A nonlocal formulation for the problem of microwave heating of material with temperature dependent conductivity

TL;DR

This paper introduces a nonlocal modeling approach for microwave heating of materials with temperature-dependent conductivity, simplifying the coupled PDE system and proving the existence of solutions.

Contribution

It presents a novel nonlocal formulation that reduces the complexity of the coupled Maxwell and heat equations with temperature-dependent conductivity.

Findings

Mathematical proof of solution existence using Schauder's fixed point theorem

A simplified nonlocal model for microwave heating processes

Potential for improved analysis of thermal systems with temperature-dependent properties

Abstract

Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell's equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initial-boundary value problem has solutions using the Schauder's fixed point theorem.