## 2 Numerical Model
### Boundary Conditions and Material Properties and Meshing
The perfect magnetic conductor condition was imposed on the plane of symmetry, which served to define the division of the model:  
\[\mathbf{n}\times\mathbf{H}=0 \tag{8}\]  
Regarding the HT domain, which was confined solely within the sample, the convective flux condition was enforced on all walls of this domain as the boundary condition [12]:  
\[\rho C_{p}\bigg{(}\frac{\partial\mathrm{T}}{\partial t}+\
abla\mathrm{T} \bigg{)}+\
abla\mathbf{q}=\mathrm{Q} \tag{2}\]0  
where \(h\) denotes the heat transfer coefficient and \(T_{ext}\) is the external temperature value. The boundaries with specified boundary conditions are presented in \[\rho C_{p}\bigg{(}\frac{\partial\mathrm{T}}{\partial t}+\
abla\mathrm{T} \bigg{)}+\
abla\mathbf{q}=\mathrm{Q} \tag{2}\]1  
\[\rho C_{p}\bigg{(}\frac{\partial\mathrm{T}}{\partial t}+\
abla\mathrm{T} \bigg{)}+\
abla\mathbf{q}=\mathrm{Q} \tag{2}\]2 Specification of the boundary conditions used in the modeling process. The model was computed in two modes: continuous (with an equal power of 360 W applied for all the time of simulation) and modulated with the power applied with a function \(f(t)\) presented in \[\rho C_{p}\bigg{(}\frac{\partial\mathrm{T}}{\partial t}+\
abla\mathrm{T} \bigg{)}+\
abla\mathbf{q}=\mathrm{Q} \tag{2}\]3  
\[\rho C_{p}\bigg{(}\frac{\partial\mathrm{T}}{\partial t}+\
abla\mathrm{T} \bigg{)}+\
abla\mathbf{q}=\mathrm{Q} \tag{2}\]4  
For the continuous mode, the study consisted of two steps: a frequency domain computation step (solved only for EMW) followed by a time-dependent computation step (only for HT). In this mode, the power was assumed to be constant. For the modulated mode, the time-dependent step was solved for both EMW and HT. In the presented simulation, the microwave antenna was modeled as an air-filled structure with aluminum edges. The structure of the sample was described previously. Table 1 presents the selected properties of the materials used in the simulation. The number of elements in the simulated model was dependent on the analyzed case. The utilized mesh consisted of 76,093 tetrahedral elements for the case with no defect, 79,677 elements for the case with a defect located in the center of the sample, and 80,049 for the case with a defect located outside the center. The generated mesh is shown in \[\rho C_{p}\bigg{(}\frac{\partial\mathrm{T}}{\partial t}+\
abla\mathrm{T} \bigg{)}+\
abla\mathbf{q}=\mathrm{Q} \tag{2}\]5 As can be noticed, the sizes of the elements changed between the domains. The mesh refinement process was performed manually by utilizing the scale option provided in the COMSOL software. This approach was specifically applied to the domains that encompassed the sample, as these regions were associated with calculations related to both the utilized physics: EMW and HT. \begin{table}
\begin{tabular}{l c c c c c} \hline  & **Air** & **Aluminum** & **Epoxy** & **CFRP** & **Concrete** \\ \hline Cp (J/(kg\text{-}K)) & & N/A & 1700 & 1700 & 750 \\ Density (kg/m\({}^{3}\)) & & N/A & 1150 & 1150 & 2400 \\ Epsilon (relative permittivity) & 1 & 1 & 3.9–2.2 j & 3.6 & 8.4–2.86 j \\ Thermal conductivity (W/(m\text{-}K)) & & N/A & 0.18 & 5 & 0.8 \\ Electrical conductivity (S/m) & 0 & \(3.77\cdot 10^{7}\) & 0 & 0.5 & 0 \\ Relative permeability & 1 & 1 & 1 & 1 & 1 \\ \hline \end{tabular}
\end{table} 
Table 1: The material properties utilized in the modeling [49; 50]. Figure 5: Diagram of the function used for simulating the modulated excitation.