A two-dimensional inverse analysis utilizing the conjugate gradient method of minimization is applied to estimate the surface thermal behavior (i.e. heat flux and temperature) of a roll which was used in steel rolling mills with water cooling. No prior information is needed for the functional forms of timewise and spacewise variation of the surface heat flux and temperature. The transient temperature recordings inside the roll are modified from the existing experimental data and serve as the simulated experimental data for the inverse analysis. The results show that the estimation of surface heat flux and temperature becomes worse when the temperature measurements are taken too far away from the surface, due to a thin thermal layer. Once the surface heat flux is determined, the surface heat transfer coefficients can be calculated based on the Fourier law, provided that the ambient temperatures are known. After the surface heat transfer coefficients of the roll are determined, an evaluation of the cooling system of the roll can be performed.
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