Perfect thermal contact

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Perfect thermal contact of the surface of a solid with the environment (convective heat transfer) or another solid occurs when the temperatures of the mating surfaces are equal.

Perfect thermal contact conditions[edit]

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

 T\big|_{}=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.


  • H. S. Carslow, 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.