Abstract: With respect to consecutive drainage， aggressive internal conditions and varying lining profile during production process in blast furnace hearth， a simple method is proposed for representing the lining profile by a set of lining profile vectors. It can convert the solving of a complicated inverse heat transfer problem with unknown geometries at a specified-temperature boundary into searching the optimal set of profile vectors in an optimization problem. Integrating numerical heat transfer theory and finite element method with genetic algorithm， an inverse problem oriented mathematical model has been developed， which can predict the lining profile of blast furnace hearth accurately. A testing example of elephant-foot erosion pattern on the basis of an intact ceramic cup synthetic hearth， is employed to examine the effectiveness， stability and accuracy of the model. The results indicate that the model would have a broad prospect of practical applications.

Key words: blast furnace hearth, lining erosion, profile vectors, heat transfer, genetic algorithm, inverse problem