Thermal Measurements

# Thermal Measurements Ontology — Flow Algebra

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

FLOW ThermalMeasurementsOntology {

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

  PURPOSE:
    Represent the semantic and mathematical structure of thermal measurement quantities, units, material properties, energy-transfer mechanisms, thermodynamic state variables, measurement methods, reference scales, uncertainty, dimensional relationships, and transformations required for consistent AI interpretation and reasoning across thermal and thermodynamic domains.

  SCOPE {
    temperature
    temperature_difference
    heat
    thermal_energy
    heat_capacity
    specific_heat_capacity
    thermal_conductivity
    thermal_resistance
    heat_flux
    heat_transfer_coefficient
    thermal_expansion
    phase_change
    entropy
    thermodynamic_state
    thermal_measurement_instruments
    uncertainty_and_calibration
  }

  ENTITY Temperature {
    TYPE: SIBaseQuantity
    SYMBOL: T
    DIMENSION: Theta
    SI_UNIT: kelvin
    SI_SYMBOL: K

    PROPERTIES:
      scalar_quantity
      state_variable
      may_vary_with_position
      may_vary_with_time
      requires_scale_definition
  }

  ENTITY TemperatureDifference {
    TYPE: ThermalDifferenceQuantity
    SYMBOL: delta_T
    DIMENSION: Theta
    SI_UNIT: kelvin
    SI_SYMBOL: K

    RELATION:
      delta_T = T_2 - T_1
  }

  ENTITY Heat {
    TYPE: EnergyTransferQuantity
    SYMBOL: Q
    DIMENSION: M*L^2*T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    DEFINITION:
      heat := energy_transfer_due_to_temperature_difference

    RULE:
      heat_is_not_a_stored_state_property
  }

  ENTITY HeatCapacity {
    TYPE: DerivedThermalQuantity
    SYMBOL: C
    DIMENSION: M*L^2*T^-2*Theta^-1
    SI_UNIT: joule_per_kelvin
    SI_SYMBOL: J/K

    SIMPLE_RELATION:
      C = delta_Q/delta_T
      UNDER applicable_process_context
  }

  ENTITY SpecificHeatCapacity {
    TYPE: MaterialProperty
    SYMBOL: c
    DIMENSION: L^2*T^-2*Theta^-1
    SI_UNIT: joule_per_kilogram_kelvin
    SI_SYMBOL: J/(kg*K)

    SIMPLE_SENSIBLE_HEAT:
      Q = m*c*delta_T
      UNDER applicable_constant_c_context
  }

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

  ENTITY HeatFlux {
    TYPE: VectorOrNormalSurfaceFluxQuantity
    SYMBOL: q_double_prime
    DIMENSION: M*T^-3
    SI_UNIT: watt_per_square_metre
    SI_SYMBOL: W/m^2
  }

  ENTITY HeatTransferCoefficient {
    TYPE: EffectiveBoundaryProperty
    SYMBOL: h
    SI_UNIT: watt_per_square_metre_kelvin
    SI_SYMBOL: W/(m^2*K)
  }

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

    RELATION:
      R_th = delta_T / heat_transfer_rate
      WHEN heat_transfer_rate != 0
  }

  ENTITY Entropy {
    TYPE: ThermodynamicStateQuantity
    SYMBOL: S
    SI_UNIT: joule_per_kelvin
    SI_SYMBOL: J/K
  }

  UNIT_SYSTEM {
    TEMPERATURE_SI:
      kelvin
      symbol: K

    COMMON_TEMPERATURE_SCALES:
      degree_Celsius
      degree_Fahrenheit

    ENERGY:
      joule

    POWER:
      watt

    RULE:
      absolute_temperature_and_temperature_difference
      MUST preserve_scale_semantics

    CELSIUS_KELVIN:
      T_K = T_C + 273.15

    TEMPERATURE_DIFFERENCE:
      delta_1_K = delta_1_degree_Celsius

    RULE:
      Celsius_offset_applies_to_absolute_reading
      NOT directly_to_temperature_difference
  }

  TEMPERATURE_MODEL {
    absolute_temperature:
      thermodynamic_temperature_on_kelvin_scale

