Кey Words: 2D model; atmospheric air temperature; beech logs; thermal treatment; model based control.
Abstract. This paper describes an approach for mathematical modeling and research of the 2D non-stationary temperature distribution and average mass temperature of logs stored in an open warehouse and influenced by the periodically changing atmospheric temperature near them. Mathematical descriptions of the thermo-physical properties (specific heat capacity, density, thermal conductivity and convective heat transfer coefficient in radial and longitudinal anatomical directions) of the non-frozen wood and also of the periodically changing during many days and nights temperature of the atmospheric air as a processing medium have been presented. They are introduced in the convective boundary conditions of our own 2D non-linear mathematical model of the logs’ heating and cooling processes. For the numerical solving of the model a software program has been prepared in the calculation environment of Visual FORTRAN Professional developed by Microsoft. Results from simulative investigation of the 2D non-stationary temperature distribution and average mass temperature of non-frozen beech logs with semi-industrial dimensions (diameter of 0.24 m and length of 0.48 m), moisture content of 0.6 kg·kg-1, and initial temperature of 20°C during their five days and nights continuous alternating heating and cooling at sinusoidal change of the air temperature with initial values of 20°C and different amplitudes are presented and analyzed. The presented approach for the computation of the 2D temperature field in logs and their average mass temperature at periodically changing ambient air temperature can help for the accurate determination of the initial temperature of the logs before their thermal treatment, depending on the duration of the logs’ storing in an open warehouse. This approach is suitable for application in the software of systems for optimized model based automatic control of the thermal treatment processes of logs and other wood materials. The obtained results can be used for development of energy saving technological regimes with an optimal duration depending on the precise determined initial temperature of the materials of each charge subjected to thermal treatment.