Thermal Conductivity Ontology

# Thermal Conductivity Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/thermal-measurements/thermal-conductivity-ontology.html

FLOW ThermalConductivityOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Thermal Measurements
    -> Thermal Conductivity Ontology

  PURPOSE:
    Represent thermal conductivity as a measurable material property describing conductive heat transport in response to a temperature gradient, including Fourier's law, isotropic and anisotropic conductivity, temperature and phase dependence, geometry relationships, thermal resistance, thermal diffusivity, measurement methods, units, dimensional structure, uncertainty, and distinctions from heat transfer coefficient, thermal diffusivity and thermal conductance.

  ENTITY ThermalConductivity {
    TYPE: IntensiveThermalMaterialProperty
    SYMBOL: k
    DIMENSION: M * L * T^-3 * Theta^-1
    SI_UNIT: watt_per_metre_kelvin
    SI_SYMBOL: W/(m*K)

    FOURIER_RELATION:
      q_vector = -k*gradient(T)
      UNDER isotropic_continuum_context

    ONE_DIMENSIONAL_FORM:
      Q_dot = k*A*(T_hot - T_cold)/L

    PROPERTIES:
      is_material_property
      has_value
      has_unit
      has_dimension
      may_depend_on_temperature
      may_depend_on_pressure
      may_depend_on_phase
      may_depend_on_composition
      may_be_direction_dependent
      may_have_uncertainty
  }

  ENTITY HeatFlux {
    TYPE: VectorThermalFluxQuantity
    SYMBOL: q_vector
    SI_UNIT: watt_per_square_metre
    SI_SYMBOL: W/m^2

    RELATION:
      q_vector = -k*gradient(T)
  }

  ENTITY TemperatureGradient {
    TYPE: VectorSpatialGradientQuantity
    SYMBOL: gradient_T
    SI_UNIT: kelvin_per_metre
    SI_SYMBOL: K/m
  }

  ENTITY ThermalResistance {
    TYPE: GeometryDependentThermalQuantity
    SYMBOL: R_th
    SI_UNIT: kelvin_per_watt
    SI_SYMBOL: K/W

    PLANE_WALL:
      R_th = L/(k*A)
  }

  ENTITY ThermalConductance {
    TYPE: GeometryDependentThermalQuantity
    SYMBOL: G_th
    SI_UNIT: watt_per_kelvin
    SI_SYMBOL: W/K

    RELATION:
      G_th = 1/R_th
      WHEN R_th != 0
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: watt_per_metre_kelvin
      symbol: W/(m*K)
    }

    COMMON_ALTERNATIVES:
      watt_per_metre_degree_Celsius
      milliwatt_per_metre_kelvin
      British_thermal_unit_per_hour_foot_degree_Fahrenheit

    INTERVAL_RULE:
      temperature_gradient_interval_K_per_m
      numerically_equals_degree_Celsius_per_m

    CONVERSION_RULE:
      conductivity_value(target_unit)
        = conductivity_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by material:
      solid_thermal_conductivity
      liquid_thermal_conductivity
      gas_thermal_conductivity
      composite_thermal_conductivity

    by directional behaviour:
      isotropic_thermal_conductivity
      anisotropic_thermal_conductivity
      orthotropic_thermal_conductivity

    by effective scale:
      intrinsic_thermal_conductivity
      effective_thermal_conductivity
  }

  FOURIER_LAW_MODEL {
    ISOTROPIC:
      q_vector = -k*gradient(T)

    ONE_DIMENSIONAL:
      q_x = -k*dT/dx

    SIGN:
      heat_flows_toward_decreasing_temperature

    CONDITIONS:
      continuum_heat_conduction
      local_thermal_equilibrium_when_required
      applicable_material_property

    RULE:
      negative_sign encodes_direction
      and_MUST be preserved_in_vector_reasoning
  }

  ANISOTROPIC_MODEL {
    GENERAL:
      q_vector = -K_tensor * gradient(T)

    conductivity_tensor:
      K_tensor

    PROPERTY:
      heat_flux_need_not_be_parallel_to_negative_temperature_gradient

    REQUIRE:
      coordinate_system
      material_orientation
      conductivity_tensor_components

    RULE:
      scalar_k MUST_NOT replace_tensor_conductivity
      when_anisotropy_is_material
  }

  PLANE_WALL_MODEL {
    STEADY_ONE_DIMENSIONAL:
      Q_dot = k*A*(T_1 - T_2)/L

    THERMAL_RESISTANCE:
      R_cond = L/(k*A)

    CONDUCTANCE:
      G_cond = k*A/L

    CONDITIONS:
      steady_state
      one_dimensional_conduction
      constant_k_or_effective_k
      uniform_area
      negligible_contact_resistance
      L > 0
  }

  COMPOSITE_LAYER_MODEL {
    SERIES_LAYERS:
      R_total = sum(L_i/(k_i*A_i))
      WHEN same_heat_path_and_defined_geometry

    HEAT_RATE:
      Q_dot = delta_T/R_total

    PARALLEL_PATHS:
      G_total = sum(G_i)

