Thin layers in the context of transient phenomena appear in many applications in aerospace engineering and other fields. Examples include external thin coatings of bare panels which are exposed to the periodic solar radiation, and the thin glue layer that connects the complex parts in a plane or satellites. Generally, the layer has different mechanical and thermal properties from its surroundings and is usually smaller by an order of magnitude from its surroundings. There are two different and extreme approaches to handle the modelling and analysis of such a thin layer. The first is to ignore the layer altogether, and the second is to fully model it, using the Finite Element (FE) method for example. The former can suffer from severe inaccuracy, while the latter is time consuming and expensive. Special asymptotic models have been developed to deal with thin layer modelling. In these models, the thin layer is replaced by an interface with zero thickness, and special jump conditions are dictated on this interface in order to enforce the special effect of the layer. One such asymptotic interface model is the first-order model proposed by Bövik and Benveniste. Previous work done by Sussmann et al. showed how to incorporate this interface model in a FE formulation for steady state heat conduction problems including thin layers. In the present work we show how the interface model can be extended to yield an accurate and efficient computational scheme in the time dependent case. This is done here for linear scalar parabolic problems in two dimensions, prototyped by transient heat conduction. We demonstrate the performance and the cost-effectiveness of the scheme compared to a full model of the layer, via numerical examples.
