Simulation and uncertainty quantification in high temperature microwave heating

Microwave heating processes are highly sensitive to variability in the operating frequency and usually there are high uncertainties associated with measurements of the materialʹs imaginary permittivity. Therefore, the harmonic Maxwellʹs equations and time dependent heat equation are considered for the simulation of high temperature ceramic microwave heating with uncertain operating frequency and dielectric constants. To analyze the uncertainty of the system, the Non-Intrusive Spectral Projection Method (NISP) is used based on the Polynomial Chaos expansion. The conclusions of this work indicate that 13 Gauss collocation points and a polynomial degree of 11 must be used with the NISP in order to obtain accurate results. Furthermore it also adds that uncertainty in frequency leads to high values of variability in the stochastic solution. The uncertainty in the materialʹs imaginary part of permittivity has only a significant impact for high temperatures of the material. Temperature probability density functions, error bars and standard deviations characterize the material heating up to high temperatures.