This 2D companion computes the same near-field radiative heat-transfer model as the 3D version, rendered a genuinely different way: a side-on gap diagram you can drag directly, plus a live log-log chart of the enhancement factor 1 + A(dref/d)^2 (capped) so you can see the whole d-dependence at once, not just the current point.
q_bb = sigma (T1^4 - T2^4), sigma = 5.67e-8 W/m2/K4
q_nf(d) = q_bb * min(cap, 1 + A*(d_ref/d)^2) (illustrative scaling,
proximity-limit form; same A/d_ref/cap per material as the 3D sim)
Standalone check (Node, scratchpad only, solving 1+A(d_ref/d)^2=cap for d): the source's own numbers are internally consistent — SiO2 (A=60, cap=1400) reaches its cap at d ≈ 20.7 nm, and gold (A=5, cap=60) reaches its cap at d ≈ 29.1 nm, both below the slider's 10 nm floor's neighbourhood but still comfortably inside the log-log chart's range; the curve is monotonic decreasing in d across the whole 10 nm-10 um span and the cap only clips the very bottom of the SiO2 curve. No inconsistency found — the 2D engine below reuses the exact same A/d_ref/cap constants and formula, just plotted logarithmically instead of read off a single number.
- Gap slider — sets the plate separation on a log scale from 10 nm to 10 um; you can also drag the hot (top) plate directly in the diagram.
- SiO2 / Gold — switches the enhancement prefactor A between the strong-resonance dielectric case and the weak-coupling metal case; both curves are drawn on the chart, with the inactive one dimmed for comparison.
- T1 / T2 sliders — set the hot and cold plate temperatures (T1 is always kept above T2); both flux readouts scale with T1^4 - T2^4.
- Dot density and how tightly the tunneling dots stay collimated between the plates scale with the same computed enhancement factor as the chart curve.
Real-world relevance: this effect underlies near-field thermophotovoltaics, nanoscale heat-assisted magnetic recording, scanning thermal microscopy, and proposed nanogap thermal management in dense electronics.