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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 [[temperature]]s of the mating surfaces are equal.
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== Perfect thermal contact conditions ==
 
Perfect thermal contact supposes that on the boundary surface <math> A </math> there holds an equality of the [[temperature]]s
 
:<math> T\big|_{}=T_e\big|_A \, </math>
 
and an equality of [[heat flux]]es
 
:<math> -k\frac{\partial T}{\partial n}\bigg|_A =-k_e \frac{\partial T_e}{\partial n}\bigg|_A \, </math>
 
where <math>T,~T_e</math> are temperatures of the solid and environment (or mating solid), respectively; <math>k,~k_e</math> are [[thermal conductivity]] coefficients of the solid and mating [[boundary layer|laminar layer]] (or solid), respectively; <math>n</math> is [[surface normal|normal]] to the surface <math> A </math>.
 
If there is a heat source on the boundary surface <math> A </math>, e.g. caused by [[sliding friction]], the latter equality transforms in the following manner
 
:<math> -k\frac{\partial T}{\partial n}\bigg|_A + k_e \frac{\partial T_e}{\partial n}\bigg|_A = q \, </math>
 
where <math>q</math> is heat-generation rate per unit area.
 
== References ==
 
* 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.
 
[[Category:Heat transfer]]
[[Category:Boundary conditions]]

Latest revision as of 05:05, 21 December 2014

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