Generalized scaling on forecasting heating patterns for microwave processing

A closed form analysis based on Finite Fourier Transformation (FFT) has been carried out to predict the heating characteristics in the presence of microwave induced volumetric heat sources. A scaling analysis shows that temperature distributions within a material during microwave heating evolve in two stages, namely small time and large time. The inverse of square of second eigenvalue along with thermal diffusivity determines the threshold time scale between these two regimes. During small time evolution, the spatial temperature distribution follows absorbed power profiles, whereas the temperature distributions are slaved by first eigenfunction and independent of volumetric heat distribution at large time evolution. In all the cases, the variation of temperature within the material is guided by a dimensionless number N G = L2q0/kTref. For NG ≪ 1, almost uniform temperature distributions are attained and a lump parameter model can be used. In contrast, nonuniformity in absorbed power distributions amplifies in temperature distribution for materials with N G ≫ 1, where there exists a possibility of local hot spot formation if absorbed power exhibits local maxima. The applicability of this analysis has been illustrated to forecast heating characteristics within various materials. © 2007 American Institute of Chemical Engineers.