Article
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Multiplicity Analysis of a Thermistor Problem
Version 1
: Received: 28 June 2023 / Approved: 28 June 2023 / Online: 28 June 2023 (16:06:16 CEST)
A peer-reviewed article of this Preprint also exists.
Krikkis, R.N. Multiplicity Analysis of a Thermistor Problem—A Possible Explanation of Delamination Fracture. J 2023, 6, 517-535. Krikkis, R.N. Multiplicity Analysis of a Thermistor Problem—A Possible Explanation of Delamination Fracture. J 2023, 6, 517-535.
Abstract
In the present study a numerical bifurcation analysis of a thermistor problem is carried out, considering a realistic heat dissipation mechanism due to conduction, nonlinear temperature dependent natural convection and radiation. The electric conductivity is modeled as a strongly nonlinear and smooth function of the temperature between two limiting values, based on measurements. The problem formulated in this way admits multiple steady state solutions that do not depend on the external circuit. The analysis reveals that the conduction-convection parameter and the type of the boundary conditions have a profound effect on the solution structure and the temperature profiles. Depending on the boundary conditions the complex multiplicity pattern appears either as a series of nested cusp points or as enclosed branches emanating from pitchfork bifurcation points.
Keywords
thermistor; Joule heating; conduction; natural convection
Subject
Engineering, Mechanical Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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