*3.3. Evaluation of the Thermal Heat Capacity*

The influence of alloy components on the specific thermal heat capacity *c*<sup>p</sup> can be evaluated utilizing the Kopp–Neumann law. The weight content of each alloy *c*wi as well as the specific heat capacity of each alloy component *c*pi needs to be known for this law:

$$c\_{\rm P} = \sum\_{i} c\_{\rm wi} \cdot c\_{\rm Pi'} \tag{31}$$

Both requirements are fulfilled for this study. Temperature-dependent measurement data of the specific heat capacities are available in the literature for silicon [22], aluminum [23], and pure iron [24]. Within this input data, the temperature dependency is considered as used in [25]:

$$c\_{\mathbb{P}}(\theta) = \sum\_{i} c\_{\text{wi}} \cdot c\_{\text{Pi}}(\theta) \tag{32}$$

The resulting heat capacities in dependency of the temperature are depicted in Figure 8. The Kopp–Neumann law is, strictly speaking, only valid for composites but the comparison of measured heat capacities of Fe-based alloys with the Kopp–Neumann law can be found in the literature, such as [26]. Further, the difference of the calculated heat capacity of the eight materials shows minor influence on the later thermal conductivity. This can be illustrated with the maximum deviation of the values at room temperature. The *c*<sup>p</sup> of M1 deviates from the M8 value at room temperature by 3.6%. The thermal diffusivity *a* of M1 is 334% larger than the value of M8 at room temperature. For further validation and estimation of the errors, the calculated values of the heat capacity based on Equation (31) are compared to the results evaluated from the commercial software JMatPro Version 8. The comparison is performed for pure iron and Materials M7 and M8, which are the materials with the highest Al and Si content, respectively. The maximum deviation between the two approaches is around 1%. For the error estimation study, a value of *δc*prel = 2% is used for all materials.

Due to the small differences between *c*<sup>p</sup> of the different materials, only a minor influence on the difference of the thermal conductivities of the materials, according to Equation (19), is expected. A minor influence on the maximum dissipated heat is expected. The value varies between 451 J/(kg K) for M1 and 465 J/(kg K) for M8. In the case of a study with fewer accuracy requirements, an average value of the expected heat capacity could be used with a maximum error of the indicated 3.6%.

**Figure 8.** Results of the calculation of the thermal heat capacity *c*p(*ϑ*).
