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Microwave heating of materials with nonohmic conductance

Journal Article


Abstract


  • The microwave heating of a material with temperature-dependent, nonohmic conductance is considered both analytically and numerically. In the case when the microwave amplitude is small, it is shown using a multiple scales expansion that the heating is governed by a Ginzburg-Landau type equation. This equation does not possess the solitary wave solutions of the full Ginzburg-Landau equation. Approximate solutions in the form of a slowly varying soliton and a front are found in certain parameter limits; these solutions compare very well with numerical solutions of the full governing equations. Initial-boundary value and initial value problems are considered numerically with particular emphasis on the structure of fronts.

Publication Date


  • 1993

Citation


  • Marchant, T. R., & Smyth, N. F. (1993). Microwave heating of materials with nonohmic conductance. SIAM Journal on Applied Mathematics, 53(6), 1591-1612. doi:10.1137/0153074

Scopus Eid


  • 2-s2.0-84975229679

Start Page


  • 1591

End Page


  • 1612

Volume


  • 53

Issue


  • 6

Abstract


  • The microwave heating of a material with temperature-dependent, nonohmic conductance is considered both analytically and numerically. In the case when the microwave amplitude is small, it is shown using a multiple scales expansion that the heating is governed by a Ginzburg-Landau type equation. This equation does not possess the solitary wave solutions of the full Ginzburg-Landau equation. Approximate solutions in the form of a slowly varying soliton and a front are found in certain parameter limits; these solutions compare very well with numerical solutions of the full governing equations. Initial-boundary value and initial value problems are considered numerically with particular emphasis on the structure of fronts.

Publication Date


  • 1993

Citation


  • Marchant, T. R., & Smyth, N. F. (1993). Microwave heating of materials with nonohmic conductance. SIAM Journal on Applied Mathematics, 53(6), 1591-1612. doi:10.1137/0153074

Scopus Eid


  • 2-s2.0-84975229679

Start Page


  • 1591

End Page


  • 1612

Volume


  • 53

Issue


  • 6