NON-STATIONARY THREE-DIMENSIONAL TEMPERATURE FIELD IN A MULTILAYER CYLINDER

Abstract

The problem of determining a non-stationary three-dimensional temperature field in a k-layer cylinder of length is solved. There is a symmetrically located cylindrical cavity in the center of this body. The absence of a 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 body 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. The periodicity condition is set for the angle φ. 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 coordinate, angle and transverse coordinate 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.