THERMAL SCIENCE

International Scientific Journal

Wenkai Qiu

,

Haolong Chen

,

Huanlin Zhou

BOUNDARY CONDITION IDENTIFICATION FOR OETHOTROPIC HEAT CONDUCTION PROBLEMS BASED ON HYBRID TREFFTZ FINITE ELEMENT METHOD WITHOUT ITERATION

ABSTRACT
It is essential to accurately identify the boundary condition of pipeline's inner wall in engineering analysis and calculation. An efficient non-iterative algorithm based on the hybrid Trefftz finite element method (HT-FEM) is presented to determine the boundary condition of the inner wall for orthotropic media heat conduction problems. The temperature of measurement points is obtained by solving the forward heat conduction problems using the HT-FEM to simulate the experimentally measured data. The evaluated temperature at these points can be formulated as a function of the temperature of the inner boundary nodes, whose boundary conditions remain to be determined. The objective function is established to quantify the deviation between the measured and evaluated temperature at measurement points by utilizing the least-squares approach. The unknown inner boundary conditions are determined by minimizing objective function. Four numerical examples are provided to analyze the inversion results for different types of pipes. The effects of various factors, encompassing the number and location of measurement point, measurement errors, and mixed boundary conditions on inversion results are discussed. The findings demonstrate that the proposed algorithm exhibits high computational efficiency and accuracy in identifying boundary conditions.
KEYWORDS
non-iterative algorithm, hybrid Trefftz finite element method, boundary condition identification, orthotropic heat conduction problems
PAPER SUBMITTED: 2025-12-07
PAPER REVISED: 2026-03-04
PAPER ACCEPTED: 2026-03-06
PUBLISHED ONLINE: 2026-04-12
DOI REFERENCE: https://doi.org/10.2298/TSCI251207039Q
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Boundary condition identification for oethotropic heat conduction problems based on hybrid Trefftz finite element method without iteration

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence