On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity

The rate of decay of end effects in steady state heat conduction in a symmetric sandwich strip with anisotropic constituents and imperfect interfaces between the layers is studied. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. In the former case, the normal component of the heat flux is continuous at the interface, whereas the temperature field undergoes a discontinuity which is proportional to the normal component of the heat flux. In the latter case, the temperature field is continuous at the interface and the normal component of the heat flux exhibits a discontinuity proportional to a surface differential operator of the temperature, called the surface Laplacian. The characteristic rate of decay of end effects is given by the smallest real and positive root of a transcendental equation. This rate decreases as the discontinuity in the temperature or the heat flux across the interface increases, in either kind of the imperfect interface. Exact duality relations are shown to exist between the decay rate of end effects in strips with imperfect interfaces of low conductivity, and that in strips with imperfect interfaces of high conductivity. (C) 1999 American Institute of Physics. [S0021-8979(99)00515-0].