On the virtual layer for modeling interfacial thermal resistance

An analytical solution is developed for transient heat conduction in a two-layer composite medium with interfacial thermal resistance. The governing diffusion equations are coupled through interface conditions that ensure heat flux continuity while allowing a temperature discontinuity proportional to interfacial resistance. Closed-form solutions are derived for both transient and steady-state temperature distributions. To enable comparison with numerical approaches, the formulation is extended to a three-layer composite system with distinct material properties and thicknesses, where both temperature and flux remain continuous across interfaces. The results are compared with numerical studies in which the resistive interface is represented as a thin virtual layer with negligible thermal storage. In addition to the closed-form solutions, this work provides a rigorous derivation of a simple relationship between the interfacial resistance and the thickness of the virtual layer, establishing the equivalence between the physical interface model and its numerical representation. The results serve as a reliable benchmark for validating numerical simulations.