Numerical method for hyperbolic inverse heat conduction problems

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

“…Thus, for inverse operation process constructed by using Eq. (10), mean (f = 0) and linear hypothesis (f = 1) are adopted to estimate boundary condition in the form of triangular function, estimated results are shown in Figs. 5 and 6, respectively.…”

“…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.…”

“…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.…”

Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation with a heat source

“…On the other hand, approximating Eq. (4) by its first-order Taylor series expansion yields the damped wave equation (DWE) [11][12][13][14][15][16][17][18][19][20][21][22][23][24] ouðr; tÞ ot þ s 0 o 2 uðr; tÞ…”

Gradient method for inverse heat conduction problem in nanoscale

“…Solving the hyperbolic heat equation, which considers the finite speed of thermal wave propagation, is the easiest way [12][13][14][15]. IHCP methods for solving hyperbolic problems have been investigated in previous works [16,17]. It should be noted that some of the studies on hyperbolic IHCPs are rather focused on stabilizing parabolic IHCPs by artificially hyperbolizing the parabolic governing equation to overcome the extreme sensitivity to measurement errors [18,19].…”