Direct and Inverse Solutions of the Hyperbolic Heat Conduction Problems

Direct and inverse solutions with non-Fourier effect on the irregular shape

“…In general, inverse operation method is usually applied when analyzing simple shape (see [2][3][4][8][9][10]13]). This paper is theoretically based on linear least-squares error method [14], but changes with the finite element method in spatial discretion to solve spatial stiffness matrix of irregular shape, and adds sequential algorithm concept to build a universal solving process.…”

“…As a result, there are only a few current studies on non-Fourier heat transfer effect inverse problem. For example, Yang [8,9] used Newton-Raphson method combined with finite difference method and iterative solution approach to estimate non-Fourier heat transfer inverse problem of one-dimension or two-dimension regular shape. Chen et al [10] adopted Laplace transform technique and control volume method in conjunction with the hyperbolic shape function to overcome numerical oscillation, and estimate the unknown surface conditions of one-dimensional hyperbolic inverse heat conduction problems.…”

An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

“…When any material is subjected to a pulse radiation, at short time levels, a discontinuity in the temperature profile is observed, which cannot be explained through Fourier's law of heat conduction [26]. In the area of non-Fourier conduction and/or radiation heat transfer problems, a few studies have been reported in the past [27][28][29][30][31][32].…”

Investigation for the dual phase lag behavior of bio-heat transfer

“…There are mathematical difficulties in dealing with the non-Fourier heat transfer problem. And also, the inverse problem is ill-posed because a small measurement error induces a large estimated error [17,18]. Therefore, the studies about the inverse non-Fourier heat transfer problem are not numerous.…”