title: Perfect thermal contact
text: # 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
  
      $T{\big |}_{A}=T_{e}{\big |}_{A}\,$
  
  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.
  
  