Steady state heat transfer within a nanoscale spatial domain.
Poletkin, Kirill V.
Date of Issue2012
School of Mechanical and Aerospace Engineering
In this paper, we study the steady state heat transfer process within a spatial domain of the transporting medium whose length is of the same order as the distance, travelled by thermal waves before these waves are dissipated by thermal diffusion. In this study, the thermal conductivity is defined as a function of a spatial variable. This is achieved by analyzing an effective thermal diffusivity that is used to match the transient temperature behavior in the case of heat wave propagation by the result obtained from the Fourier theory. Then, combining the defined sizedependent thermal conductivity with Fourier’s law allows us to study the behavior of the heat flux at nanoscale and predict that a decrease of the size of the transporting medium leads to an increase of the heat transfer coefficient which reaches its finite maximal value, contrary to the infinite value predicted by the classical theory. The upper limit value of the heat transfer coefficient is proportional to the ratio of the bulk value of the thermal conductivity to the characteristic length of thermal waves in the transporting medium.
Journal of heat transfer
© 2012 ASME.