Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse.

A thin metal film subjected to an ultrashort laser pulse is considered. With a sufficiently high laser intensity the process of the film heating may cause metal melting and even ablation. In this work, the numerical model of the melting and resolidification processes is presented. The mathematical model is based on the dual phase lag equation in which two positive constants appear, this means the relaxation and thermalization times. The considered equation contains a second-order time derivative and higher order mixed derivative in both time and space and should be supplemented by the appropriate boundary and initial conditions. The model of the melting and resolidification is presented in two versions. The first can be called 'the introduction of the artificial mushy zone sub-domain', while the second 'the two forms of the basic energy equation'. At the stage of numerical computations, the implicit scheme of the finite difference method is used. The numerical algorithm is tested for the two proposed models which are applied to the computations concerning the thermal processes occurring in the cylindrical micro-domain (chromium, gold) subjected to an ultrashort laser pulse.

Simulations of thermal processes in tooth proceeding during cold pulp vitality testing.

PURPOSE: This paper deals with the mathematical modeling of the thermal processes occurring in the tooth, during a very brief contact (a few seconds) with a very cold liquid on a part of the tooth crown. In this way one can simulate a heat transfer in tooth proceeding during a dental diagnostic test - pulp vitality testing. The impact of rapid ambient thermal changes acting on the tooth can cause toothache. METHODS: The mathematical model: a system of partial differential equations with initial-boundary conditions (the axiallysymmetrical problem) and their numerical solutions using the control volume method is discussed. RESULTS: Simulation results of the kinetics of the temperature changes inside the tooth are presented. The example of the control volume mesh (using the Voronoi polygons) well describing the shape of a molar tooth is given. CONCLUSIONS: The simulation results (the temperature distribution in the tooth at any moment of the simulation time and the kinetics of temperature variation at the points of the tooth domain considered) can help dentists in the selection of an appropriate method of treatment.

The BEM-FDM model of thermal processes proceeding in the domain of the human finger.

PURPOSE: The problem of the numerical modeling of thermal processes proceeding in the non-homogeneous domain of the human finger is discussed. The domain considered constitutes the assembling of soft and bone tissues and the system of supplying blood vessels (arteries and veins). The mathematical description of the process analyzed corresponds to the so-called vascular models. METHODS: At the stage of numerical modeling the algorithm being the composition of the boundary element method (BEM) and the finite difference method (FDM) is applied. RESULTS: The algorithm presented allows one to determine the steady state temperature field in the finger domain in natural convection conditions. To verify the effectiveness and exactness of the method of the problem solution, the thermal imaging measurements of the finger surface temperature have been done. CONCLUSIONS: The compatibility of numerical and experimental results (the natural convection conditions) has proved to be quite satisfactory. It is possible to use the algorithm proposed for the modeling of thermal processes proceeding in the conditions of low or high ambient temperatures and the big values of heat transfer coefficients. The impact of protective clothing on the temperature field in the domain of the finger can also be analyzed.