    Celsius_temperature:
      offset_scale_relative_to_kelvin

    Fahrenheit_temperature:
      affine_scale_with_different_interval_size

    absolute_zero:
      0 K

    CONSTRAINT:
      thermodynamic_absolute_temperature >= 0 K
      under_standard_equilibrium_thermodynamic_interpretation
  }

  HEAT_ENERGY_DISTINCTION_MODEL {
    internal_energy:
      state_function

    heat:
      energy_transfer_across_system_boundary_due_to_temperature_difference

    work:
      other_energy_transfer_mode

    FIRST_LAW:
      delta_U = Q - W_by_system
      UNDER stated_sign_convention

    RULE:
      heat MUST_NOT be treated_as_energy_contained_in_body
      without clarifying informal_usage
  }

  SENSIBLE_HEAT_MODEL {
    CONSTANT_SPECIFIC_HEAT_APPROXIMATION:
      Q = m*c*delta_T

    GENERAL:
      Q = m*integral(c(T) dT)

    CONDITIONS:
      no_phase_change
      applicable_process_and_material_model

    RULE:
      specific_heat MAY depend_on temperature_pressure_and_process_constraint
  }

  LATENT_HEAT_MODEL {
    PHASE_CHANGE:
      Q = m*L_phase

    examples:
      latent_heat_of_fusion
      latent_heat_of_vaporisation
      latent_heat_of_sublimation

    CONDITION:
      phase_transition_context_defined

    RULE:
      temperature_may_remain_approximately_constant_during_phase_change
      while_energy_is_transferred
  }

  CONDUCTION_MODEL {
    FOURIER_LAW:
      q_vector = -k*gradient(T)

    ONE_DIMENSIONAL_STEADY_PLANE_WALL:
      heat_transfer_rate = k*A*(T_hot - T_cold)/L

    THERMAL_RESISTANCE:
      R_cond = L/(k*A)

    CONDITIONS:
      continuum_model
      applicable_conductivity
      defined_geometry

    RULE:
      negative_sign indicates_heat_flow_toward_decreasing_temperature
  }

  CONVECTION_MODEL {
    NEWTON_COOLING:
      heat_transfer_rate = h*A*(T_surface - T_fluid)

    HEAT_FLUX:
      q_double_prime = h*(T_surface - T_fluid)

    RULE:
      h is_effective_context_dependent_coefficient
      not_intrinsic_material_constant
  }

  RADIATION_MODEL {
    STEFAN_BOLTZMANN_SURFACE:
      heat_transfer_rate =
        epsilon*sigma_SB*A*(T_surface^4 - T_surroundings^4)

    PARAMETERS:
      epsilon = emissivity
      sigma_SB = Stefan_Boltzmann_constant

    CONDITIONS:
      absolute_temperature_in_kelvin
      applicable_radiative_exchange_model

    RULE:
      Celsius_or_Fahrenheit MUST_NOT be inserted_directly_into_T_fourth_power_relation
  }

  THERMAL_EXPANSION_MODEL {
    LINEAR:
      delta_L = alpha*L_0*delta_T

    VOLUMETRIC:
      delta_V = beta*V_0*delta_T

    PARAMETERS:
      alpha = linear_thermal_expansion_coefficient
      beta = volumetric_thermal_expansion_coefficient

    CONDITIONS:
      applicable_temperature_range
      material_state_defined
  }

  THERMAL_DIFFUSIVITY_MODEL {
    ENTITY ThermalDiffusivity {
      SYMBOL: alpha_th
      SI_UNIT: square_metre_per_second
      SI_SYMBOL: m^2/s

      RELATION:
        alpha_th = k/(rho*c_p)
    }

    INTERPRETATION:
      rate_at_which_temperature_disturbances_diffuse_through_material
  }

  HEAT_TRANSFER_BALANCE_MODEL {
    system_energy_balance:
      accumulation =
        heat_in - heat_out
        + work_or_other_energy_terms
        + generation
      UNDER defined_sign_convention

    steady_state:
      accumulation = 0

    RULE:
      system_boundary_and_sign_convention MUST be explicit
  }

  ENTROPY_MODEL {
    REVERSIBLE_TRANSFER:
      dS = delta_Q_rev/T

    CLAUSIUS_INEQUALITY:
      entropy_generation >= 0
      for_real_irreversible_processes

