Non-linear Mathematical Model of Determination of Temperature Regimes in a Two-layer Thermo-sensitive Plate with a Point Source of Heat

A nonlinear mathematical model for determining the thermal regime in an isotropic thermosensitive double-layer plate in the conditions of thermal insulation of external surfaces and the ideal thermal contact between the boundary surfaces of layers was investigated. At the contact surfaces of the plate layers, the point source of heat of constant intensity is concentrated. A transformation (linearizing function) applied to a nonlinear problem was introduced. Thus, the problem is transformed to partially linearized. The approximation of temperature on the contact surfaces of the plate layers allowed to obtain a linear boundary value problem, which is solved using the method of integral transformations. With the help of the solution obtained, the transformation introduced and the specific analytical dependences of the thermal conductivity coefficients of the plate layers on the temperature, the temperature field in the two-layer thermosensitive plate is determined.