Extending the thermal slip boundary condition at the solid-fluid interface

Heat transfer across an interface of dissimilar materials results in a temperature jump. The extent of this jump for a given temperature gradient is determined by the Kapitza resistance (or the interfacial thermal resistance). This thermal boundary condition is analogous to the velocity slip boundary condition and so are the Kapitza and slip lengths. It has been shown that in the case of the velocity (Navier) slip boundary condition, there are three implicit assumptions made, namely 1) the slip length is a constant for a given wall-fluid pair, 2) that the flow is steady, and 3) that velocity only varies in the direction normal to the interface. Taking into consideration the analogous nature of the thermal and velocity boundary conditions, the objective of this paper to explore whether similar implicit assumptions are also made in the thermal slip boundary condition. We intend to verify if there is an implicit assumption that the 1) Kapitza length is constant for a given wall-fluid pair, 2) temperature gradient only exists normal to the interface, and 3) temperature field is time independent. This If so, we intend to extend the thermal slip boundary condition by relaxing these assumptions. Finally, using molecular dynamics simulations we aim to validate these assumptions and this extended thermal slip boundary condition.