Abstract
When layerwise synthesis of new material occurs, only thin surface area, thin melt film or thin powder layer undergo essential changes. To describe the behaviour of thin layer where temperature and composition change, a model similar to shallow-water theory is suggested. The equations for thin layer behaviour are deduced for the Maxwell model of viscoelastic body in the approximation of incompressibility. The hydrodynamic part of the problem is coupled with thermal-kinetical one.
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