Determination of the Radiation Exchange Factor in the Bundle of Steel Round Bars

A method to obtain a radiation exchange factor F R in the bundle of steel round bars is presented. This parameter is required for determination of the radiative thermal conductivity k rd , which is one of the basic thermal properties of the bar bundles. In the presented approach, the analyzed parameter is calculated indirectly. The initial point for calculations is the geometric model of the medium defined as a unit cell. Then, for the elements present in this cell, the thermal resistance of both conduction and radiation is determined. The radiation resistance is calculated from the radiosity balance of the surfaces enclosing the analyzed system. On this basis, the radiation thermal conductivity k rd is calculated. Next, taking into account the bar diameter, the value of parameter F R is also determined. The analysis is performed at the process temperature range of 200 to 800 °C for three bar diameters: 10, 20 and 30 mm, and for the three porosities of the bundle. Different emissivity of bars in the range of 0.5 to 0.9 was also taken into account. Finally, a relationship that allows calculating the F R factor correlated with the emissivity of the bars and the bundle porosity was established. The k rd obtained from the methodology presented and compared with the values calculated directly do not exceed 9%; however, after averaging over the entire temperature range of the process, the difference does not exceed 0.2%.