Study of temperature fields in a rectangular plate with a temperature-dependent internal source with the aid of fast expansions
A.D. Chernyshov1, V.V. Goryainov2, and A.N. Marchenko1
1Voronezh State University of Engineering Technologies, Voronezh, Russia
2Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia
E-mail: chernyshovad@mail.ru; gorvit77@mail.ru
Keywords: analytic solution, temperature, variable internal source, rectangular shape, fast expansions
Pages: 237–245
Abstract
The approximate analytic solution of the problem of temperature field in a rectangular plate with an internal temperature-dependent source is obtained by the method of fast expansions. The critical value of a parameter characterizing heat release, which fun-damentally affects the analytic solution form, is found. The maximum solution error is shown to amount to 0.02 at the consideration of the first three terms of the Fourier series in fast expansion. Temperature fields are presented, and an analysis of the influence of the plate sizes and the heat release magnitude on their formation is given. Recommendations on the plate shape choice are given.
DOI: 10.1134/S0869864316020104
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