This investigation involves the axisymmetric transient temperature calculations using the finite-element analysis during heating of an ingot. Two types of nonlinearities are considered: the first one is the nonlinear variations of the material properties and the second one is the nonlinear radiative boundary conditions. Based on the temperature distribution the thermal stresses are calculated. These results are compared with the results obtained by the two-dimensional finite-element and finite-difference methods. The effect of the variation of the slenderness ratio of the ingot on the temperature and stress distribution are also studied. The optimal heating schedule of the ingot is obtained considering the maximum allowable stresses based on various failure theories and the maximum temperature as constraints.

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