Perfect thermal contact

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

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.

References

This article is issued from Wikipedia - version of the Friday, March 22, 2013. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.