Temperature Dependence of Thermal Conductivity of Thermal Insulation Bricks--Approach by Improvement of Model and Numerical Analysis

摘要

Taking a cue from a request to investigate the temperature dependence of the thermal conductivity of alumina brick, the authors are continuing research on not only the qualitative tendencies of the thermal conductivity but also to obtain quantitative values that are as accurate as possible at the present time. Due to inadequate experimental apparatus and a change in situation that one of authors retired from the laboratory by age-limit rules, the investigation method was directed to simulation systems with model building rather than experimental measurements. However, the authors believe that their researches in this simulation area have achieved a certain level of success. The research superimposed many investigations to explain the various phenomena, not only qualitatively but also quantitatively, by assuming and improving a model. At first, because of time restrictions of the requesting company, research was initiated using an extremely simple two-dimensional two-grain model as shown in Fig. 3. This was based on the thought that curvature of thermal current and thermal resistance at the aperture portion must have great influence on the thermal conductivity of brick and these two phenomena could possibly provide some quantitative explanation of the thermal conductivity. However, this model was too simple to provide satisfactory results. Therefore the authors attempted to improve the model to a two-dimensional multi-grain system and further into a three-dimensional system (Fig. 8). However in the model shown in Fig. 8 the number of grains was low and results were more unsatisfactory than those by the previous model. Consequently the authors decided, by necessity, to apply the random model that we had used for a long time during research on dispersion system materials (This research considered a dispersion of high thermal conductivity particles in a base material with poor thermal conductivity, a relation that is the inverse of the present case). Thanks to application of this new model, much new knowledge was obtained, but at the same time some extra problems were discovered. Therefore we intend to continue the study on this theme. The following list gives in itemized order the knowledge obtained until now and the problems to be investigated in the future: 1) It was clarified that the temperature dependence of the effective thermal conductivity of alumina brick decreases with an increase in temperature. The thermal conductivity is greatly affected by the fact that, although the thermal conductivity of air in the internal portions of the brick increases with temperature, the conductivity of alumina material in the brick is strongly negative with temperature. 2) The simulation model was making progress on the basis of considering the insulation brick as a composite with air dispersed through the entire body, but the improvement in the model was not sufficient for quantitative calculations. In particular, an important problem is whether or not thermal resistance exists between alumina crystals. If it indeed exists, its quantitative evaluation will be serious problem and therefore it will also be attractive item for research. 3) In relation to the above point, if it is possible to insert a suitable evaluation term for the contact heat resistance into a random model, the possibility to realize an estimation of the thermal conductivity of other kinds of brick from a basic brick type without experimental measurements may be anticipated.