New closed form analysis of resonances in microwave power for material processing

A new closed form material invariant analysis on resonances of microwave induced power absorption is presented. It is shown that resonances in average power is confined within two asymptotic limits of thin and thick samples, and the resonances occur if λ m ⩽ 1.5 D p,m for λ m ≈ λ 0 and λ m ⩽ 3 D p,m for λ m ≉ λ 0 . Here λ m and D p,m denote the wavelength and penetration depth within the sample, respectively, and λ 0 is the wavelength within the free space. It has been shown that average absorbed power does not exhibit resonance for one side incidence if λ m ≈ λ 0 , while the occurrence of resonance is independent of ϕ l for λ m ≉ λ 0 . Here, ϕ l is the fractional power input from the left side. The amplitudes of subsequent resonating peaks are also shown to decay monotonically with sample length for λ m ≈ λ 0 , while they vary nonmonotonically for λ m ≉ λ 0 and ϕ l ≉ 0, 1 or 1/2 due to suppressions of odd (for λ m < λ 0 ), or even (for λ m > λ 0 ) resonating peaks, which increase as ϕ l approaches 1/2 from either 0 or 1. Finally, at ϕ l ≈ 1/2 with λ m ≉ λ 0 odd (for λ m < λ 0 ), or even (for λ m > λ 0 ) resonating peaks of average absorbed power vanish reducing the number of resonating points by a factor of two from one side incidence (ϕ l ap; &0 or 1), to both side incidence with equal power input from left and right sides (ϕ l ≈ 1/2). This work provides correlations (corresponding to λ m ≈ λ 0 and λ m ≉ λ 0 ) for predicting the locations of resonating peaks as function of λ m /λ 0 , λ m / D p,m , and ϕ l . The theoretical prediction on average power characteristics have been shown to be useful in forecasting the heating patterns for efficient material processing. © 2006 American Institute of Chemical Engineers AIChE J, 2006