Ballistic-diffusive heat-conduction equations.
We present new heat-conduction equations, named ballistic-diffusive equations, which are derived from the Boltzmann equation. We show that the new equations are a better approximation than the Fourier law and the Cattaneo equation for heat conduction at the scales when the device characteristic length, such as film thickness, is comparable to the heat-carrier mean free path and/or the characteristic time, such as laser-pulse width, is comparable to the heat-carrier relaxation time.
Chen
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Nanoscale Heat Transfer and Thermoelectics Laboratory, Mechanical and Aerospace Engineering Department, University of California at Los Angeles, Los Angeles, California 90095-1597, USA.