Özet:

Based on the solutions of inverse problems of differential geometry using S-functions, modeling methodology of shaping surfaces, described by weight functions that accurately describe the equations of complex boundaries was developed. An algorithm of surface description in the complex area in the form of an inverted flat-bottom plate outside the boundary belt of the area was built. It has allowed to construct an approximate mathematical model of the thermal process using the proposed conservative solution structure of the heat conduction problem in such a way that it is fully consistent with the physical model of the thermal process, including the case, when the value of the heat transfer coefficient tends to infinity. The constructed analytical solution structure of the heat conduction problem exactly satisfies the Newton's boundary condition at any given values of the heat transfer coefficient and ambient temperature for complex areas. Conservativeness of the solution structure lies in the fact that it takes into account the influence of the boundary effects only in the boundary belt of the area of the problem solution. Author Biographies Анатолий Павлович Слесаренко, A.N. Podgorny Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Str. Dm. Pozharsky, 2/10, Kharkiv, Ukraine, 61046 Doctor of Physics and Mathematics, Professor, Senior Researcher, Laureate of State Prize of Ukraine Department designs of authentication of thermal processes  

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