Phenomenological theories of interfacial interactions are founded on the core idea to model macroscopically the thin layer that forms between media in contact as a two-dimensional continuum (surface phase or interface) characterised by physical properties per unit area; the temporal evolution of the latter is governed by surface balance equations whose set acts as bridging channel in between the governing equations of the volume phases. These theories have targeted terrestrial applications since long time and their exploitation has inspired our research programme to build up, on the same core idea, a macroscopic theory of gas-surface interactions targeting the complex phenomenology of hypersonic reentry flows as alternative to standard methods in aerothermodynamics based on accommodation coefficients. The objective of this paper is the description of methods employed and results achieved in the exploratory study that kicked off our research programme, that is, the unsteady heat transfer between two solids in contact in planar and cylindrical configurations with and without interface. It is a simple numerical-demonstrator test case designed to facilitate quick numerical calculations but, at the same time, to bring forth already sufficiently meaningful aspects relevant to thermal protection due to the formation of the interface. The paper begins with a brief introduction on the subject matter and a review of relevant literature within an aerothermodynamics perspective. Then the case is considered in which the interface is absent. The importance of tension (force per unit area) continuity as boundary condition

The interface of two solids in contact introduces a thermal boundary resistance (TBR), which is challenging to measure from experiments. Besides, if the interface is reactive, it can form an intermediate recrystallized or amorphous region, and extra influencing phenomena are introduced. Reactive force field Molecular Dynamics (ReaxFF MD) is used to study these interfacial phenomena at the (non-)reactive interface. The non-reactive interfaces are compared using a phenomenological theory (PT), predicting the temperature discontinuity at the interface. By connecting ReaxFF MD and PT we confirm a continuous temperature profile for the homogeneous non-reactive interface and a temperature jump in case of the heterogeneous non-reactive interface. ReaxFF MD is further used to understand the effect of chemical activity of two solids in contact. The selected Si/SiO 2 materials showed that the TBR of the reacted interface is two times larger than the non-reactive, going from 1 . 65 × 10 - 9 to 3 . 38 × 10 - 9 m 2 K/W. This is linked to the formation of an intermediate amorphous layer induced by heating, which remains stable when the system is cooled again. This provides the possibility to design multi-layered structures with a desired TBR.