MATHEMATICAL MODELING OF THERMAL PROCESSES AT SURFACE TREATMENT OF METAL PRODUCTS WITH HIGHLY CONCENTRATED ENERGY FLOWS

The modeling tasks of thermal effect of power impulse action on a surface of the plate of VК10 (КS) alloy were considered and solved. As modeling tasks for homogeneous equations of parabolic and hyperbolic heat conductions, a wave equation in a cylindrical solid of final sizes with boundary conditions of III kind were chosen. The action of power impulse from an exterior radiant was modeled by sudden appearance of initial high temperature, which spreads on a plate body under the laws expressed by various heat conduction equations, on one of the surface ends of a cylinder. Approaches of temperature fields were received in the form of a series segment of functions from eigenvalues of tasks, gradients of fields were defined. Simultaneous presence in the equation of heat conductivity of private derivatives on time of the first and second usages (the hyperbolic equation), statement of the task for it with boundary conditions of III kind and the entry condition at a cylinder end surface provides two ways (modes) of the problem’s decision, both of diffusion type. For the value of the relaxation time of the heat flux of 10–11  s, the complete cooling of the cylindrical sample (tungsten carbide) in the first mode is minutes, in the second  –  10–10  s. It can be concluded that the modes for solving the problem for the hyperbolic heat equation do not correspond to the actual pattern of heat propagation. However, the linear combination of these modes as a solution of the problem preserves the possibility of obtaining a diffusion dynamics adequate to the actual process. Gradients of the temperature field in the solutions of the problems for the parabolic heat conduction equation and the wave equation are in the same order of values. The temperature field of the moving thermal wave for several of its first reflections in experimental samples should be taken into account when evaluating phase transformations and temperature stresses. The results of the theoretical analysis are compared with changes in the microstructure of the near-surface layer of a plate of alloy VK10 (KS), subjected to electric explosive loading by plasma of a titanium foil.

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