    RULE:
      entropy_change_and_heat_transfer
      MUST_NOT be treated_as_semantically_equivalent
  }

  RELATIONSHIPS {
    Temperature -> DRIVES -> HeatTransfer
    TemperatureDifference -> DRIVING_POTENTIAL_FOR -> ThermalTransport
    Heat -> TRANSFERS -> Energy
    HeatCapacity -> RELATES -> HeatAndTemperatureChange
    SpecificHeatCapacity -> MATERIAL_PROPERTY_FOR -> SensibleHeating
    ThermalConductivity -> RELATES -> TemperatureGradientAndHeatFlux
    HeatFlux -> REPRESENTS -> HeatTransferRatePerArea
    HeatTransferCoefficient -> RELATES -> SurfaceTemperatureDifferenceAndConvectiveFlux
    ThermalResistance -> RELATES -> TemperatureDifferenceAndHeatTransferRate
    ThermalDiffusivity -> RELATES -> ConductivityDensityAndSpecificHeat
    Entropy -> RELATES_TO -> ReversibleHeatTransferAndTemperature
  }

  SEMANTIC_EQUIVALENCE {
    "temperature" ~= thermal_temperature WHEN thermal_context
    "kelvin" ~= "K"
    "degree Celsius" ~= "°C"
    "heat flux" ~= heat_transfer_rate_per_unit_area

    heat != temperature
    heat != internal_energy
    heat_capacity != specific_heat_capacity
    thermal_conductivity != thermal_diffusivity
    thermal_resistance != electrical_resistance
    heat_flux != heat_transfer_rate
    entropy != heat
  }

  CONSTRAINTS {
    absolute_temperature_scale_must_be_identified = true
    temperature_difference_and_absolute_temperature_must_be_distinguished = true
    heat_is_energy_transfer_not_state_property = true
    material_properties_require_applicable_conditions = true
    phase_change_context_must_be_preserved = true
    radiation_T_fourth_power_requires_absolute_temperature = true
    heat_flux_and_total_heat_transfer_rate_are_not_semantically_equivalent = true
    system_boundary_and_sign_convention_are_required_for_energy_balance = true
  }

  MEASUREMENT_MODEL {
    TEMPERATURE_INSTRUMENTS:
      thermocouple
      resistance_temperature_detector
      thermistor
      liquid_in_glass_thermometer
      infrared_thermometer
      radiation_pyrometer

    HEAT_AND_FLUX_INSTRUMENTS:
      calorimeter
      heat_flux_sensor
      heat_flow_meter
      thermal_conductivity_apparatus

    RECORD:
      quantity_type
      numerical_value
      unit
      temperature_scale
      absolute_or_difference
      spatial_location
      timestamp
      material
      phase
      pressure_when_relevant
      humidity_when_relevant
      heat_transfer_mode
      system_boundary
      instrument
      sensor_contact_or_noncontact
      calibration_state
      sampling_rate
      response_time
      uncertainty

    UNCERTAINTY:
      thermal_measurement = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF Celsius_temperature_known
      THEN Kelvin_temperature = Celsius_temperature + 273.15

    IF mass_specific_heat_and_temperature_change_known
      AND constant_specific_heat_model_applies
      THEN sensible_heat = mass*specific_heat*temperature_change

    IF mass_and_latent_heat_known
      AND applicable_phase_change_occurs
      THEN phase_change_heat = mass*latent_heat

    IF conductivity_and_temperature_gradient_known
      THEN conductive_heat_flux = -conductivity*temperature_gradient

    IF heat_transfer_coefficient_area_and_surface_fluid_temperature_difference_known
      THEN convective_heat_transfer_rate =
        coefficient*area*temperature_difference

    IF emissivity_area_surface_and_surroundings_absolute_temperatures_known
      THEN net_radiative_heat_transfer_rate =
        emissivity*sigma_SB*area*(T_surface^4 - T_surroundings^4)

    IF thermal_resistance_known AND temperature_difference_known
      AND thermal_resistance != 0
      THEN heat_transfer_rate = temperature_difference/thermal_resistance

