{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T10:04:08Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 20.9, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a09511-fe6b-7740-96e5-6a10c1abb254\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: Graetz number for heat transfer\nSense to describe: (none recorded)\nDomain code: INF.MED\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n#", "usd": 0.0, "recall": true }, "codex": { "seconds": 69.5, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a09511-fe7d-7290-aa85-45fc724370df\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: Graetz number for heat transfer\nRegistry id: vr.tr.graetz-number-for-heat-transfer\nPlane / domain: INF / INF.MED\nRegistry definition: (none recorded)" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:39:46+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners", "visual_identification" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T10:10:33+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q903886", "registryId": "vr.tr.graetz-number-for-heat-transfer", "name": "Graetz number for heat transfer", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q903886/", "model": { "registry_id": "vr.tr.graetz-number-for-heat-transfer", "name": "Graetz number for heat transfer", "purpose": "Enable an agent to identify, calculate and interpret a thermal Graetz number while checking the conventions and physical assumptions required for its use.", "definition": "The Graetz number for heat transfer is a dimensionless parameter, commonly defined for internal flow as Gz = Re Pr D/L, that characterizes thermal development by comparing transverse thermal diffusion time with fluid residence time over an axial length L.", "scope_statement": "This model owns the definition, calculation context, comparability and permitted interpretation of the heat-transfer Graetz number registered as vr.tr.graetz-number-for-heat-transfer in INF / INF.MED.", "in_scope": [ "Thermal Graetz-number definitions and normalization conventions", "Characteristic transverse dimension and axial distance from the thermal entrance", "Flow and thermal-property inputs used to calculate the number", "Interpretation of thermal development under specified flow conditions", "Compatibility with heat-transfer correlations and their validity limits" ], "out_of_scope": [ "Mass-transfer Graetz numbers using species diffusivity", "Complete solutions of the Graetz temperature-field problem", "Independent models of Reynolds, Prandtl, Péclet and Nusselt numbers", "Detailed pipe, duct and heat-exchanger design", "Fluid-property databases and measurement-instrument models" ], "distinguishing_features": [ "Uses thermal diffusivity, or equivalently the Prandtl number; a formulation using Schmidt number represents the mass-transfer analogue.", "Under the diameter-based convention, Gz = Re Pr D_h/x, so it includes an axial-to-transverse geometry relationship absent from Pe = Re Pr alone.", "Describes thermal-development scaling; it is not the Nusselt number h D_h/k and does not independently specify a heat-transfer coefficient.", "Is a dimensionless scalar evaluated for a specified flow and location, whereas the Graetz problem is a boundary-value problem.", "Numerical equality requires matching conventions: a circular-tube mass-flow definition can differ from the diameter-based definition by π/4." ], "characteristics": [ { "name": "Graetz-number value", "kind": "measurement", "unit_or_values": "Dimensionless; finite positive value for positive flow magnitude, diffusivity and downstream distance", "why_it_matters": "Supplies the thermal-development parameter used in compatible analyses." }, { "name": "Normalization convention", "kind": "category", "unit_or_values": "Diameter-based Re Pr D_h/x; mass-flow-based m_dot c_p/(k x); explicitly documented alternative", "why_it_matters": "Prevents numerical comparisons and correlation substitutions across incompatible definitions." }, { "name": "Thermal entrance and evaluation distance", "kind": "measurement", "unit_or_values": "x or heated length L in m, with a named origin", "why_it_matters": "The thermal entrance may differ from the hydraulic inlet, changing the calculated value." }, { "name": "Transverse length basis", "kind": "measurement", "unit_or_values": "D_h in m; hydraulic diameter 4A/P_w or a source-specified dimension", "why_it_matters": "Controls the geometry factor and must match the Reynolds-number and correlation definitions." }, { "name": "Flow and property basis", "kind": "relation", "unit_or_values": "Linked bulk velocity or mass flow, density, heat capacity, conductivity and their evaluation conditions", "why_it_matters": "Makes the calculation reproducible and exposes inconsistent temperatures or averaging choices." }, { "name": "Thermal and hydraulic development", "kind": "state", "unit_or_values": "Thermally developing or developed; hydrodynamically developing or developed; unknown", "why_it_matters": "These states determine whether an entrance-region