Application of the hybrid method to inverse heat conduction problems

Analytical solution of spray cooling characteristics on a hot surface using the Laplace transform

“…The numerical inversion of the Laplace transform proposed by [11] is based on a Fourier series expansion. We established a sub-routine about the inverse Laplace transform and the main programme in conjunction with the sub-routines given by [11] to solve all kinds of transient heat conduction problems, as shown in [9,10,12,13]. It is seen in [12,13] that the results obtained are close to the exact solution.…”

Estimation of Surface Conditions for Nonlinear Inverse Heat Conduction Problems Using the Hybrid Inverse Scheme

“…In general, the smaller the time step is, the more ill-posed the problem becomes. In order to overcome this drawback, Chen and Chang [12] first introduced a hybrid scheme of the Laplace transform and finite-difference methods to estimate the unknown surface temperature in one-dimensional IHCPs using measured nodal temperatures inside the material without measurement errors. However, the measurement location had to be placed near the active boundary in order to obtain a more accurate estimation.…”

“…The main difficulty of the IHCP is that its solution is very sensitive to changes in the input data resulting from measurement errors [1][2][3]. To date, various methods [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], such as the regularization, least-squares, sequential, conjugate gradient, function specification, Kalman filter, group-preserving, and hybrid inverse methods, have been developed for solving the IHCP. Most of the previous works were confined to problems with constant thermal properties.…”

Retrieval of thermal properties in a transient conduction–radiation problem with variable thermal conductivity

“…The Laplace transform method, the finite element method in conjunction with the least-squares method was employed by Chen and Chang [1] to estimate surface heat flux/ temperature from measured temperature inside the solid in an inverse heat conduction problem. Wang et al [2] have carried out an inverse analysis for turbomachinery blading.…”