    RULE:
      thermal_network_topology MUST match_physical_heat_flow_geometry
  }

  CYLINDRICAL_MODEL {
    STEADY_RADIAL_CONDUCTION:
      Q_dot =
        2*pi*k*L_axial*(T_1 - T_2)
        / ln(r_2/r_1)

    THERMAL_RESISTANCE:
      R_cyl =
        ln(r_2/r_1)/(2*pi*k*L_axial)

    CONDITIONS:
      r_2 > r_1 > 0
      steady_radial_conduction
      constant_k
  }

  SPHERICAL_MODEL {
    THERMAL_RESISTANCE:
      R_sph =
        (1/(4*pi*k))*(1/r_1 - 1/r_2)

    CONDITIONS:
      r_2 > r_1 > 0
      steady_radial_conduction
      constant_k
  }

  TEMPERATURE_DEPENDENCE_MODEL {
    GENERAL:
      k = k(T, p, composition, phase, structure)

    VARIABLE_K_ONE_DIMENSION:
      Q_dot/A =
        -(1/L)*integral_T1_to_T2(k(T) dT)
      with_sign_according_to_coordinate_definition

    RULE:
      large_temperature_ranges SHOULD use_temperature_dependent_conductivity_when_material
  }

  PHASE_AND_STRUCTURE_MODEL {
    dependencies:
      phase
      porosity
      moisture_content
      density
      crystal_orientation
      grain_structure
      composition

    porous_material:
      effective_k may_include solid_fluid_radiative_and_contact_effects

    RULE:
      effective_conductivity MUST preserve_sample_structure_and_environment_context
  }

  THERMAL_DIFFUSIVITY_RELATION {
    alpha_th = k/(rho*c_p)

    WHERE:
      alpha_th = thermal_diffusivity
      rho = density
      c_p = specific_heat_capacity

    RULE:
      thermal_conductivity_and_thermal_diffusivity
      are_related_but_not_semantically_equivalent
  }

  HEAT_TRANSFER_COEFFICIENT_DISTINCTION {
    thermal_conductivity:
      intrinsic_or_effective_bulk_material_transport_property

    heat_transfer_coefficient:
      boundary_or_system_level_parameter
      h with_unit W/(m^2*K)

    RULE:
      k != h
      and_units_and_physical_meaning_must_remain_distinct
  }

  RELATIONSHIPS {
    ThermalConductivity -> RELATES -> HeatFluxAndTemperatureGradient
    ThermalConductivity -> HAS_DIMENSION -> M*L*T^-3*Theta^-1
    ThermalConductivity -> MEASURED_IN -> WattPerMetreKelvin
    ThermalConductivity -> DEPENDS_ON -> Material
    ThermalConductivity -> MAY_DEPEND_ON -> Temperature
    ThermalConductivity -> MAY_DEPEND_ON -> Pressure
    ThermalConductivity -> MAY_DEPEND_ON -> Phase
    ThermalConductivity -> CONTRIBUTES_TO -> ThermalResistance
    ThermalConductivity -> CONTRIBUTES_TO -> ThermalConductance
    ThermalConductivity -> RELATES_TO -> ThermalDiffusivity
  }

  SEMANTIC_EQUIVALENCE {
    "thermal conductivity" ~= heat_conductivity
    "W/m K" ~= "W/(m*K)"

    thermal_conductivity != thermal_diffusivity
    thermal_conductivity != thermal_conductance
    thermal_conductivity != thermal_resistance
    thermal_conductivity != heat_transfer_coefficient
    thermal_conductivity != heat_flux
  }

  CONSTRAINTS {
    dimensional_formula = M*L*T^-3*Theta^-1
    SI_unit = W/(m*K)
    conductivity_is_material_property = true
    geometry_dependent_thermal_conductance_is_not_conductivity = true
    conductivity_and_diffusivity_are_not_semantically_equivalent = true
    conductivity_and_heat_transfer_coefficient_are_not_semantically_equivalent = true
    anisotropic_materials_require_tensor_semantics_when_directionality_is_material = true
    material_temperature_phase_and_structure_conditions_should_be_preserved = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      ThermalConductivity

    STEADY_STATE_METHODS:
      guarded_hot_plate
      heat_flow_meter
      comparative_cut_bar
      radial_heat_flow

    TRANSIENT_METHODS:
      transient_hot_wire
      transient_plane_source
      laser_flash_with_density_and_heat_capacity
      needle_probe

    RECORD:
      numerical_value
      unit
      material
      composition
      phase
      density
      porosity
      moisture_content
      orientation
      temperature
      pressure
      sample_geometry
      heat_flux_or_heat_rate
      temperature_gradient_or_difference
      measurement_method
      instrument
      calibration_state
      contact_resistance_correction
      radiation_correction
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_thermal_conductivity = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF heat_flux_vector_known AND temperature_gradient_known
      AND isotropic_Fourier_conditions_apply
      AND gradient_magnitude != 0
      THEN infer_thermal_conductivity_with_direction_consistency

