Calculation of nonstationary temperature fields in multilayer glazing of vehicles
Abstract
A method for calculation of nonstationary thermal fields in a multilayer glazing of vehicles under the effect of impulse film heat sources is offered. The multilayer glazing is considered as a rectangular multilayer plate made up of isotropic layers with constant thickness. The temperature on the side surface of the plate is zero. Convective heat transfer occurs on outer surfaces of the plate; on layers' interfaces film heat sources are arranged. The heat conduction equation for an arbitrary plate layer after the Laplace transformation on time is reduced to the functional equation. In the same way initial and boundary conditions are transformed. A solution of the functional equation we search in the form of three space functions product. That enables us to get the system of ordinary differential equations. We represent the system solution as double trigonometrical series taking into account boundary conditions on the plate side surface. Series expansion factors are determined from a system of linear algebraic equations which is formed of boundary conditions on outer surfaces and layers' interfaces. The system right member contains factors of expansion of interlayer film heat source functions. After determination of factors a transform of the required function is found by the second expansion theorem, and the problem solution has the form of double trigonometrical series. As an example, we solved the nonstationary heat conduction problem for a five-layer glazing element of the airplane under heating by the film heat source. The heat source has the rectangular form. It is arranged between the first and the second layers of the glazing element. The comparative analysis of the temperature distribution over the element thickness with the results of other method is carried out. The method offered can be used for designing a safe multilayer glazing under operational and emergency thermal and force loading in different vehicles.
