Thermal Conduction near a Metal Surface Exposed to Blackbody Radiation

Abstract

A method of calculating thermal conductivity near the surface of a metal is proposed. Kinetic theory is used to show that the thermal conductivity decreases near the surface and becomes zero at the surface if there is no heat flow across the surface. Kinetic theory is also applied to the problem of heat conduction in the surface region of a metal exposed to blackbody radiation. The resultant temperature distribution is exponential. From a practical standpoint, a useful consequence of the theory is that the absorption depth for blackbody radiation should equal the mean free path of electrons in metals. In the layer of a metal which absorbs incident radiation, the electrons possess increments of energy from both absorbed radiation and thermal conduction. The fraction of the electron's energy lost per collision is taken from the kinetic theory of gases as a first approximation. Thus, thermal conduction is reduced by factors of 10-5 to 10-6 in the surface region of the metal. The factor is not needed for the conduction process in the bulk of the material because the energies entering and leaving an elemental layer are independent of each other, permitting random walk to equilibrate the energy. Application of the theory to the heating rate of a tantalum sample exposed to 1500 W/cm2 leads to results consistent with the experimental data available.