Blast furnace layer lining erosion problem based on inverse the heat conduction model

A blast furnace lining mathematical model was established based on the inverse heat transfer problem. After determining the boundary conditions of the model, this inverse heat transfer problem is divided into three problems which are the direct problem, the sensitivity problem and the adjoint problem, and these were solved using the conjugate gradient method. The feasibility of this model was proved by the inversion results of different shape functions and then it was discussed that the initial guess shape and number of measurement points effect on the inversion results. The results show that the accuracy of the inverse solution is independent of the the initial guess shape, but the number of measurement points has some impact on these results, whereby the more points are measured, the better the curve features are captured. An accurate inverse solution can be obtained with fewer measurement points and an average relative error within 3%, even though the arrangement of more points can achieve a slightly better solution.