Air velocity Air humidity In the second class two parameters are relevant: Metabolic heat production Clothing insulation Sensation of the thermal comfort is related to the magnitude of two physiological variables: temperature and, sweat secretion. An analysis of the heat transfer in a tissue involves a model of the tissue. As see in the Fig. 1 the tissue has a complex structure [5] and a mathematical model to include all components is difficult to be developed. subsystem the mathematical models are different and the computation complexity is increased. 2 Heat transfer models With advances in the computer architectures and organization, and the new and modern therapy technologies, new mathematical models must be developed in space 2-D and 3-D. One-dimensional (1- D) model can be considered in some practical applications and the approximation accuracy is good. Motivations of computer-aided analysis of the heat Fig.1 The multi-layer structure of the tissue In all professional literature for the modelling of the heat transfer the multi-layered model is used. These models include the following layers: epidermis (with corneum and living epidermis), dermis and hypodermis. These layers differ by structure and the material properties so that a single homogeneous layer for the behaviour of the tissue is a bad approximation. In our study we use a domain decomposition approach for the analysis of the thermal comfort with a natural interface boundary: the human. In other words we identify two subdomains: the human body and, the surrounding environment. In our analysis we consider the effects of the environmental factors on the thermal comfort although an accurate model involves tha analysis of the whole system. In each transfer in human body are multiple starting from the assistance of the clinicians in thermal therapies to the understanding of the macroscale tissue responses to heat-induced micro-structural transformations. 2.1 The modelling of the tissue In the heat transfer is mainly a heat conduction process where the blood perfusion is one of the most important heat source or heat sink (the case of cooling). Mathematical models for the heat transfer in the are based on Pennes equation called the bioheat equation [4]. The Pennes bioheat equation describes the thermal behaviour based on the classical Fourier s law and has the form [8]: ISSN: 1790-2769 66 ISBN: 978-960-474-180-9
c ( k ) c ( T T ) q q (1) t b b b a met ext Here, ρ, c, k and T denote density, specific heat, thermal conductivity and temperature of tissue. The 4 4 k ( T T ) (5) where n is the outward normal at the boundary of computational domain, ε is emissivity and σ is Fig. 2 Typical positions for target example density, specific heat, and perfusion rate of blood are denoted by ρ b, c b and ω b, respectively. The heat source is denoted by q and represents the sum of two components: q met which is the metabolic heat generation in the tissue and q ext is the heat source due to external heating. T a is the arterial temperature and it is regarded as a constant and equal to 37 0 C. The effect of blood perfusion rate has a significantly large influence on temperature distribution during cooling than that during heating. In general, the temperature decreases with an increasing blood perfusion rate [7]. Besides the thermal parameters and metabolic rate of tissue, the temperature is also determined by any other factors such as the humidity, radiation emissivity of and parameters of surrounding air. These factors can be incorporated into the boundary condition (BC) at surface. The boundary condition for the heat transfer occurring at surface is generally included in one of the following kinds of conditions [9]: 1. Dirichlet condition (constant temperature): T T (2) 2. Neumann condition (specified heat flux): k qs (3) 3. Convective condition: k h( T T ) (4) 4. Radiation condition: Stefan Boltzmann s constant in W/(m 2 K 4 ). First kind BC represents heating/cooling at a constant temperature T, second kind BC represents heating/cooling by constant heat flux q S, third kind BC represents heating/ cooling by convective heat transfer, which means heat exchange between the tissue surface and fluid at a constant temperature T, and fourth BC represents heating/cooling by radiative heat transfer. Radiation is the loss of heat in the form of infrared waves. All objects continually radiate energy in accordance with the Stefan Boltzmann law. When the surrounding is cooler than the body, net radiative heat loss occurs. Under normal conditions, close to half of body heat loss occurs by radiation. In contrast, a net heat gain via radiation occurs when the surrounding is hotter than the body. At the outer surface of the human body, heat transfer can consist of a liner combination of all kinds of boundary conditions (convection, radiation, and sweat). The generalized boundary condition for the heat transfer occurring at surface is generally composed of three parts, i.e. convection, radiation and evaporation. It thus can be written as 4 4 k h( T T ) ( T T ) Qe (6) where Q e is the evaporative heat losses due to sweat secretion. The boundary condition defined by Eq. (6) is nonlinear due to occurrence of the εσt 4 term so that the mathematical model is non-linear. Consequently, an analytical solution or a direct method can not be used. ISSN: 1790-2769 67 ISBN: 978-960-474-180-9
An iteration procedure must be used in the problem solution. The mathematical model is a partial derivative equation of elliptic or parabolic type so that discretization in time and/or space must be done. A combination of the finite differences and finite element method can be used [9]. in the rooms with a temperature difference between the floor and walls temperature. 2.2 Heat transfer in indoor environment A first target example is a person in a room where the walls are the boundary of our system with the outer environment. We consider half of this space in case of a symmetrical position of the occupant. We consider a model 2-D. Mathematical model for the thermal field is the heat conduction equation [9]: x ( k x )+ x y ( k y ) + q = c (7) y t with: T (x, y, t) - environment temperature in the point with co-ordinates (x, y) at the time t; k x, k y thermal conductivities of the environment; ρ -specific mass; c specific heating; q heating source. The Eq. (7) is solved with initial and boundary conditions that can be convection, radiation, Dirichlet condition or a mixed condition. 