**6. Conclusions**

**Figure 7** presents the change of the thermal energy *<sup>Q</sup>*fr‐bw‐total during the 30 h refrigeration of the studied logs, which is calculated according to Eq. (32). The change of this energy is similar to that of the energy *<sup>Q</sup>*fr‐bw(see **Figure 6**, left). At the end of the 30 h freezing, the energy *<sup>Q</sup>*fr‐bw‐total reaches the following values:

This paper presents a methodology for mathematical modeling and research of two mutually connected problems: 2D nonstationary temperature distribution in logs subjected to refrigeration and change in two important energy characteristics of the bound water in logs during its freezing—thermal energy of the phase transition of the bound water in 1 m<sup>3</sup> wood from liquid into solid state, *<sup>Q</sup>*fr‐bw, and latent thermal energy of the bound water, *<sup>Q</sup>*Lat‐bw, which is released in 1 m<sup>3</sup> of the logs

Mathematical descriptions and an approach for computing of the energies *<sup>Q</sup>*fr‐bw and *<sup>Q</sup>*Lat‐bw during the freezing of the bound water at temperatures below �1°C have been carried out. These descriptions are introduced in our own 2D nonlinear mathematical model of the 2D heat distribution in logs during their refrigeration at convective boundary conditions. The model was transformed in a form suitable for programming with the help of explicit schemes of the finite difference method,

A software program for numerical solution of the mathematical model and computation of 2D nonstationary change of the temperature in logs subjected to refrigeration and of the thermal energies *<sup>Q</sup>*fr‐bw and *<sup>Q</sup>*Lat‐bw has been prepared in Fortran, which has been input in the calculation environment of Visual Fortran

With the help of the program, computations for the determination of the energies *<sup>Q</sup>*fr‐bw and *<sup>Q</sup>*Lat‐bw and their difference, *<sup>Q</sup>*fr‐bw‐total <sup>¼</sup> *<sup>Q</sup>*fr‐bw � *<sup>Q</sup>*Lat‐bw, have been

which excludes the necessity of any simplifications of the model.

5.992 kWh�m�<sup>3</sup> for P1 and 6.657 kWh�m�<sup>3</sup> for S1.

*Change in <sup>Q</sup>*fr‐bw‐total *during the refrigeration of the studied logs.*

**5. Discussions**

**Figure 7.**

*Low-temperature Technologies*

during water crystallization.

Professional developed by Microsoft.

**126**

Good adequacy and precision of the model toward the results from wide own experimental studies allow the carrying out of various calculations with the model, which are connected to the nonstationary temperature distribution and energy characteristics of logs from different wood species during their refrigeration. The mathematical model, after its connection with other our model of the logs' defrosting process [9, 10], could be input into the software of programmable controllers for optimized model-based automatic control [8, 20, 21, 35] of thermal treatment of frozen logs in the production of veneer.

The approach for the computation of the thermal energies of the bound water in logs during their refrigeration could be used for the creation of analogous models for the computation of the temperature distribution and the energy required for the refrigeration of different capillary porous materials (fruits, vegetables, meet, meet products, etc.).

#### **Nomenclature**

