Modelling of transient heat transport in one-dimensional crystalline solids using the interval lattice Boltzmann method

摘要

In the paper the numerical modelling of heat transfer in one-dimensional crystalline solids is presented. The problem analyzed is described by the Boltzmann transport equation transformed in the phonon energy density equation supplemented by the adequate boundary - initial conditions. Such approach in which the parameters appearing in the problem analyzed are treated as the constant values is widely used, but in the paper the interval values of relaxation time and boundary conditions are taken into account. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. The examples of numerical computations are presented in the final part of the paper.