    IF conductivity_density_and_specific_heat_known
      AND density != 0 AND specific_heat != 0
      THEN thermal_diffusivity = conductivity/(density*specific_heat)
  }

  REFERENCE_MODEL {
    temperature:
      scale_and_reference_definition_required

    temperature_difference:
      interval_size_and_scale_required

    material_properties:
      temperature_pressure_phase_and_composition_may_be_required

    heat_transfer:
      system_boundary_direction_and_sign_convention_required

    radiation:
      absolute_temperature_required

    RULE:
      missing_reference_or_state_conditions
      reduce_semantic_confidence
  }

  UNCERTAINTY_MODEL {
    sources:
      sensor_calibration
      sensor_resolution
      thermal_contact_resistance
      radiation_error
      conduction_along_sensor_leads
      response_time
      spatial_gradients
      environmental fluctuations
      emissivity_uncertainty
      material_property_uncertainty
      geometry_uncertainty
      model_assumptions

    PROPAGATION:
      derived_thermal_quantity_uncertainty
      <- measurement_material_geometry_and_model_uncertainties
  }

  CONFIDENCE {
    quantity_definition_confidence: 1.00
    SI_unit_confidence: 1.00
    temperature_scale_confidence: 1.00
    heat_transfer_relationship_confidence: 0.99
    material_property_relationship_confidence: 0.98
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when scale, state, material,
      phase, pressure, system boundary, heat transfer mode,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK temperature_scale
    CHECK absolute_vs_difference_temperature
    CHECK heat_vs_internal_energy_semantics
    CHECK heat_capacity_vs_specific_heat_capacity
    CHECK thermal_conductivity_vs_diffusivity
    CHECK heat_flux_vs_total_heat_rate
    CHECK material_temperature_pressure_phase_context
    CHECK phase_change_conditions
    CHECK absolute_temperature_for_radiation
    CHECK system_boundary_and_sign_convention
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      identify_quantity_type
      validate_unit
      identify_temperature_scale_when_relevant
      identify_absolute_or_difference_quantity
      normalize_to_canonical_SI
      preserve_original_value_and_unit
      attach_spatial_location
      attach_timestamp
      identify_material_and_phase
      attach_pressure_when_relevant
      identify_heat_transfer_mode
      attach_system_boundary_when_relevant
      attach_uncertainty
      update_thermal_state

    ON material_state_change:
      update_temperature
      update_pressure
      update_phase
      update_material_properties
      recompute_derived_quantities_when_model_available
      preserve_previous_state

    ON phase_change:
      record_initial_phase
      record_final_phase
      record_latent_heat_transfer
      preserve_transition_conditions

    ON calibration_revision:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_domain: ThermalMeasurements

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_temperature_scale
      distinguish_absolute_from_difference_temperature
      identify_material_and_phase
      identify_temperature_pressure_and_state_conditions
      identify_heat_or_energy_context
      identify_heat_transfer_mode
      identify_geometry_and_system_boundary
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_thermal_relationships

    ambiguity_controls:
      distinguish_temperature_from_heat
      distinguish_heat_from_internal_energy
      distinguish_heat_capacity_from_specific_heat_capacity
      distinguish_thermal_conductivity_from_thermal_diffusivity
      distinguish_heat_flux_from_heat_transfer_rate
      distinguish_thermal_resistance_from_electrical_resistance
      distinguish_absolute_temperature_from_temperature_difference
      distinguish_sensible_heat_from_latent_heat
      preserve_material_phase_pressure_and_reference_conditions
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_thermal_quantity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_domain
      ontology_path
      scope
      temperature_model
      heat_energy_distinction_model
      sensible_heat_model
      latent_heat_model
      conduction_model
      convection_model
      radiation_model
      thermal_expansion_model
      thermal_diffusivity_model
      heat_transfer_balance_model
      entropy_model
      units
      relationships
      constraints
      measurement_model
      reference_model
      uncertainty_model
      reasoning_rules
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      thermal_quantity_model_changes
      heat_transfer_model_changes
      material_property_model_changes
      phase_change_model_changes
      unit_or_scale_model_changes
      measurement_model_changes
      reference_model_changes
      constraint_model_changes
      reasoning_rule_changes
  }

}

END FLOW