{"uid":"cap_SogPj538_ZlBG8boeeQAv","slug":"one-phase-stefan-problem-moving-interface-solver-c2de21b3","name":"One-Phase Stefan Problem Moving Interface Solver","description":"Evaluate a mathematical moving phase boundary and its latent/conductive heat balance.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/one-phase-stefan-similarity-moving-interface-latent-heat-profile?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"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}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_UeK6RysXYxWc9vzD1UBph","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Permafrost freezing depth estimation","prompt":"I need to figure out how deep the frost front penetrates in permafrost soil. The soil has a density of 1800 kg/m³, latent heat of 100000 J/kg, specific heat of 1500 J/kg·K, thermal conductivity of 1.5 W/m·K, cold surface temperature of -15°C, and phase temperature of 0°C. Can you evaluate the moving phase boundary at 1 hour, 6 hours, and 24 hours after freezing starts, at positions 0.05 m, 0.1 m, and 0.2 m?"},{"title":"Ice layer growth in a cold storage wall","prompt":"I'm designing a cold storage facility and need to model ice growth in an insulating wall. The water/ice properties are: density 920 kg/m³, latent heat 334000 J/kg, specific heat 2000 J/kg·K, thermal conductivity 2.1 W/m·K, cold wall temperature -10°C, and freezing point 0°C. Please evaluate the Stefan similarity solution at t=600s, t=3600s, and t=7200s at positions 0.02 m and 0.05 m."},{"title":"Solidification front in metal casting","prompt":"I'm modeling the solidification of a casting with these properties: density 7800 kg/m³, latent heat 270000 J/kg, specific heat 500 J/kg·K, thermal conductivity 50 W/m·K, mold temperature -200°C relative to liquidus, and phase transition temperature 1500°C. Can you compute the latent heat balance and moving interface position at times 10s and 100s, at positions 0.01 m and 0.05 m?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:38:57.463Z","isFirstParty":false,"canonicalSlug":"one-phase-stefan-problem-moving-interface-solver-c2de21b3"}