Moving boundary analysis in heat conduction with multilayer composites by finite block method.

*(English)*Zbl 1403.80020Summary: An inverse reconstruction investigation is presented to determine the inner boundary location (corrosion points) for the heat transfer in composite walls from measurement data on exterior boundary. Finite Block Method (FBM) is utilized in this paper to deal with transient heat problems across the multilayered composite walls. Starting from one-dimensional problems, Lagrange interpolation with equally spaced nodes is applied to create first order differential matrices and thereafter the higher order differential matrices are obtained. Then combining with mapping technique, physical domain is mapped into a normalized domain for two-dimensional or three-dimensional problems with 8 seeds or 20 seeds respectively. Both time-spatial approach and Laplace transform technique with Durbin’s inversion method are employed in the simulating procedure. In addition, roots of Chebyshev polynomial of first kind are considered in FBM for the first time, which can improve the degree of convergence significantly. Three numerical examples are presented to validate the accuracy of FBM. Comparisons between Finite Element Method (FEM), FBM and Point Collocation Method (PCM) are demonstrated respectively. Numerical observation indicates that FBM has much higher degree of accuracy even with few collocation points.

##### MSC:

80M15 | Boundary element methods applied to problems in thermodynamics and heat transfer |

65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |

80A23 | Inverse problems in thermodynamics and heat transfer |

##### Keywords:

moving boundary; inverse problem of heat transfer; inhomogeneous heat transfer; finite block method; Lagrange interpolation; roots of Chebyshev polynomial
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\textit{M. Lei} et al., Eng. Anal. Bound. Elem. 89, 36--44 (2018; Zbl 1403.80020)

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