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.
In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a Forklift-truck robot motion. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. On the other hand, the equations of motion of a Forklift-truck robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented.
The presented paper describes the results of an experiment determining the instantaneous values of velocity vector components of the air stream at selected spots of the boundary layer formed at the sidewalls of the mine heading in the ŁP type steel arch support. The experiment was carried out in a mine heading in an active hard coal mine. A 3-axis thermoanemometric probe was used to obtain three-dimensional distributions of the velocity and turbulent values, such as turbulence intensity and turbulent kinetic energy of the flowing ventilation air stream. The analysis of the measurement results was aided by a numerical solution of the discussed case of flow. The research results presented in this paper provide a basis for extensive studies of the description of velocity distribution and other turbulent quantities within the near-sidewall structures of a mine heading. The objective of these tasks is to improve the accuracy and reliability of numerical calculations relating to air flow in mine headings.
In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.