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The present study introduces a numerical method to analyze inverse heat conduction problem concerning the prediction of the surface behavior. The numerical algorithm combines the Laplace transform technique and the finite difference method in conjunction with the least square scheme. Time-dependent terms in the governing equation are removed by using the Laplace transform technique, and then the resulting differential equation are solved by using the finite difference method. Temperature distributions in the domain are obtained by using the numerical inversion of Laplace transform. Due to the application of the Laplace transform technique, the temperature can be calculated at a specific time without step-by-step computation in the time domain. By using the least square scheme, the convergence of iteration is fast and stable. In the estimation of the unknown boundary temperature, various examples are illustrated to show the applicability and efficiency of the present numerical method. The influences of measurement time intervals and thermocouple locations are investigated. It can be seen from various illustrated examples that the present numerical method can accurately and efficiently estimate the unknown boundary temperature and the thermocouple can be located far from the estimated surface. In addition, the effect of the measurement error and noises on measurements will be investigated. It is fount that the present numerical method can also estimate the boundary surface well while the measurement error and noises are considered. Thus, it can be concluded that the present numerical method can successfully be to analyze inverse heat conduction problem applied.
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