Basic boundary-value problems of calculating harmonic physical fields for toroidal forms (including the cases of complex sectors and nonlinear boundary-value conditions) are considered on the basis of exact analytical representation of the solution in the form of a series in toroidal harmonics. The results obtained can be used in calculating harmonic fields in problems of heat and mass transfer and of electromagnetism, coefficients of the medium of specific technical objects of toroidal form, as well as a test problem when employing other methods.
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References
S. V. Kotenev and A. N. Evseev, Calculation and Optimization of Toroidal Transformers and Throttling Valves [in Russian], Goryachaya Liniya–Telekom, Moscow (2013).
G. Korn and T. Korn, Handbook of Mathematics [in Russian], Nauka, Moscow (1973).
A. N. Tikhonov and A. A. Samarskii, Formulas, Tables, and Graphs. IV. Different Orthogonal Coordinate Systems, in: Equations of Mathematical Physics [in Russian], Izd. MGU, Nauka, Moscow (2004), pp. 732–733.
Eric W. Weisstein, Toroidal Coordinates, From MathWorld — A Wolfram Web Resource.
B. P. Kondrat′ev, A. S. Dubrovskii, and N. G. Trubitsyna, Potential in the "gap" of a torus: Expansion in spherical functions, Zh. Tekh. Fiz., 82, Issue 12, 7–10 (2012).
M. V. Norkin, Curvilinear coordinates in mixed problems of hydrodynamic impacts, Rostov-on-Don (2015); http://openedu.rsu.ru/files/MET-1%28Norkin%29.pdf.
V. S. Kirilyuk, Spatial Problems of the Elasticity Theory for Toroidal and Ellipsoidal Regions, Author′s Abstract of Candidate′s Dissertation (in Physics and Mathematics), Kiev (1984).
A. A. Kudryash and G. E. Shunin, Finite-element analysis of distribution of the magnetic field near a superconducting torus, Vestn. Voronezhsk. Gos. Tekh. Univ., Fizika, 11, No. 6 (2015).
S. G. Cherkasov and I. V. Laptev, Approximate analytical solution of two-dimensional problem of a heat conducting, emmiting fin, Teplofiz. Vys. Temp., 55, No. 1, 81–84 (2017).
V. A. Kudinov and I. V. Kudinov, Obtaining and analysis of exact analytical solution of the hyperbolic heat conduction equation for a plane wall, Teplofiz. Vys. Temp., 50, No. 1, 18–125 (2012).
A. F. Aleksandrov, I. B. Timofeev, V. A. Chernikov, and U. Yusupaliev, Plasma toroidal vortex in air, Teplofiz. Vys. Temp., 26, No. 4, 639–643 (1988).
A. Yu. Repin and E. L. Stupitskii, Dynamics and interaction with a barrier of a toroidal plasma clot. Dynamics of a toroidal plasma clot in a vacuum, Teplofiz. Vys. Temp., 42, No. 1, 31–37 (2004).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 92, No. 4, pp. 889–900, July–August, 2019.
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Nekrasov, S.A. Simulation of Harmonic Temperature and Magnetic Fields Based on the Method of Separation of Variables in Regions of Complex Toroidal Forms. J Eng Phys Thermophy 92, 861–871 (2019). https://doi.org/10.1007/s10891-019-01997-5
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DOI: https://doi.org/10.1007/s10891-019-01997-5