Direct and Inverse Steady-State Heat Conduction in Materials with Discontinuous Thermal Conductivity: Hybrid...

Area of Science:

• Materials Science
• Computational Physics
• Heat Transfer

Background:

• Steady-state heat conduction analysis is vital for layered composites, thermal barrier coatings, and electronic packaging.
• Materials often exhibit stepwise discontinuities in thermal conductivity, complicating thermal analysis.
• Accurate modeling of heat transfer in heterogeneous materials is essential for performance and reliability.

Purpose of the Study:

• To develop and assess novel computational models for steady-state heat conduction in two-dimensional composite materials.
• To address both direct (temperature field prediction) and inverse (material property identification) problems.
• To introduce a hybrid meshless Monte Carlo approach for efficient and accurate thermal analysis.

Main Methods:

• Development of deterministic finite-difference and meshless (Moving Least Squares) models.
• Implementation of Monte Carlo methods for both standard and meshless formulations.
• Introduction of an inverse problem-solving algorithm for material parameter and internal source reconstruction.

Main Results:

• The hybrid difference-meshless Monte Carlo framework demonstrated accurate temperature predictions.
• Reliable identification of material parameters and internal heat sources was achieved through inverse analysis.
• Numerical experiments validated the robustness and accuracy across various geometric complexities and conductivity contrasts.

Conclusions:

• The proposed hybrid framework offers a powerful tool for analyzing heat conduction in complex materials.
• The methodology is effective for both direct temperature prediction and inverse material characterization.
• This approach has significant potential for applications in thermal design, material characterization, and failure analysis.