Perfect thermal contact of the surface of a solid with the environment (

convective heat transfer Convection (or convective heat transfer) is the heat transfer, transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combin ...

) or another solid occurs when the

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

s 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

s :

T\big, _=T_e\big, _A \,

and an equality of

heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time. In SI its units are watts per square metre (W/m2). It has both a ...

es :

-k\frac\bigg, _A =-k_e \frac\bigg, _A \,

where

T,~T_e

are temperatures of the solid and environment (or mating solid), respectively;

k,~k_e

are

thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...

coefficients of the solid and mating laminar layer (or solid), respectively;

n

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to the surface

A

. If there is a heat source on the boundary surface

A

, e.g. caused by

sliding friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...

, the latter equality transforms in the following manner :

-k\frac\bigg, _A + k_e \frac{\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. Heat transfer Boundary conditions