Near-Field Radiative Heat Transfer between Macroscopic Planar Surfaces

Near-field radiation allows heat to propagate across a small vacuum gap at rates several orders of magnitude above that of far-field, blackbody radiation. Although heat transfer via near-field effects has been discussed for many years, experimental verification of this theory has been very limited. We have measured the heat transfer between two macroscopic sapphire plates, finding an increase in agreement with expectations from theory. These experiments, conducted near 300 K, have measured the heat transfer as a function of separation over mm to $\mu \mathrm{m}$ and as a function of temperature differences between 2.5 and 30 K. The experiments demonstrate that evanescence can be put to work to transfer heat from an object without actually touching it.

Figure 1

Heat-transfer coefficient vs distance for $z$-cut sapphire. The temperatures of the two media are $T_{\mathrm{hot}}=310\mathrm{K}$ and $T_{\mathrm{cold}}=300\mathrm{K}$, respectively. The dash-dotted curve shows ${\mathcal{W}}_{\mathrm{pr}}^{\parallel }+W_{\mathrm{pr}}^{\perp }$ which dominate at far distances. The long-dashed curve shows ${\mathcal{W}}_{\mathrm{ev}}^{\parallel }$. The short-dashed curve shows ${\mathcal{W}}_{\mathrm{ev}}^{\perp }$. The evanescent terms dominate at close distances. The solid curve is the total heat-transfer coefficient $\mathcal{W}$.

Figure 2

Experimental apparatus. Stepper motors allow adjustment of the spacing, tip, and tilt (read capacitively) of two sapphire plates. The temperature of the hot plate is controlled by a feedback circuit, and the power required to maintain a temperature difference gives the heat transfer from the hot plate to the cold plate and to the thermal bath.

Figure 3

Heat-transfer coefficient vs distance. The curves are each offset vertically by $2\mathrm{W}/{\mathrm{m}}^2·\mathrm{K}$ from the one below; their zeros are indicated by the horizontal lines extending from the left axis. The points are the data, with error bars determined from the scatter in the heat-transfer measurements and the uncertainty in the distance calibration. The solid lines are the theoretical predictions for flat plates while the dashed lines are the theoretical predictions for slightly curved plates (see text). Each measured curve has a reproducible addendum due to other heat leaks which are not included in the model and which has been subtracted from the data. The temperatures are (top to bottom; hot–cold): 327.0–308.0 K, 322.0–307.0 K, 317.0–305.8 K, and 312.0–305.2 K.

Figure 4

Near-field heat flux vs distance for multiple temperature differences and multiple runs. (One run is shown with open symbols and other runs with filled symbols.) The inset shows the near-field heat flux vs temperature difference for several specific separation distances.