## 2 Materials and Methods
### Heat Sources and Heat Losses Mechanisms  
The heat in the body can be produced by cell metabolism (the last term in Equation (1)). The heat also can be transferred by blood flow (the second term on the right side of Equation (1)). The tissue can also dissipate heat (negative heat source) using radiation, evaporation, and convection. In normal conditions, radiation is the most significant source accounting for approximately 60% of heat loss [17]. At rest, evaporation accounts for 22% of heat loss. However, sweating (evaporation) is the primary means of cooling the body during exercise. Different heat loss mechanisms interplay with each other. For example, evaporation and conduction of the air are accelerated by convection. The energy transfer (and skin temperature) is also determined by the surrounding environment's temperature and moisture. The radiative heat loss of the human skin in the ambient air [W/m\({}^{2}\)] can be described as  
\[q_{r}\ =\ \varepsilon\sigma\Big{(}T_{skin}^{4}-T_{\infty}^{4}\Big{)} \tag{2}\]  
where \(T_{skin}\) and \(T_{\infty}\) are the skin and ambient air temperatures [K], \(\sigma\) is the Stefan-Boltzmann constant, and \(\varepsilon\) is the emissivity of the skin. The emissivity of human skin is close to the perfect blackbody. It is at least 0.91 in the MWIR range and even higher (0.97-0.98) in the LWIR range [2]. Because the human body acts almost like a blackbody, it is very well suited for thermographic assessment. In particular, the reflected energy flow, which may impact measurements, is typically relatively minimal. The convective heat loss can be described as  
\[q_{c}\ =\ h_{c}(T_{skin}-T_{\infty}) \tag{3}\]  
where \(h_{c}\) is a heat transfer coefficient due to convection [W/m\({}^{2}\)/K]. The heat transfer coefficient can be estimated in two important cases: free convective flow and forced convection [18]  
\[h_{c}\ =\ \begin{cases}2.44(T_{skin}-T_{\infty})^{0.25},\textit{free convective flow}\\The insensible evaporative heat loss assumes no visible sweating on the skin. It can be estimated as being 6% of the maximum rate of evaporative heat loss \(q_{ev}\)(max) [19]. where  
\[q_{ev}(\text{max})\ =\ 0.0166h_{c}(P_{skin}-P_{\infty}) \tag{5}\]  
Here, \(P_{skin}\) and \(P_{\infty}\) are the skin and atmospheric water vapor pressures, respectively [Pa]. It should be noted that the skin surface is assumed to be at saturated vapor pressure, and the atmosphere has a fractional relative humidity, \(RH\). The saturated vapor pressure \(P_{sat}\) [Pa] at temperature \(T\) [K] can be approximated as  
\[P_{sat}(T)\ =\ 3.99\times 10^{-5}\times 10^{0.0265T} \tag{6}\]  
The liquid heat loss is dependent on the latent heat loss of evaporation (for water \(c\) = 2461 kJ/kg), the difference in the vapor pressures at the skin surface and the atmosphere, and the relative area of the skin covered with the sweat \(W\):  
\[q_{ev,liq}\ =\ 5.45\times 10^{-3}h_{c}W(P_{skin}-P_{\infty}) \tag{7}\]  
While in some sources (see, e.g., [11]), \(W\) is called the skin humidity, this term can be ambiguous. Thus, to avoid confusion, we will use the term \"skin wetness\" instead to signify the presence of visible free moisture. In general, if we refer to large skin areas partially covered by moisture (e.g., sweat), then \(0\leq W\leq 1\). However, for local patches of skin, this parameter can be perceived as binary, where \(W\) = 0 and 1 respectively correspond to dry and entirely wet skin. Thus, the total heat loss can be described as  
\[ \begin{split} q\ =\ q_{r}+q_{c}+q_{ev}\ =\ \varepsilon\sigma \big{(}T_{skin}^{4}-T_{\infty}^{4}\big{)}+h_{c}\big{(}T_{skin}-T_{\infty} \big{)}\\ +\big{(}9.66\times 10^{-4}+5.45\times 10^{-3}h_{c}W\big{)} \big{(}P_{sat}(T_{skin})-RH\ P_{sat}(T_{\infty})\big{)}\end{split}  \tag{8}\]  
The first and second operands in the third term are responsible for insensible and liquid evaporation, respectively. Based on the briefly described skin model, we can consider the following simplistic two-layer model from a heat source perspective.