Key Words: Calculation of energy; wood containing ice; melting frozen water; thermal treatment; Table Curve 2D.
Abstract. A mathematical description of the thermal energy consumption Qice required to melt the ice formed in the wood by the natural freezing of both free and bound water in it, using the software package Table Curve 2D v.5.01 has been presented. This package allows for the selection of equations, which provide the best similarity between the calculated with them values of Qice during thermal treatment of wood containing ice and the respective numerical data obtained experimentally or using an adequate temperature-energy model of Qice. For the determination of Qice, the classical approach from thermodynamics was used to calculate the energy required to heat a solid body from any initial temperature to a certain final temperature. In our case, the energy Qice is represented as a sum of the energy Qice-bw required to melt the initial temperature-dependent frozen portion of the bound water in the wood, and the energy Qice-fw required to melt the ice formed by freezing all the free water in the wood. The energies Qice-bw and Qice-fw are represented as a product of the ice density with the specific heat capacities of the frozen bound and free water in the wood and the temperature ranges in which the melting of the two types of frozen water takes place. Mathematical descriptions of the specific heat capacities of frozen bound and free water in wood are also presented, taking into account the latent heat of the phase transition of water. The calculations of the energies Qice-bw, Qice-fw, and their sum Qice were made for the case of thermal treatment of frozen beech wood with an initial temperature of −1 °C, −10 °C, −20 °C, −30 °C, −40 °C and moisture content of 0.4 kg·kg-1, 0.6 kg·kg-1, and 0.8 kg·kg-1. The obtained results were processed using the Table Curve 2D software package. Three logarithmic equations of the same type were selected, which mathematically describe the dependence of Qice on the initial temperature of the frozen wood for each of the investigated values of its moisture content. It was found that there is a very small error (within the limits of only 3.5%) between the equations calculated with Table Curve and the approximate values of the Qice. The equations obtained can be used for development and automatic implementation of scientifically based energy-efficient regimes and technologies for steaming or boiling of frozen wood materials with different properties and purposes.