    IF heat_rate_area_length_and_temperature_difference_known
      AND area != 0 AND temperature_difference != 0
      AND steady_one_dimensional_plane_wall_conditions_apply
      THEN k =
        heat_rate*length/(area*temperature_difference)

    IF k_length_and_area_known AND k != 0 AND area != 0
      THEN conductive_thermal_resistance =
        length/(k*area)

    IF k_area_and_length_known AND length != 0
      THEN thermal_conductance =
        k*area/length

    IF k_density_and_specific_heat_known
      AND density != 0 AND specific_heat != 0
      THEN thermal_diffusivity =
        k/(density*specific_heat)

    IF anisotropic_conductivity_tensor_known AND temperature_gradient_known
      THEN heat_flux =
        -conductivity_tensor*temperature_gradient

    IF series_layer_resistances_known
      THEN total_thermal_resistance = sum(layer_resistances)
  }

  MATERIAL_CONTEXT_MODEL {
    REQUIRE:
      material_identity
      composition
      phase
      temperature

    WHEN_RELEVANT:
      pressure
      density
      porosity
      moisture
      orientation
      microstructure

    RULE:
      tabulated_k_value SHOULD preserve_reference_conditions
  }

  INTERFACE_MODEL {
    thermal_contact_resistance:
      temperature_drop_at_interface / heat_transfer_rate

    causes:
      surface_roughness
      contact_pressure
      interstitial_material
      oxidation
      interface_quality

    RULE:
      measured_effective_conductivity MAY be biased
      if_contact_resistance_is_not_separated_from_bulk_conduction
  }

  UNCERTAINTY_MODEL {
    sources:
      heat_rate_measurement
      heat_flux_measurement
      temperature_measurement
      geometry
      sample_thickness
      contact_resistance
      radiation_loss
      convection_loss
      material_nonuniformity
      moisture
      orientation
      calibration
      model_assumptions

    PROPAGATION:
      derived_conductivity_uncertainty
      <- thermal_geometry_material_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    Fourier_relationship_confidence: 1.00
    geometry_relationship_confidence: 0.99
    material_context_confidence: 0.98
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when material, phase, temperature,
      orientation, geometry, contact resistance,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK material_identity_and_phase
    CHECK temperature_and_pressure_when_relevant
    CHECK isotropic_vs_anisotropic_model
    CHECK Fourier_sign_and_direction
    CHECK geometry_model
    CHECK steady_vs_transient_method
    CHECK conductivity_vs_diffusivity_distinction
    CHECK conductivity_vs_conductance_distinction
    CHECK conductivity_vs_heat_transfer_coefficient_distinction
    CHECK contact_resistance_and_heat_losses
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_material_composition_and_phase
      attach_temperature
      attach_pressure_when_relevant
      attach_density_porosity_moisture_when_relevant
      identify_orientation
      identify_sample_geometry
      identify_measurement_method
      normalize_to_W_per_m_K
      preserve_original_value_and_unit
      attach_uncertainty
      update_conductivity_state

    ON temperature_or_phase_change:
      update_state_conditions
      recompute_conductivity_when_model_available
      preserve_previous_state

    ON composition_or_structure_change:
      update_composition
      update_porosity_moisture_density_or_orientation
      recompute_effective_conductivity_when_valid
      preserve_material_provenance

    ON geometry_or_interface_change:
      update_sample_geometry
      update_contact_resistance
      recompute_inferred_bulk_conductivity
      preserve_previous_geometry_state

    ON calibration_revision:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: ThermalConductivity
    canonical_symbol: k
    canonical_dimension: M*L*T^-3*Theta^-1
    canonical_SI_unit: W/(m*K)

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_material_composition_and_phase
      identify_temperature_and_pressure
      identify_isotropic_or_anisotropic_context
      identify_orientation
      identify_heat_flux_and_temperature_gradient
      identify_geometry
      identify_steady_or_transient_measurement_method
      identify_contact_and_loss_corrections
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_conduction_relationships

    ambiguity_controls:
      distinguish_thermal_conductivity_from_thermal_diffusivity
      distinguish_thermal_conductivity_from_thermal_conductance
      distinguish_thermal_conductivity_from_thermal_resistance
      distinguish_thermal_conductivity_from_heat_transfer_coefficient
      distinguish_material_property_from_geometry_dependent_quantity
      distinguish_scalar_isotropic_from_tensor_anisotropic_conductivity
      preserve_material_phase_temperature_structure_and_orientation_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_thermal_conductivity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Thermal Measurements
      -> Thermal Conductivity Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      Fourier_law_model
      anisotropic_model
      plane_wall_model
      composite_layer_model
      cylindrical_model
      spherical_model
      temperature_dependence_model
      phase_and_structure_model
      thermal_diffusivity_relation
      heat_transfer_coefficient_distinction
      material_context_model
      interface_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      Fourier_or_transport_model_changes
      anisotropic_model_changes
      geometry_model_changes
      material_or_phase_model_changes
      temperature_dependence_changes
      interface_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW