Heat Transport in Nanoscale Heterosystems: A Numerical and Analytical Study

Figure 4

(a) Surface temperature evolution $?(?=0,\tilde{t}=?t/d^2)$ including the first 200 terms of the analytical solution of the heat diffusion equation for ${\tilde{s}}_K=d/(R_{K}K)=0.01297$, corresponding to a 10?nm thin Bi-film on an Si-substrate with an initially exponential (solid line) and constant (dashed line) temperature distribution. (b) close up view of (a) for $0<\tilde{t}<1$. In (b), the first expansion terms ${?}_{{?}_1}$ corresponding to ${?}_1$ are separately displayed. (c) Double-logarithmic plot of Eigenvalues ${?}_1$ to ${?}_4$ versus ${\tilde{s}}_K$. The solid and dotted line represent $\sqrt{{\tilde{s}}_K}$ and $p/2,$ respectively.

(a)

(b)

(c)