Modeling of Transient Nonlinear Heat Conduction with Temperature-Dependent Material Properties

Document Type : Original Article

Author

Department of Mechanical Engineering, Isfahan University of Technology

Abstract

In recent years, growing attention has been directed toward developing more realistic physical models for simulating complex and technically significant problems. This approach often leads to the formulation of nonlinear, multidimensional, and highly intricate models, whose analysis and solution require advanced numerical and analytical techniques. One of the most notable examples in this context is the transient and nonlinear heat conduction problem with temperature-dependent material properties. This paper presents, analyzes, and evaluates a comprehensive set of possible mathematical models for simulating this phenomenon, some of which are introduced here for the first time. Special emphasis is placed on the application of the Kirchhoff integral transform, typically used in steady-state nonlinear problems, and its precise implementation under transient conditions is thoroughly investigated. Based on this transform, both linear and nonlinear models are derived and compared. The linear models are particularly valuable due to their ability to yield accurate analytical solutions, facilitate inverse heat conduction analyses, enable temperature field control strategies, and offer clearer physical interpretations. Additionally, three new nonlinear models are proposed, two of which demonstrate very high accuracy, while the third, despite its lower precision, provides superior computational simplicity and faster performance. The findings of this study can serve as a foundation for developing more advanced thermal models and optimizing the design of engineering heat transfer systems

Keywords

Main Subjects

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Journal of Computational Methods in Engineering
Volume 44, Issue 2 - Serial Number 30
December 2025
Pages 167-188

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