Part of the book: Convection and Conduction Heat Transfer
Two-dimensional mutually connected mathematical models have been created, solved, and verified for the transient non-linear heat conduction in logs during their freezing and subsequent defrosting. The models reflect the influence of the internal sources of latent heat of both the free and bound water on the logs’ freezing process and also the impact of the temperature on the fiber saturation point of wood species, with whose participation the current values of the thermo-physical characteristics in each separate volume point of the subjected to freezing and subsequent defrosting logs are computed. The chapter presents solutions of the models with explicit form of the finite-difference method and their validation towards own experimental studies. Results from experimental and simulative investigation of 2D non-stationary temperature distribution in the longitudinal section of beech and pine logs with a diameter of 0.24 m and length of 0.48 m during their many hours freezing in a freezer and subsequent defrosting at room temperature are presented, visualized, and analyzed.
Part of the book: Heat and Mass Transfer
This study suggests an approach for modeling of the total thermal energy needed for freezing the bound water in logs subjected to refrigeration. The approach maximally considers the physics of the freezing process of the bound water in wood. It considers the nonstationary change in the icing degree of logs formed by the crystallization of the bound water in them, as well as the influence of the fiber saturation point of each wood species on its current amount of nonfrozen bound water depending on temperatures below −1°C. Mathematical descriptions of the thermal energy of the phase transition of bound water in logs and also of the latent thermal energy of the bound water released in logs during their freezing have been executed. These descriptions were introduced in our own 2D nonlinear mathematical model of the freezing process of logs. The model was transformed in a form suitable for programming with the help of explicit schemes of the finite difference method. For the solution of the model and energy simulations with it, a software program was prepared, which was input into the calculation environment of Visual Fortran Professional.
Part of the book: Low-temperature Technologies
A two-dimensional mathematical model has been created, solved, and verified for the transient nonlinear heat conduction in logs during their thawing in an air environment. For the numerical solution of the model, an explicit form of the finite-difference method in the computing medium of Visual FORTRAN Professional has been used. The chapter presents solutions of the model and its validation towards own experimental studies. During the validation of the model, the inverse task of the heat transfer has been solved for the determination of the logs’ heat transfer coefficients in radial and longitudinal directions. This task has been solved also in regard to the logs’ surface temperature, which depends on the mentioned coefficients. The results from the experimental and simulative investigation of 2D nonstationary temperature distribution in the longitudinal section of poplar logs with a diameter of 0.24 m, length of 0.48 m, and an initial temperature of approximately –30°C during their many hours thawing in an air environment at room temperature are presented, visualized, and analyzed.
Part of the book: Modeling and Simulation in Engineering