In the present work a full-scale mathematical model of the gaseous flow and the thermal exchange of gases with the scrap were proposed in the exhaust system of an Energy Optimizing Furnace (EOF). The analysis of the flow and heat transfer of the gases in the exhaust system is fundamental to predict the thermal use in the pre-heating of the scrap and the best scrap allocation profile in the system to predict the continuity of the current industrial process. The objective of this work is to improve the overall energy efficiency of the EOF process, thereby reducing the direct and indirect emission of gases that contribute to climate change. Industrial tests were carried out to obtain the real values of the variables such as gas and scrap temperature. The results of the variables were used in the mathematical model. The results of the mathematical modelling demonstrated that the heat transfer between the gases and the metal scrap depends mainly on the previous preparation in the scrap yard and on the control of the size and compaction of the scrap. In this work it was possible to predict the variables of gas flow and scrap pre-heating during the steel production process in the EOF using mathematical simulation and validating with the results collected in the industrial furnace.