The aim of the present work is to verify a numerical implementation of a binary fluid, heat conduction dominated solidification model with a novel semi-analytical solution to the heat diffusion equation. The semi-analytical solution put forward by Chakaraborty and Dutta (2002) is extended by taking into account variable in the mushy region solid/liquid mixture heat conduction coefficient. Subsequently, the range in which the extended semi-analytical solution can be used to verify numerical solutions is investigated and determined. It has been found that linearization introduced to analytically integrate the heat diffusion equation impairs its ability to predict solidus and liquidus line positions whenever the magnitude of latent heat of fusion exceeds a certain value.
The purpose of this paper is to depict the effect of diffusion and internal heat source on a two-temperature magneto-thermoelastic medium. The effect of magnetic field on two-temperature thermoelastic medium within the three-phase-lag model and Green-Naghdi theory without energy dissipation i discussed. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. Numerical results for the field quantities given in the physical domain are illustrated on the graphs. Comparisons are made with results of the two models with and without diffusion as well as the internal heat source and in the absence and presence of a magnetic field.
In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.