Thermal properties (thermal conductivity or diffusivity, heat capacity)
Thermal conductivity refers to the quantity of thermal energy transmitted through a unit thickness of fabric in a direction normal to the surface of unit area due to the unit temperature gradient under steady-state conditions. According to Fourier’s law, the thermal conductivity of any fabric can be represented by Eq. (7.2), where, k=thermal conductivity of fabric (W/m °C); q = conductive thermal energy transfer (W); s = fabric thickness (m); A = thermal energy transfer area (m2); and, dt=temperature difference across the fabric (°C). Additionally, the thermal diffusivity (a) refers to the thermal conductivity (k) divided by the product of the density (p) and heat capacity per unit mass (Cp) at constant pressure (Eq. 7.3). According to Eqs. (7.2), (7.3), if the thermal conductivity or diffusivity of a fabric is greater, it will transmit more thermal energy through its surface. It is expected that the fabrics used for thermal protective clothing must have a lower thermal conductivity or diffusivity in order to provide a better thermal insulation to wearers [307,393,542-546]. Sometimes a high thermal conductivity-based fabric may transmit thermal energy quickly from a radiant heat- or flame-exposed area to a nonexposed area; eventually, it may prevent the localized burning of wearers in the exposed area. Contextually, it has been pointed out that the term “thermal conductivity” of a fabric does not have a precise physical meaning because thermal energy is usually transferred through the fabric by convection or radiation as well as conduction [541,547,548]. Researchers have suggested that the appropriate term “thermal transmissivity” be used instead of “thermal conductivity” for scientific purposes. Furthermore, thermal conductivity or thermal transmissivity is only applicable in thermal equilibrium conditions of a fabric; in nonthermal equilibrium conditions, heat capacity needs to be evaluated to understand thermal properties of a fabric.
Heat capacity (C) of a fabric is the measurable physical quantity that characterizes the amount of heat required (Д0 to change the fabric’s temperature (ДT) by a given amount (Eq. 7.4) . According to Eq. (7.4), if the heat capacity of a fabric is high, it requires more heat to change a certain temperature of the fabric. Eventually, a fabric with high heat capacity possesses high thermal insulation characteristics or thermal protective performance during thermal exposures. However, a high heat capacity can store more thermal energy inside the fabric, which may take longer to dissipate (even after the thermal exposures) and cause burns to wearers . The heat capacity also varies with respect to temperature. For example, the heat capacity of any synthetic fabric increases up to 50% when the temperature rises from 500 to 1000 K .
In order to establish a relationship between temperature (T) and heat capacity (C), an empirical formula has been developed by Schoppe et al.  (Eq. 7.5, where, T is in Kelvin and C is in J/kg K). Generally, it has been established that the specific heat or heat capacity of any synthetic fiber-based fabric lies between 0.29 and 0.39 cal/g/K at 20°C. Although Eqs. (7.4), (7.5) are widely used to predict the heat capacity of a fabric, many researchers also use various instruments to accurately measure the heat capacity at various temperatures [36,348,477,550].
In summary, thermal properties (thermal conductivity or diffusivity, heat capacity) significantly affect the thermal insulation characteristics of fabrics, and these properties are dependent upon various attributes (eg, selection of fibers, amount of air/fiber phase inside the fabrics). Although these attributes can provide a guideline to achieve required thermal properties, it is a cumbersome process to accurately control the attributes during fabric manufacturing. To overcome this, some of the latest technologies (intelligent textiles, smart textiles) can be applied during fabric manufacturing to achieve the required thermal properties of the fabric. For example, Buhler, Popa, Scherer, Lehmeier, and Rossi  and Rossi and Bolli  concluded that an application of phase change materials (PCMs) such as water, salt hydrates, and fatty acids may control the thermal properties of a fabric used in protective clothing. These PCMs have the high heat of fusion, which allows them to store a large amount of energy during their phase change. This situation lowers thermal conductivity or diffusivity (or increases heat capacity) of a fabric; hence, the thermal insulation characteristics of the fabric enhances to provide a better protection for wearers. In this regard, it is necessary to remember that a PCM may change from solid to liquid during its phase change and could drop down on wearers’ bodies. To combat this, PCMs should be micro/macro-encapsulated in fabrics; this can prevent dissolution of PCMs by maintaining their same form with little volumetric expansion.