# ⚛  L1 Principle — Conjugate Heat Transfer — coupled fluid-solid thermal

**ID:** `L1-201` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Heat Transfer — *Fluid-solid interface heat flux matching*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** coupled fluid solid temp
> **📡 Carrier:** thermal · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034

---

## 🧠 1. Introduction

**Conjugate Heat Transfer — coupled fluid-solid thermal** is a **nonlinear inverse problem** whose unknown lives in **coupled fluid solid temp** space, within the **Fluid-solid interface heat flux matching** sub-domain of **Heat Transfer**.

Measurements consist of thermal radiation / temperature measurements via a **ir pitot thermocouples** sensing mechanism.

The forward operator applies, in order: L · fluid heat operator; L · solid conduction operator; L · interface coupling operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · fluid heat → L · solid conduction → L · interface coupling → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.interface_coupling` `L.solid_conduction` `L.fluid_heat` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.fluid_heat` | L · fluid heat operator |
| `L.solid_conduction` | L · solid conduction operator |
| `L.interface_coupling` | L · interface coupling operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Heat Transfer |
| Sub domain | Fluid-solid interface heat flux matching |
| Carrier | thermal |
| Problem class | nonlinear_inverse |
| Solution space | coupled_fluid_solid_temp |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `conjugate_ht` · **Forward operator:** `conjugate_ht_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N fluid | — | 10000 |
| N solid | — | 10000 |
| Wall k error | — | 0 |
| Fluid kappa error | — | 0 |
| Interface h error | — | 0 |
| Contact resistance error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N fluid | — | 500 – 1000000 |
| N solid | — | 500 – 500000 |
| Wall k error | — | 0.0 – 0.1 |
| Fluid kappa error | — | 0.0 – 0.1 |
| Interface h error | — | 0.0 – 0.3 |
| Contact resistance error | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 21.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xee4ce3bbe6fa747fe6013b18610aba9d143e098a27cabd571ad4ac152e3e6605`
- **Chain tx hash:** `0x34e21da0bfeacfafb8be77103aa1080f4ba12bf87a5c27dc778c9e060ec9006c`
- **Chain block:** `41554034`

---

## File Mapping

This bundle consists of: `L1-201.md`, `L1-201.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-201.md` | Source of truth — edit this | Human or LLM |
| `L1-201.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-201`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._