# One-Phase Stefan Problem Moving Interface Solver

> One-Phase Stefan Problem Moving Interface Solver is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Evaluates the mathematical moving phase boundary of a one-phase Stefan problem, computing the latent heat balance and conductive heat profile at specified times and positions.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/one-phase-stefan-similarity-moving-interface-latent-heat-profile?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/one-phase-stefan-problem-moving-interface-solver-c2de21b3
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_SogPj538_ZlBG8boeeQAv

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability one-phase-stefan-problem-moving-interface-solver-c2de21b3 -d '<json body>'
```

Example prompt: Using the Stefan similarity solution, evaluate the moving phase boundary and latent/conductive heat balance for a material with density 900 kg/m³, latent heat 334000 J/kg, specific heat 2090 J/kg·K, thermal conductivity 2.2 W/m·K, cold temperature -20°C, and phase temperature 0°C — query the interface at time 3600 seconds and position 0.1 m.

## When to prefer this

Choose this endpoint when you need an analytical similarity-solution evaluation of a one-phase Stefan moving boundary problem — specifically when material properties (density, latent heat, specific heat, thermal conductivity, temperatures) are known and you want the mathematical phase front position and heat balance at explicit time-position query points. Ideal for geotechnical freezing, solidification modeling, permafrost analysis, and cold storage design. Prefer this over finite-element or numerical PDE solvers when the one-phase simplification applies and you need fast, deterministic results.

## Known failure modes

- Invalid or out-of-range thermal property values (e.g. negative density or thermal conductivity below 0.001) result in schema validation errors
- Query array exceeds maximum of 32 items returns a validation error
- Cold temperature exceeds phase temperature (non-physical setup) may yield undefined or error results
- Time or position values at boundary extremes (e.g. very small time ~1e-6) may produce numerically unstable outputs
- Missing required fields in the stefanFreeze.data object cause request rejection

## How this service works

Evaluate a mathematical moving phase boundary and its latent/conductive heat balance.

## Output

Returns the evaluated moving phase boundary position and the latent/conductive heat balance profile at each queried time-position pair, based on the one-phase Stefan similarity solution given the input material thermal properties.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "stefanFreeze"
   ],
   "properties": {
    "stefanFreeze": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "density",
        "latent_heat",
        "specific_heat",
        "thermal_conductivity",
        "cold_temperature",
        "phase_temperature",
        "queries"
       ],
       "properties": {
        "density": {
         "type": "number",
         "maximum": 10000,
         "minimum": 1
        },
        "queries": {
         "type": "array",
         "items": {
          "type": "object",
          "required": [
           "time",
           "position"
          ],
          "properties": {
           "time": {
            "type": "number",
            "maximum": 1000000,
            "minimum": 0.000001
           },
           "position": {
            "type": "number",
            "maximum": 10000,
            "minimum": 0
           }
          },
          "additionalProperties": false
         },
         "maxItems": 32,
         "minItems": 1
        },
        "latent_heat": {
         "type": "number",
         "maximum": 10000000,
         "minimum": 1
        },
        "specific_heat": {
         "type": "number",
         "maximum": 10000,
         "minimum": 1
        },
        "cold_temperature": {
         "type": "number",
         "maximum": 5000,
         "minimum": -1000
        },
        "phase_temperature": {
         "type": "number",
         "maximum": 6000,
         "minimum": -1000
        },
        "thermal_conductivity": {
         "type": "number",
         "maximum": 1000,
         "minimum": 0.001
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/one-phase-stefan-problem-moving-interface-solver-c2de21b3/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)