Thermomechanical behavior of a plate composed of layers with different transparencies under the action of thermal radiation

Abstract

We study the thermal and mechanical processes running in a two-layer plate (in the case of perfect mechanical contact between the opaque and semitransparent layers) caused by the thermal radiation of a heated plane surface parallel to the composite plate and located on the side of the opaque layer. The contact boundary-value problem of heat conduction is reduced to an equivalent system of three nonlinear Volterra-type equations solved by the method of successive approximations. The dependences of the distributions of temperature and stresses in the plate on the ratio of thicknesses of the layers are investigated. It is shown that the influence of the thermal radiation of the opaque layer on the computed temperature in the plate is significant at temperatures higher than 530°K. As the thickness of the semitransparent layer decreases for a fixed thickness of the opaque layer, the temperature gradient across the thickness of the semitransparent layer sharply increases. The maximum tensile stresses in the plate may appear in the opaque or semitransparent layer depending on the ratio of the their thicknesses. For certain thicknesses of the semitransparent layer, they can attain the maximum permissible values.