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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: Uniform heating of thin ceramic slabs in a multimode microwave cavity
Author: Agrawal, Shuchi
View Online: njit-etd2011-087
(xv, 122 pages ~ 15.2 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Kriegsmann, Gregory A. (Committee chair)
Whitman, Gerald Martin (Committee member)
Booty, Michael R. (Committee member)
Petropoulos, Peter G. (Committee member)
Moore, Richard O. (Committee member)
Date: 2011-05
Keywords: Microwave cavity
Uniform heating
Rectangular slab
S-shaped curve
Cylindrical wafer
Multi mode
Availability: Unrestricted

Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled in the small Biot number limit and a thin silicon wafer situated in a TM101 cylindrical cavity modeled in the small fineness ratio limit are studied to gain insight into the dynamics of the heating process. The evolution of temperature is governed by a two-dimensional reaction diffusion equation and a spatially non-homogeneous reaction term. Numerical methods are applied to accurately approximate the steady state leading order temperature of this equation and to determine the stability of solutions for Neumann boundary conditions. The choices of parameters in the equation that lead to uniform heating of the ceramic slab have been characterized.

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