A generalized analysis on material invariant characteristics for microwave heating of slabs

A generalized dimensionless formulation has been developed to predict the spatial distribution of microwave power and temperature. The 'dimensionless analysis' is mainly based on three numbers: wave number, Nw; free space wave number, Nw0; and penetration number, Np, where Nw is the ratio of sample thickness to wavelength of microwaves within a material, Nw0 is based on wavelength within free space and Np is the ratio of sample thickness to penetration depth. The material dielectric properties and sample thicknesses form the basis of these dimensionless numbers. The volumetric heat source due to microwaves can be expressed as a combination of dimensionless numbers and electric field distributions. The spatial distributions of microwave power for uniform plane waves can be obtained from the combination of transmitted and reflected waves within a material. Microwave heating characteristics are obtained by solving energy balance equations where the dimensionless temperature is scaled with respect to incident microwave intensity. The generalized trends of microwave power absorption are illustrated via average power plots as a function of Nw, Np and Nw0. The average power contours exhibit oscillatory behavior with Nw corresponding to smaller Np for smaller values of Nw0. The spatial distributions of dimensionless electric fields and power are obtained for various Nw and Np. The spatial resonance or maxima on microwave power is 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 whereas the spatial power follows the exponential decay law for higher Np regimes irrespective of Nw and Nw0. These trends are observed for samples incident with microwaves at one face and both the faces. The heating characteristics are shown for various materials and generalized heating patterns are shown as functions of Nw, Np and Nw0. The generalized heating characteristics involve either spatial temperature distributions or uniform temperature profiles based on both thermal parameters and dimensionless numbers (Nw,Nw0,Np).