2 Numerical results The numerical models were obtained by the finite element method [10]. This is a general method for distributed-parameter systems described by partial derivative equations. There is a large professional literature for this method so that it is not necessary to present this method [9]. The method involves a discretization of the continuous variables in discrete variables and the result is a set of the equations with unknowns the physical variables in different points of the analysis domain [7]. Case 1: A non-uniform temperature of the room walls The first case in discussion consists in a temperature difference between wall temperature and the floor temperature [7]. For our example we considered the wall temperature as T=22 0 C and the floor temperature as T=20 0 C. The Figure 3 shows the temperature map and the heat flux vectors in the room. The influence of the difference of temperature between the floor and vertical walls is obviously. Figure 4 shows the variation of the heat flux along the human with the start point the head and the end point- the foot. It is obviously that the strongest variation of the heat flux is in the foot zone. Many people have health problems with the feet when they live for a long time Fig. 3 The temperature and heat flux vectors (case 1) 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 2 Heat flux (W/m 2 ) 0 400 800 1200 1600 2000 Fig.4 Heat flux on the human L (mm) Case 2: A uniform temperature of the room walls If the floor temperature is increased at 22 0C, an important change is observed in the heat flux. Fig. 5 shows the temperature map and the heat flux for this case. From this analysis we can see the influence of the floor temperature on the distribution of the temperature in the neighbour of the human body, especially in the foot area. In this way we can select the heat sources so that we can control the nonuniform distribution of the heat flux. Another important parameter for the temperature control is the floor insulation or boots insulation. ISSN: 1790-2769 68 ISBN: 978-960-474-180-9
walls etc. In Fig. 7 the temperature map and the heat flux vectors are shown for a floor temperature less than the wall temperatures. In our example the floor temperature was 20 0 C and walls temperature were 22 0 C. Fig.7. Temperature map and heat flux vectors Fig. 5. The temperature and heat flux vectors (case 2) In these figures the results of the numerical simulation were for a constant temperature. In the program can be included the effects of radiant temperature of the wall and the human body by considering this type of boundary condition in the mathematical model. Case 3. A foot in contact with the floor The second target example is the foot in contact with the floor (Fig.6) with different temperatures. We can study the influence of the floor temperature on the temperature distribution in the foot area. In our study we did not considered the appendages such as hair/fur and sweat glands that play significant roles in thermoregulation. In some situations the hair strands are so dense that they work as an insulation layer. Practically the hair strands can trap a layer of air that has a thermal conductivity less than of the hair conductivity. Thus, the thermal conductivity is about 0.37 W/mK for human air and 0.026 W/mK for air. In other words the hair enhances the heat transfer from the and thus is an unwanted effect in the thermal insulation sense due to the heat loss. In this area many studies were reported where the was considered as a medium with isothermal surface and the air-hair layer was regarded as an orthotropic material [5]. An optimum hair strand diameter can be found foe minimum total heat loss. The mathematical model for the heat transfer in the air-hair layer is the Eq. (1) without the free term q. A model 1-D is presented in reference [8]. Fig. 5. The foot in contact with the floor There floor temperature has an important effect on the heat flux vector on the surface so that a reduction of this influence has a clinical importance. The temperature distribution can be controlled by the heat sources positions, by the insulation of the 6 Conclusions The main objective of this paper was to investigate the influence of the environmental factors on the thermal comfort in indoor environment using numerical models based on the finite element method. By numerical simulation we can predict in laboratory conditions the influence of different factors on the human body. We limited our study to the environment where the mathematical model was reduced to a classical heat diffusion equation. It is obviously that a complete model involves the distribution of the temperature inside the human where the bioheat equation must be used. This is our objective for a new future work. ISSN: 1790-2769 69 ISBN: 978-960-474-180-9
Although we limited our presentation to some cases, the model can be used to include the heat loss due to sweat evaporation. An analysis of the interior surface temperatures for different wall temperatures with their effect on thermal comfort was presented. Simulation results proved the influence of the spatial temperature distribution on the body segments. A special case is the heat transfer in the foot area and this aspect will be presented in a future work. References [1]. Ashrae. Handbook-fundamentals. Physiological principles and thermal comfort. Atlanta, 1993 (chapter 8). USA. Online: Science.direct.com [2]. Matjaz Prek, Thermodynamical analysis of human thermal comfort. In: Energy 31 (2006) [3]. Eda Didem Yildirim, Baris Ozerdem., A numerical simulation study for the human passive thermal system. In: Energy and Buildings 40 (2008) 1117 1123 Elsevier [4]. H.H.Pennes, Analysis of tissue and arterial blood temperature in the resting forearm. In: Journal of Applied Physiology 1 (1948) 93-122. [5]. Anthony D. Metcalfe, Mark W.J. Ferguson, Bioengineering using mechanisms of regeneration and repair. In: Biomaterials 28 (2007) 5100 5113 [6]. Bejan,A., Theory of heat transfer from a surface covered with hair. In: Trans. ASME., J. Heat Transfer 112 (1990) [7]. Iulia Maria Cârstea, A numerical simulation of the passive human thermal system using the finite element method. In: Abstracts Journal, 11th Craiova International Medical students Conference, November 2009, Romania [8]. F.Xu, T.J.Lu, K.A.Seffen, Biothermomechanics of tissues. Journal of the Mechanics and Physics of Solids 56 (2008) 1852 1884 [9]. Carstea, D., Cârstea, I. CAD in electrical engineering. Sitech, 2001. Romania. [10]. *** QuickField program Version 5.6. User s guide. Tera Analysis.C ISSN: 1790-2769 70 ISBN: 978-960-474-180-9