For analytical purposes, the chosen human thermal model must fulfil some basic conditions. For optimal thermal comfort three basic conditions must be fulfilled: heat balance must exist, and skin temperature and sweat rate must be within the comfort range. The human body produces heat, exchanges heat with the environment, and loses heat by diffusion and evaporation of body liquids. During normal rest and exercise these processes result in an average vital organ temperature of around 37 °C. The body’s temperature control system tries to maintain these temperatures even when thermal disturbances occur. The human thermoregulatory system is quite effective and creates heat balance within wide limits of the environmental variables (air temperature, mean radiant temperature, air humidity, and relative air velocity). For a given activity level (metabolism), skin temperature and sweat rate are seen to be the major physiological variables influencing heat balance.
The model used as a starting point is comprised of a physiological part based on the Gagge two-node model [2] and a physical model describing the heat and mass transfer properties of clothing. The physiological model contains a number of control functions for physiological processes, as well as the heat transfer properties of the human body. Core, skin, and mean body temperatures are used as inputs for several set-point-defined feedback loops controlling effector responses [12] and [13]. The effector responses together with metabolic heat production result in a certain heat loss or gain, which then affects the body resulting in a new body temperature (i.e. feedback). The relation between effectors and the resulting body temperature is affected by environmental parameters (heat and mass transfer properties) and heat production level (activity).
Thermal regulation by the human body is mainly achieved by regulating blood flow [14]. The body regulates blood distribution by vasoconstriction and vasodilatation in order to control skin temperature and to increase or decrease heat loss to the environment. During work, blood carries the extra heat produced to the body surface where higher skin temperature increases heat loss through convection and radiation. During cold stress, vasoconstriction shunts blood flow from arteries to veins at deeper layers. Veins and arteries are paired and veins carry heat from the arteries back to the core. This counter-current heat exchange is a major process in decreasing heat loss and maintaining core temperature in a cold environment. In a hot environment, convective and radiative heat transfer from the body decreases due to the small difference between skin and ambient temperature. In this case, heat release from the body is governed by water diffusion and evaporation (latent heat). This mechanism enables the human body to release heat even in a hot environment where the ambient temperature is above skin temperature and the human body is gaining heat from the environment. Therefore, a thermal model for the body is only as accurate as the information provided about the heat and moisture exchange with the environment.
2.1. Heat balance equations
The effects of ambient conditions on the human thermoregulatory system and on heat flow within the human body can be investigated using the two-compartment (or two node) model [2]. This model represents the body as two concentric cylinders, where the inner cylinder represents the body core and the outer cylinder represents the skin layer. The core is the compartment with a regulated and defined temperature, while the skin is a buffer between the core and environment whose temperature is defined by heat and mass exchanges with the core and with the environment. The core and skin compartments exchange energy passively through direct contact and through the thermoregulatory controlled peripheral blood flow. Metabolic heat production at the core is released to the environment by two paths. The predominant pathway is the transfer of heat to the skin by blood flow and heat conduction, followed by release from the skin to the environment by convection, radiation, and evaporation. The minor pathway is the direct release of heat (and mass) to the environment through respiration. Therefore, two heat balance equations for the body core and the skin layer can be built up. The transient energy balance states that the rate of heat storage equals the net rate of heat gain minus heat loss. This thermal model is described by two coupled heat balance equations for the two compartments: