Perfect thermal contact

Perfect thermal contact conditions

Perfect thermal contact supposes that on the boundary surface A there holds an equality of the temperatures

: T\big|_{A}=T_e\big|_A ,

and an equality of heat fluxes

: -k\frac{\partial T}{\partial n}\bigg|_A =-k_e \frac{\partial T_e}{\partial n}\bigg|_A ,

where T,~T_e are temperatures of the solid and environment (or mating solid), respectively; k,~k_e are thermal conductivity coefficients of the solid and mating laminar layer (or solid), respectively; n is normal to the surface A .

If there is a heat source on the boundary surface A , e.g. caused by sliding friction, the latter equality transforms in the following manner

: -k\frac{\partial T}{\partial n}\bigg|_A + k_e \frac{\partial T_e}{\partial n}\bigg|_A = q ,

where q is heat-generation rate per unit area.

References

• H. S. Carslaw, J. C. Jaeger (1959). Conduction of heat in solids. Oxford: Clarendon Press.
• M. Shillor, M. Sofonea, J. J. Telega (2004). Models and analysis of quasistatic contact. Variational methods. Berlin: Springer.