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## Thermal Mechanical Stress Analysis of Ladle Lining with Integral Brick Joint

### Abstract

Based on the theory of heat transfer, the influence of expansion joints on the temperature and stress distribution of ladle lining is discussed. In view of the current expansion joint, the mathematical model of heat transfer and the three dimensional finite element model of ladle lining brick are established. By analyzing the temperature and stress distribution of ladle lining brick when the expansion joints are in different sizes, the thermal mechanical stress caused by the severe temperature difference can be reduced by the suitable expansion joint of the lining brick during the ladle baking and working process. The analysis results showed that the thermal mechanical stress which is caused by thermal expansion can be released through the 2 mm expansion joint, which is set in the building process. So we can effectively reduce the thermal mechanical stress of the ladle lining, and there is no risk of steel leakage, thus the service life of ladle can be effectively prolonged.
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## Mathematical Modeling of Heat and Mass Transfer Process Under Heat Treatment of Grain Materials in Dense Layer

### Abstract

Postharvest processing of grain is an important step in the overall grain production process. It makes possible not only quantitative and qualitative preservation of the harvest, but also ensures maximum profit from its sale at the most favorable market conditions. Convective heat treatment (drying, cooling) guarantees commercial harvest conservation, prevents its loss, and in some cases improves the quality of the finished product. The necessity of intensification and automation of technological processes of postharvest grain processing requires the development of methods of mathematical modeling of energy-intensive processes of convective heat treatment. The determination and substantiation of optimum modes and parameters of equipment operation to ensure the preservation of grain quality is possible only when applying mathematical modeling techniques. In this work, a mathematical model of particulate material drying is presented through a system of differential equations in partial derivatives of which the variable in time and space relationship between heat and mass transfer processes in the material and a drying agent is reflected. The aim of the research was to determine the dynamics of the interrelated fields of unsteady temperature and moisture content of the material and the drying agent on the basis of mathematical models of heat and mass transfer in the layer of particulate material in convective heat approach or heat retraction. The implementation of the mathematical model proposed in the standard mathematical set allows analyzing efficiency of machines and equipment for the convective heat treatment of particulate agricultural materials in a dense layer, according the determinant technological parameters and operating modes.
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## Modeling of Melting and Resolidification in Domain of Metal Film Subjected to a Laser Pulse

### Abstract

Thermal processes in domain of thin metal film subjected to a strong laser pulse are discussed. The heating of domain considered causes the melting and next (after the end of beam impact) the resolidification of metal superficial layer. The laser action (a time dependent belltype function) is taken into account by the introduction of internal heat source in the energy equation describing the heat transfer in domain of metal film. Taking into account the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered, the mathematical model of the process is based on the dual phase lag equation supplemented by the suitable boundary-initial conditions. To model the phase transitions the artificial mushy zone is introduced. At the stage of numerical modeling the Control Volume Method is used. The examples of computations are also presented.
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## Dual Phase Lag Model of Melting Process in Domain of Metal Film Subjected to an External Heat Flux

### Abstract

Heating process in the domain of thin metal film subjected to a strong laser pulse are discussed. The mathematical model of the process considered is based on the dual-phase-lag equation (DPLE) which results from the generalized form of the Fourier law. This approach is, first of all, used in the case of micro-scale heat transfer problems (the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered). The external heating (a laser action) is substituted by the introduction of internal heat source to the DPLE. To model the melting process in domain of pure metal (chromium) the approach basing on the artificial mushy zone introduction is used and the main goal of investigation is the verification of influence of the artificial mushy zone ‘width’ on the results of melting modeling. At the stage of numerical modeling the author’s version of the Control Volume Method is used. In the final part of the paper the examples of computations and conclusions are presented.
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