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Laplace transform-based BEM for unsteady heat conduction in space-time anisotropic functionally graded materials with
Derese Wendimu Ayitaged1, Tamirat Temesgen Dufera2, Mesfin Mekuria Woldaregay2
1Departement of Applied Mathematics, Adama Science and Technology University, Adama, Adama, 1888, Oromia, Ethiopia. derese.wendimu@astu.edu.et.
Scientific Reports
|May 20, 2026
Summary
This study presents a boundary element method for transient heat conduction in anisotropic functionally graded materials. The approach accurately solves complex heat transfer problems with variable thermal properties.
Area of Science:
- Heat Transfer
- Materials Science
- Computational Mechanics
Background:
- Transient heat conduction analysis is crucial for advanced materials.
- Anisotropic functionally graded materials (FGMs) present unique thermal challenges.
- Existing methods struggle with spatially and temporally varying thermal properties.
Purpose of the Study:
- To develop a novel boundary element method (BEM) for transient heat conduction in anisotropic FGMs.
- To handle materials with spatially and temporally varying thermal properties and internal heat sources.
- To validate the accuracy, convergence, and stability of the proposed numerical approach.
Main Methods:
- Variable transformation to simplify the governing heat equation.
- Laplace domain transformation to eliminate time derivatives.
- Boundary integral formulation using fundamental solutions.
- Numerical integration of domain integrals via particular solutions.
- Stehfest algorithm for Laplace transform inversion.
Main Results:
- The boundary element formulation accurately models transient heat conduction in anisotropic FGMs.
- The method demonstrates good convergence and stability for benchmark problems.
- Numerical results align well with known analytical solutions.
Conclusions:
- The developed BEM is an effective tool for analyzing transient heat conduction in anisotropic FGMs with variable properties.
- The transformation techniques simplify complex heat transfer problems.
- This method provides a reliable framework for future FGM thermal analysis.
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