Study of temperature fields in a rectangular plate with a temperature-dependent internal source with the aid of fast expansions

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 fundamentally 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.