In the present thesis the energy equation is solved for the temperature distribution in a two dimensional steel strip, which moves with Constant velocity through a furnace and is submited to several different radiation and convection fluxes. Steady state conditions are supposed to exist, if the reference frame is attached to the furnace walls. Thus, one more term arises in the energy equation to take into account the strip movement. The non-linearity of the problem is restricted to the radiation boundary conditions. The discretized algebraic equations are set up, utilizing a finite difference, scheme with the control volume approach. The complete set of equations has shown that there are seven non-dimensional parameters to be specified. Due to the elliptic nature of the equation, it was stabilished that at some distance before and after the furnace, the axial heat conduction in the strip would vanish. A first attempt was done in order to find these distances. The results have shown that the boundary condition after the furnace, the axial heat conduction in the strip would vanish. A first attempt was done in order to find these distances. The results have shown that the boundary condition after the furnace could be substituted, taking a section of the strip closer to the furnace outlet and simply stating the heat flux balance in terms of conduction, convection and radiant emission, considering that this is an end of the strip. Examining the resultant temperature profiles and the heat exchanged by the strip, the influence of each non-dimensional parameter was investigated. Three of them are believed to be the more important: the péciét number related to the furnace rate of production, the incident radiation parameter related to the rate of fuel consumption and the geometrical aspect ratio of the strip. A thermal abalysis of the furnace was then carried out, in order to achieve prescribed data on averade temperature of the strip at the furnace outlet, degree od temperature homogenelty in the strip and heat transfer efficiency. To make a more realistic simulation of the furnace, it was also subdivided into three cones of different incident radiation fluxes and then typical operational situations could be reproduced, as they usually occur in slab reheating furnaces. These simulations were compared with data available in the literature, showing a reasonable qualitative accordance with them.