MATHEMATIC SIMULATION OF GENERALIZED PROBLEM OF HEAT-EXCHANGE IN THE BODIES WITH HEMISPHERICAL SHAPE
DOI:
https://doi.org/10.34185/1562-9945-6-125-2019-05Keywords:
diamond-drilling bit, multiindex, integral transformation, finite element methodAbstract
The article presents the first mathematical model for calculating temperature fields of hemispherical bodies, which approximately simulates operation of the diamond-drilling bit and takes into account angular velocity of drilling operations and finite velocity of heat conduction, and which was created as a physicomathematical boundary problem for hyperbolic equation of heat conduction with the Dirichlet boundary conditions. Besides, a new integral transformation was formulated for the two-dimensional finite space, with the help of which and with the help of finite element method and Galerkin method a temperature field was found in the form of convergence series.
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