relation is applicable." }, { "name": "Wall thermal condition", "kind": "category", "unit_or_values": "Prescribed wall temperature; prescribed wall heat flux; mixed; conjugate; other specified condition", "why_it_matters": "A Graetz-number value alone does not select the appropriate heat-transfer relation." }, { "name": "Calculation uncertainty", "kind": "measurement", "unit_or_values": "Dimensionless interval or relative uncertainty with propagation method", "why_it_matters": "Supports defensible comparisons and development-state decisions near a chosen criterion." } ], "affordances": [ "Calculate a thermal Graetz number from consistent flow, geometry and thermal-property inputs.", "Convert between explicitly documented conventions when geometry and property assumptions permit.", "Compare thermal development across locations or operating conditions under a common convention.", "Check whether a proposed Nusselt correlation accepts the recorded definition and physical conditions.", "Identify missing inputs, singular entrance evaluations and unsupported extrapolations.", "Estimate a downstream distance for a sourced thermal-development criterion." ], "agent_conduct": { "may": [ "Compute the Graetz number from stated inputs and show the definition used.", "Explain what it says about thermal development in pipe or channel flow." ], "must_not": [ "Present a result without stating which definition and length scale were used.", "Apply correlations based on it outside their validated range for a safety-relevant design.", "Confuse it with the mass-transfer Graetz number or other dimensionless groups." ], "requires_human": [ "Signing off a heat-exchanger or cooling design that relies on the result." ] }, "ethics": { "considerations": [ "Wrong heat-transfer estimates can lead to overheating in equipment people depend on." ], "affected_parties": [ "Engineers and students", "Users of thermal equipment", "Operators of process plants" ] }, "owners": { "steward": "Nobody owns it; it is a concept of heat-transfer science.", "master_systems": [] }, "visual_identification": [ "Written with the symbol Gz in equations and correlations." ], "failure_modes_and_hazards": [ "Using the wrong length scale gives values off by large factors.", "Undersized heat exchangers can overheat or fail." ], "what_it_is_for": [ "The thermal Graetz number is used in internal-flow heat transfer analysis to assess thermal development along pipes and channels.", "It helps select and interpret heat transfer correlations when the geometry, flow regime, boundary conditions and characteristic length match the correlation's assumptions." ], "facets_not_applicable": { "interfaces": "No specific standard or regulation governs this dimensionless parameter independently of its engineering application." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q903886: Graetz number for heat transfer", "url": "https://www.wikidata.org/wiki/Q903886", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Graetz number", "url": "https://en.wikipedia.org/wiki/Graetz_number", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "thermal-definition-and-conventions", "name": "Thermal definition and conventions", "description": "Establish which thermal Graetz quantity is represented and how its normalization is defined.", "rationale": "The symbol Gz alone does not determine a unique numerical convention.", "layers": [ { "id": "thermal-transport-identity", "name": "Thermal transport identity", "description": "Identify the transported quantity and distinguish the number from adjacent concepts.", "findings": [ { "id": "heat-diffusion-basis", "name": "Heat diffusion basis", "description": "Record a thermal definition using alpha = k/(rho c_p), or its equivalent Prandtl-number formulation.", "questions": [ { "text": "Does the definition use thermal diffusivity or Prandtl number rather than species diffusivity or Schmidt number?", "kind": "definition", "id": "heat-diffusion-basis-q01" }, { "text": "Does the record represent a Graetz-number value, a heat-transfer correlation or the Graetz boundary-value problem?", "kind": "boundary", "id": "heat-diffusion-basis-q02" } ] } ] }, { "id": "normalization-and-conversion", "name": "Normalization and conversion", "description": "Preserve the defining equation and conditions for conversion.", "findings": [ { "id": "explicit-geometric-prefactor", "name": "Explicit geometric prefactor", "description": "Record all prefactors: the circular-tube example in [COMSOL documentation](https://doc.comsol.com/6.3/doc/com.comsol.help.models.heat.circular_tube_nitf_laminar/circular_tube_nitf_laminar.html) uses Gz = (π/4) Re Pr D/z.", "questions": [ { "text": "What exact equation and geometric prefactor does the defining source use?", "kind": "provenance", "id": "explicit-geometric-prefactor-q01" }, { "text": "What geometry and averaging assumptions justify conversion to Re Pr D_h/x?", "kind": "action", "id": "explicit-geometric-prefactor-q02" } ] } ] } ] }, { "id": "flow-geometry-and-properties", "name": "Flow