Levchenko V.A., Kascheev M.V., Dorokhovich S.L., Zaytsev A.A.
The Limited Liability Company "Simulation Systems Ltd.", Obninsk, Russia
The problem of determining a two-dimensional non-stationary temperature field in a k-layer cylinder and plate of length l is solved. There is a symmetrically located gap (plate) or cylindrical cavity (cylinder) in the center of these bodies. The absence of a gap or cavity is a special case of the problem. In each layer, there are heat sources, depending on the coordinates and time. The initial temperature of the layers is a function of the coordinates. In the center of the bodies the symmetry condition is fulfilled. At the boundary of contact of the layers — ideal thermal contact: continuity of temperatures and heat flows. On the inner and outer side surfaces and ends, heat exchange occurs according to Newton's law with environments whose temperatures change over time according to an arbitrary law. With the help of the geometric parameter Г in the mathematical formulation of the problem, one differential equation for both multilayer bodies is written. The problem in this statement is solved for the first time. For the solution of the problem the following approach is used: by means of the method of finite
integral transformations differential operations on longitudinal and transverse coordinates are sequentially excluded, and the determination of time dependence of temperature is reduced to the solution of the ordinary differential equation of the first order.
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