Mathematical modeling of tube cooling in a continuous bed

• The study of heat treatment during the cooling tubes in an industry.
• Experimental data were collected.
• The cooling process is modeled by the FVM.

The bar and profile manufacturing process in the steel industry utilizes controlled speed cooling in order to facilitate transformations in their shape as well as to bring about changes in the mechanical properties of steel. A computational algorithm is developed in this work that is able to reproduce thermal behavior of tubes as they pass through a cooling bed. This model takes into consideration axial, radial and angular temperature gradients of the tube, heat losses by radiation and forced convection in the first part of the bed and radiation and natural convection in the second part. Various radiation configuration factors and convective coefficients are utilized to represent the conditions of the problem. Results coming from resolution of the model by the employment of the Finite Volume Method were compared with data from literature and with results of experiments carried out in the thermal treatment hangar of the Vallourec & Mannesmann Tubes steel company located in Belo Horizonte, Brazil, which correlate well.The mathematical model developed is utilized to determine the variation of the temperature profile in relation to radial, angular, and axial coordinates.