Analytical study for numerical instability of steady-state heat conduction problems in exchanger tubes using degenerate kernels in the null-field boundary integral equation method

doi:10.1016/j.ijheatmasstransfer.2024.125785

淡江大學機構典藏 > 工學院 > 土木工程學系暨研究所 > 期刊論文 > Item 987654321/125860

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題名:	Analytical study for numerical instability of steady-state heat conduction problems in exchanger tubes using degenerate kernels in the null-field boundary integral equation method
作者:	Lee, Jia-wei
日期:	2024-06-24
上傳時間:	2024-08-06 12:05:52 (UTC+8)
摘要:	This paper not only derives an analytical solution for steady-state heat conduction problems in exchanger tubes but also can predict the location of numerical instability due to a degenerate scale in the boundary element method or the boundary integral equation method. Four shapes of the exchanger tubes including concentric annulus, eccentric annulus, confocal ellipses, and elliptical tube with a confocal crack are analytically studied by using degenerate kernels of polar, bipolar and elliptical coordinates, respectively. This work extends our prior research on numerical instability and its treatment for steady-state heat conduction problems in exchanger tubes using the dual boundary element method. Analytical solutions of the temperature field and conduction shape factor can be derived. Two main analytical tools, the degenerate kernel for the closed-form fundamental solution and the generalized Fourier expansion for the boundary densities in the null-field boundary integral equation are required. The analytical derivation process can clearly examine the occurring mechanism of numerical instability due to a zero denominator. The effectiveness of regularization techniques to promote the rank-deficiency by one to a full-rank system can be analytically examined in this paper.
關聯:	International Journal of Heat and Mass Transfer 231,　125785
DOI:	10.1016/j.ijheatmasstransfer.2024.125785
顯示於類別:	[土木工程學系暨研究所] 期刊論文

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