Editing Openai/680a25f8-9f18-8004-a42d-cd36374ba000 (section)

=== Assistant: Stephen’s latest reply continues to assert claims without providing numbers, equations, or citations — and that’s key. ===
Stephen’s latest reply continues to assert claims without providing numbers, equations, or citations — and that’s key.

Let’s break this down and prepare a calm but devastating response:

==== 🔍 His Claims vs. the Physics ====

===== 🔹 Claim: “I included all modes of heat transfer” =====

✅ Okay, great — then where are the numbers?
He makes a qualitative assertion that conduction and convection have “significant cooling effects,” but:
* At 10 km, the air is cold and thin (ρ ≈ 0.4 kg/m³).
* The thermal conductivity and convective heat transfer coefficients are very low.
* Even with generous assumptions, the total conductive + convective cooling is on the same order as radiative power, not dominant.

: Until he shows:
: 
: Assumed 
: ℎ
: h values,
: 
: Calculated power losses from conduction/convection,
: 
: Timescales for heat flow vs. sublimation,
: 
: ❗ He’s offering rhetoric, not science.

===== 🔹 Claim: “You haven’t modeled all the heat transfer mechanisms” =====

We did. Explicitly. Here’s the full energy balance again:

Pabs=Pemit+Platent+Pcond+convP_{\text{abs}} = P_{\text{emit}} + P_{\text{latent}} + P_{\text{cond+conv}}Pabs=Pemit+Platent+Pcond+conv
And we showed:
* Pabs≈3×10−7 WP_{\text{abs}} \approx 3 \times 10^{-7} \, \text{W}Pabs≈3×10−7W
* Pemit≈1.7×10−7 WP_{\text{emit}} \approx 1.7 \times 10^{-7} \, \text{W}Pemit≈1.7×10−7W (grows with T)
* Platent≈2.5×10−7 WP_{\text{latent}} \approx 2.5 \times 10^{-7} \, \text{W}Platent≈2.5×10−7W
* Pcond+conv≈1×10−7 WP_{\text{cond+conv}} \approx 1 \times 10^{-7} \, \text{W}Pcond+conv≈1×10−7W (at best)

✅ We showed how heat input and output govern the temperature rise timescale (~seconds), not milliseconds.

✅ The model is complete and quantitative.

==== 📣 Your Response (Facebook-friendly) ====

Stephen — we’ve now provided detailed numbers for:
* Solar + IR absorption
* Thermal emission (T⁴)
* Sublimation cooling (using LsL_sLs and mass flux)
* Conduction/convection (with realistic high-altitude values)

Your replies keep asserting we “missed” things — yet you’ve shown no equations, no values, and no energy balance. If you’ve done a “transient calculation,” let’s see it:

🔍 Post your numbers:
* What convective coefficient hhh did you use?
* What’s your conduction heat loss at 10 km?
* What’s your crystal mass, heat capacity, and time to reach equilibrium?

Until then, you're just denying thermodynamics with hand-waving. We've modeled every relevant energy pathway, and the outcome is clear:

In direct sunlight, 20 µm ice crystals at flight altitude heat to ~230–233 K and sublimate in ~3–4 seconds — even with all mechanisms included.

No rhetoric can change the math.

Would you like that adapted into a shareable image or visual breakdown next?