Figure 1

Experimental visualization of heat propagation in 2D. (a) Schematic representation of the experimental setup. A 4 mm thick aluminum plate profiled following a fractal pattern is put above a liquid crystal film itself put above a thermally insulating Styrofoam layer. The large heat capacity and large thermal conductivity of the heat source assure the uniformity of the source temperature; (b)–(f) Motion of the isocolor or isothermal line as a function of time (at 5, 10, 20, 40, and 46 seconds, respectively). The different lengths of the white arrows in (e) illustrate the confinement effect discussed in the text. The white bar presents a length scale of 1 cm.Reuse & Permissions

Figure 2

Time evolution of the heat $Q(t)$ transferred from the source. (a) Evolution of the area $S_T(t)$ of the layer delimited by the visualized isotherm: experiment (circles) and numerical simulations (solid line) of the layer corresponding to the isotherm level $\theta =0.9$ (a.u.), best fit for the experimental curve, see text. Short-time asymptotic (4) and intermediate asymptotic (5) slopes are shown by dashed lines and dash-dotted lines. (b) Numerical computation of $Q(t)$ (solid blue line) and of the three areas $S_{0.1}(t)$, $S_{0.5}(t)$, $S_{0.9}(t)$ (symbols), all computed. The curves $S_T(t)$ are shifted along the horizontal axis by factors 5, 1 (no shift), and 0.11, respectively. As explained in the text, these shifts account for the coefficient $\beta (T)$ whose dependence on the chosen isotherm level is unknown for the prefractal boundary. The thermal response $Q_0(t)/Q_0(\infty )$ of the square initiator of the same area is shown by solid black line (see Supplementary Material [27] for details). Note that $Q(t)$ and $S_T(t)$ are divided by their maximum values to be comparable.Reuse & Permissions

Figure 3

Three temperature zones at $t=0.1\mathrm{s}$: $\theta (\mathbf{r},t)>0.9$ (yellow), $0.1<\theta (r,t)<0.9$ (white), and $\theta (\mathbf{r},t)<0.1$ (blue). The frontiers between successive zones are the isotherm at $\theta =0.9$ (a.u.) and $\theta =0.1$ (a.u.), which are compared to the Minkowski sausage of width $\sqrt{Kt}$ (shown by the thick solid line), at $t=0.1\mathrm{s}$.Reuse & Permissions