Generalized analysis on microwave-assisted material processing for one-dimensional slabs: Metallic support versus free space

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Tanmay Basak
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The dimensionless analysis has been carried out to predict the generalized trend in distribution of microwave power and temperature irrespective of thermal and dielectric properties of materials. The analysis is mainly based on three numbers: wavenumber, Nw; free-space wavenumber, Nw0; and penetration number, Np, where Nw is the ratio of sample thickness to wavelength of microwaves within a material, Nw0 is based on the wavelength within free space, and Np is the ratio of sample thickness to penetration depth. The spatial distributions of microwave power for uniform plane waves can be obtained from the combination of transmitted and reflected waves within a material. The generalized trends of microwave power absorption are illustrated via average power plots as a function of N w, Np, and Nw0. The average power contours exhibit oscillatory behavior, with Nw corresponding to smaller N p. The spatial distributions of dimensionless electric fields and power are obtained for various Nw and Np. The spatial resonance or maxima on microwave power are represented by zero phase difference between transmitted and reflected waves. It is observed that the number of spatial resonances increases with Nw for smaller Np regimes based on relationships Nw = 0.5n - 0.25 (for metallic support) and Nw = 0.5n (for free space), where n is any integer. We have also investigated the spatial resonance patterns, with n being a noninteger, and it is observed that the location of the spatial resonance varies with n, but the number of resonance regimes is increased when n increases to an integer value. The spatial power follows an exponential decay law for higher Np regimes irrespective of Nw and Nw0. The heating characteristics are shown for various materials, and generalized heating patterns are shown as functions of Nw, Np, and N w0. The generalized heating characteristics involve either spatial temperature distributions or uniform temperature profiles based on both thermal parameters and dimensionless numbers (Nw, Nw0, and N p). Microwaves can be optimally used with/without metallic support for the Np ≤ 2 regime. The metallic support corresponds to greater heating rates for Nw = 0.25 and 0.75, whereas Nw = 0.5 is optimal for samples without any support. © 2005 American Chemical Society.