A semi-analytical finite element method is presented which enables the calculation of temperature distribution over the cross-section of the rolling stock as it passes through the individual stands and cooling zones of a wire rod mill. Conformal mapping techniques have been used to subdivide the numerous cross-sectional areas that occur during rolling into suitable macro-elements. The system of ordinary differential equations resulting from the application of Galerkin's method to the diffusion-convection equation is solved by means of the eigenvalue method. The accuracy of the developed mathematical method was checked by means of comparison with numerical results obtained from the conventional finite element method. The method is an integral part of a complete process model predicting the temperature distribution of wire rod and bars during hot rolling to be dealt with later.
