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 lambda(m) <= 1.5D(p,m) for lambda(m) approximate to lambda(0) and lambda(m) <= 3D(p,m) for lambda(m) not approximate to lambda(0). Here lambda(m) and D-P,D-m denote the wavelength and penetration depth within the sample, respectively, and lambda(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 lambda(m) approximate to lambda(0), while the occurrence of resonance is independent of phi(1) for lambda(m) not approximate to lambda(0). Here, phi(1) 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 lambda(m) approximate to lambda(0), while they vary nonmonotonically for lambda(m) not approximate to lambda(0) and phi(1) not approximate to 0,1 or 1/2 due to suppressions of odd (for lambda(m) < lambda(0)), or even (for lambda(m) > lambda(0)) resonating peaks, which increase as phi(1), approaches 1/2 from either 0 or 1. Finally, at phi(1) approximate to 1/ 2 with lambda(m) not approximate to lambda(0) odd (for lambda(m) < lambda 0), or even (for lambda(m)>lambda(0)) resonating peaks of average absorbed power vanish reducing the number of resonating points by a factor of two from one side incidence (phi(1) approximate to 0 or 1), to both side incidence with equal power input from left and right sides (phi(1) approximate to 1/2). This work provides correlations (corresponding to lambda(m) approximate to lambda(0) and lambda(m) not approximate to lambda(0)) for predicting the locations of resonating peaks as function of lambda(m)/lambda(0),lambda(m)/D-p,D-m, and The theoretical prediction on average power characteristics have been shown to be useful in forecasting the heating patterns for efficient material processing. (c) 2006 American Institute of Chemical Engineers AIChE J, 52: 3707-3721, 2006.