Time Dependence of Thermophysical Properties

As described in the previous sections, the changes in the effective thermophysical properties (density, thermal conductivity, and specific heat capacity) are mainly determined by the decomposition process. This process, being kinetic, is not just an univariate function of temperature, but also on time. Therefore, and in contrast to true material properties, effective properties are dependent not only on temperature, but also on time. In order to model the time-dependent physical properties, related kinetic processes must be taken into account, as described by the kinetic equations in Chapter 2. 

The decomposition model, Eq. (2.19) is a differential equation with respect to time t that is able to take the effects of complex thermal loading (thermal loading at variable heating rates) into account. As any thermal loading procedure is also a function of time, and based on a finite difference method, the temperature at each finite time step can be approximated as a constant. At a time step,j, with a constant heating rate fip Eq. (2.19) can be converted to  

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