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

convective heat transfer Convection (or convective heat transfer) is the 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 combined processes of ...

) or another solid occurs when the

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

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 In physics and engineering, 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 (physics), time. Its SI units are watts per sq ...

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 heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...

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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...

, 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