geometry and properties", "description": "Capture the physical inputs and reference conditions behind each evaluation.", "rationale": "An apparently valid dimensionless value can conceal inconsistent length scales or property states.", "layers": [ { "id": "thermal-origin-and-duct-scale", "name": "Thermal origin and duct scale", "description": "Locate the evaluation point relative to heating or cooling onset and define the transverse scale.", "findings": [ { "id": "consistent-length-scales", "name": "Consistent length scales", "description": "Record x or L separately from the transverse dimension, including the hydraulic-diameter construction where used.", "questions": [ { "text": "Is the axial distance measured from the onset of the relevant thermal boundary condition?", "kind": "measurement", "id": "consistent-length-scales-q01" }, { "text": "Which cross-sectional area and wetted perimeter define D_h, and does the selected correlation use that same scale?", "kind": "boundary", "id": "consistent-length-scales-q02" } ] } ] }, { "id": "flow-and-thermal-inputs", "name": "Flow and thermal inputs", "description": "Bind transport properties and velocity or mass flow to an operating condition.", "findings": [ { "id": "reproducible-input-state", "name": "Reproducible input state", "description": "Record bulk velocity or mass flow and the thermophysical properties, including temperature, pressure and averaging basis.", "questions": [ { "text": "Which measurements or property sources supply the flow rate, density, heat capacity and thermal conductivity?", "kind": "provenance", "id": "reproducible-input-state-q01" }, { "text": "At what temperature and pressure are properties evaluated, and how are spatial variations treated?", "kind": "measurement", "id": "reproducible-input-state-q02" } ] } ] } ] }, { "id": "thermal-development-and-applicability", "name": "Thermal development and applicability", "description": "Connect the number to thermal-development reasoning within a stated physical regime.", "rationale": "Calculating Gz does not establish that a classical entrance-flow interpretation is valid.", "layers": [ { "id": "development-interpretation", "name": "Development interpretation", "description": "Relate the chosen value to transverse thermal diffusion and axial residence time.", "findings": [ { "id": "development-criterion", "name": "Development criterion", "description": "For Gz = U D_h²/(alpha x), interpret the value as a transverse diffusion-time scale divided by an axial residence-time scale; attach any development classification to an explicit criterion.", "questions": [ { "text": "What observable and tolerance define thermally fully developed conditions for this application?", "kind": "definition", "id": "development-criterion-q01" }, { "text": "Under fixed flow and properties, how does the value change with distance from the thermal entrance?", "kind": "measurement", "id": "development-criterion-q02" } ] } ] }, { "id": "physical-regime-constraints", "name": "Physical regime constraints", "description": "Record conditions that affect the validity of a Graetz-based analysis.", "findings": [ { "id": "entrance-flow-assumptions", "name": "Entrance-flow assumptions", "description": "Check flow regime, velocity-profile development, inlet temperature distribution and wall conditions; assess omitted effects against the chosen analysis.", "questions": [ { "text": "Does the analysis require laminar, hydrodynamically developed flow and a specified inlet temperature profile?", "kind": "boundary", "id": "entrance-flow-assumptions-q01" }, { "text": "Could axial conduction, buoyancy, viscous heating, property variation or phase change invalidate the selected relation?", "kind": "boundary", "id": "entrance-flow-assumptions-q02" } ] } ] } ] }, { "id": "calculation-and-correlation-use", "name": "Calculation and correlation use", "description": "Control numerical evaluation and the downstream use of the result.", "rationale": "Agents need explicit checks before turning a dimensionless value into a heat-transfer estimate or design decision.", "layers": [ { "id": "evaluation-quality", "name": "Evaluation quality", "description": "Check units, input consistency, singularities and uncertainty.", "findings": [ { "id": "auditable-graetz-calculation", "name": "Auditable Graetz calculation", "description": "Retain the equation and inputs, verify dimensional cancellation, and flag x = 0 as a singular evaluation of the inverse-distance definition.", "questions": [ { "text": "Do the inputs produce a dimensionless result, and are diffusivity and axial distance positive?", "kind": "measurement", "id": "auditable-graetz-calculation-q01" }, { "text": "How do uncertainty and shared inputs in Re and Pr affect the reported Graetz-number uncertainty?", "kind": "measurement", "id": "auditable-graetz-calculation-q02" } ] } ] }, { "id": "heat-transfer-inference", "name": "Heat-transfer inference", "description": "Attach every inferred heat-transfer quantity to a compatible, sourced relation.", "findings": [ { "id": "correlation-compatibility", "name": "Correlation compatibility", "description": "Record the correlation's Graetz convention, geometry, wall condition, validity ranges and whether its Nusselt number is local or length-averaged.", "questions": [ { "text": "Which source establishes the correlation and its applicable ranges of Re, Pr and Gz?", "kind": "provenance", "id": "correlation-compatibility-q01" }, { "text": "Does the requested local or average heat-transfer estimate match the correlation's output definition and boundary conditions?", "kind": "action", "id": "correlation-compatibility-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Definitions can differ by numerical or geometric factors; check the convention in each correlation.", "Using hydraulic diameter for a noncircular duct does not by itself make a circular-tube correlation applicable.", "This is a recall-based description; no sources or standards were consulted." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of Graetz number for heat transfer this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-identifiers", "name": "Identifiers and schemes", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "scheme": "Conventional mathematical symbol", "value_or_pattern": "Gz", "note": "A quantity symbol rather than a registry identifier; the defining equation and characteristic lengths must accompany it." } ], "questions": [ { "id": "evidence-identifiers-q01", "text": "Which of these identifiers and schemes hold for the sense of Graetz number for heat transfer this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Characterizing the thermally developing region of flow through tubes and ducts.", "Selecting and applying entrance-region heat-transfer correlations.", "Estimating heat-transfer coefficients in heat exchangers.", "Comparing internal-flow heat-transfer conditions across different fluids, dimensions and flow rates." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of Graetz number for heat transfer this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-measurements", "name": "Typical measurements", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "quantity": "Graetz number", "typical_range": "No universal typical range; larger values indicate less time for transverse thermal diffusion over the specified flow length.", "unit": "Dimensionless" }, { "quantity": "Defining relationship", "typical_range": "Gz = Re Pr D/L = U D²/(α L), when Re = U D/ν and Pr = ν/α.", "unit": "Dimensionless" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of Graetz number for heat transfer this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Mixing definitions that use different geometric factors or characteristic lengths.", "Using total tube length when a correlation requires distance from the start of heating or cooling.", "Applying a correlation outside its flow regime, geometry or wall-boundary-condition assumptions.", "Confusing hydrodynamically developed flow with thermally developed flow.", "Assuming that matching Graetz numbers alone guarantees equivalent heat transfer when other governing effects differ." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of Graetz number for heat transfer this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "name": "Péclet number", "difference": "The thermal Péclet number Pe = Re Pr compares advection and thermal diffusion using a characteristic length; the common Graetz definition additionally includes D/L." }, { "name": "Reynolds number", "difference": "Compares inertial and viscous effects; it does not incorporate thermal diffusivity." }, { "name": "Prandtl number", "difference": "Compares momentum diffusivity with thermal diffusivity and does not include flow speed or passage length." }, { "name": "Nusselt number", "difference": "Expresses a dimensionless heat-transfer coefficient; the Graetz number is a governing parameter used in correlations for that coefficient." }, { "name": "Graetz problem", "difference": "A mathematical thermal-entry flow problem whose solutions depend on parameters including the Graetz number; it is not itself a dimensionless quantity." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of Graetz number for heat transfer this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which normalization should serve as the registry's preferred display convention while preserving source-specific alternatives?", "Which authoritative references establish supported correlations for noncircular ducts, including their aspect-ratio and heating-pattern limits?", "Which observable and tolerance should define thermal development for each intended agent workflow?", "How should evaluations with strongly varying properties or interrupted heating define effective properties and the thermal origin?", "Does an existing Vercy world model already own this thermal dimensionless quantity, requiring a registry link instead of a separate publication?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 14, "questions": 22 } }