Asymptotic modelling of thin almost circular nonlinear interphases in the setting of heat transfer featuring significant sources/sinks

This article gives an overview of several problems describing the process of heat transfer in a composite with a thin layer. This layer shows a distinct nature in comparison with the media surrounding it (i.e. low conductive or highly conductive), and in addition is very thin, which may cause numerical instability in a model of such a composite. In order to tackle this issue we use asymptotic approach, so that in the model the thin layer is replaced by an interface of zero thickness and a set of transmission conditions that stand for the physical properties of the original layer. A number of numerical examples has been constructed to support and validate this method.