Heat Ontology

# Heat Ontology — Flow Algebra

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

FLOW HeatOntology {

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

  PURPOSE:
    Represent heat as energy transferred across a system boundary because of a temperature difference, including sensible and latent heat, conduction, convection and radiation, heat transfer rate, heat flux, thermodynamic sign conventions, units, dimensional structure, calorimetric measurement, uncertainty, and distinctions from temperature, internal energy and thermal energy stored in a system.

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

    DEFINITION:
      heat := energy_transferred_across_system_boundary_due_to_temperature_difference

    PROPERTIES:
      is_scalar_transfer_quantity
      has_value
      has_unit
      has_dimension
      has_direction_of_transfer_by_sign_convention
      is_process_dependent
      is_not_state_function
      may_be_transferred_by_multiple_modes
      may_have_uncertainty
  }

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

    RELATION:
      temperature_difference -> thermodynamic_driving_condition_for_heat_transfer
  }

  ENTITY InternalEnergy {
    TYPE: ThermodynamicStateQuantity
    SYMBOL: U
    DIMENSION: M*L^2*T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    RELATION:
      heat_transfer MAY change_internal_energy
  }

  ENTITY HeatTransferRate {
    TYPE: PowerQuantity
    SYMBOL: Q_dot
    DIMENSION: M*L^2*T^-3
    SI_UNIT: watt
    SI_SYMBOL: W

    RELATION:
      Q_dot = dQ/dt
  }

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

    RELATION:
      heat_transfer_rate = surface_integral(heat_flux dot dA)
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: joule
      symbol: J
    }

    COMMON_ALTERNATIVES {
      kilojoule
      megajoule
      calorie
      kilocalorie
      British_thermal_unit
      therm
    }

    POWER_RATE_UNIT:
      watt = joule_per_second

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

  CLASSIFICATION {
    by thermal_effect:
      sensible_heat
      latent_heat

    by transfer_mode:
      conductive_heat
      convective_heat
      radiative_heat

    by system direction:
      heat_into_system
      heat_out_of_system

    by process:
      isothermal_heat_transfer
      nonisothermal_heat_transfer
      phase_change_heat_transfer
  }

  HEAT_INTERNAL_ENERGY_DISTINCTION_MODEL {
    heat:
      boundary_transfer_quantity

    internal_energy:
      system_state_function

    RULE:
      a_system_contains_internal_energy
      but_in_formal_thermodynamics_does_not_contain_heat_as_state_property

    CONSTRAINT:
      informal_phrase "heat stored"
      SHOULD be interpreted_as thermal_or_internal_energy
      unless process_context_explicitly_defines_heat_transfer
  }

  FIRST_LAW_MODEL {
    SIGN_CONVENTION_A:
      delta_U = Q - W_by_system

    WHERE:
      Q > 0 means_heat_added_to_system
      W_by_system > 0 means_work_done_by_system

    ALTERNATIVE_CONVENTIONS:
      permitted_if_explicitly_declared

    RULE:
      sign_convention MUST be preserved
      before combining_heat_work_and_internal_energy
  }

  SENSIBLE_HEAT_MODEL {
    CONSTANT_SPECIFIC_HEAT:
      Q = m*c*delta_T

    GENERAL:
      Q = m*integral_T1_to_T2(c(T) dT)

    PARAMETERS:
      m = mass
      c = specific_heat_capacity

    CONDITIONS:
      no_phase_change
      applicable_process_constraint
      material_state_defined

    RULE:
      specific_heat_capacity MAY depend_on temperature_pressure_and_process
  }

  LATENT_HEAT_MODEL {
    PHASE_CHANGE:
      Q = m*L_phase

    TYPES:
      latent_heat_of_fusion
      latent_heat_of_vaporisation
      latent_heat_of_sublimation

    CONDITIONS:
      phase_transition_defined
      appropriate_pressure_or_state_condition

    RULE:
      energy_transfer_can_occur_with_little_or_no_temperature_change_during_phase_transition
  }

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

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

    THERMAL_RESISTANCE:
      R_cond = L/(k*A)

    ALTERNATIVE:
      Q_dot = delta_T/R_cond

    CONDITIONS:
      applicable_continuum_model
      defined_geometry
      thermal_conductivity_known
  }

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

    HEAT_FLUX:
      q_double_prime = h*(T_surface - T_fluid)

    PARAMETERS:
      h = heat_transfer_coefficient

    RULE:
      h is_effective_context_dependent_parameter
      and_not_intrinsic_material_constant
  }

  RADIATION_MODEL {
    NET_GREY_SURFACE_APPROXIMATION:
      Q_dot =
        epsilon*sigma_SB*A*(T_surface^4 - T_surroundings^4)

    REQUIRE:
      absolute_temperature_in_kelvin
      emissivity
      radiating_area
      applicable_view_and_environment_model

    RULE:
      Celsius_or_Fahrenheit MUST_NOT be inserted_directly_into_fourth_power_temperature_relation
  }

  HEAT_TRANSFER_RATE_MODEL {
    INSTANTANEOUS:
      Q_dot = dQ/dt

    CONSTANT_RATE:
      Q = Q_dot*delta_t

    VARIABLE_RATE:
      Q = integral(Q_dot dt)

    RULE:
      heat_and_heat_transfer_rate
      MUST_NOT be treated_as_semantically_equivalent
  }

  HEAT_FLUX_MODEL {
    VECTOR_OR_NORMAL_FLUX:
      q_double_prime_vector

    TOTAL_RATE:
      Q_dot = surface_integral(q_double_prime_vector dot dA)

    UNIFORM_NORMAL_CASE:
      Q_dot = q_double_prime*A

    RULE:
      heat_flux_and_total_heat_transfer_rate
      MUST_NOT be treated_as_identical
  }

  CALORIMETRY_MODEL {
    principle:
      infer_heat_transfer_from_measured_temperature_or_phase_changes
      using_known_heat_capacity_or_calorimeter_calibration

    SIMPLE_BODY:
      Q = m*c*delta_T

    ENERGY_BALANCE:
      sum(heat_transfers) = 0
      FOR ideal_thermally_isolated_calorimeter
      under_consistent_sign_convention

    REQUIRE:
      calorimeter_heat_capacity
      material_heat_capacity
      losses_or_corrections
      initial_and_final_states
  }

  RELATIONSHIPS {
    Heat -> TRANSFERS -> Energy
    Heat -> HAS_DIMENSION -> M*L^2*T^-2
    Heat -> MEASURED_IN -> Joule
    TemperatureDifference -> DRIVES -> HeatTransfer
    HeatTransferRate -> RATE_OF -> HeatTransfer
    HeatFlux -> HEAT_TRANSFER_RATE_PER -> Area
    SensibleHeat -> RELATES -> MassSpecificHeatAndTemperatureChange
    LatentHeat -> RELATES -> MassAndPhaseChange
    ThermalConductivity -> RELATES -> TemperatureGradientAndConductiveHeatFlux
    HeatTransferCoefficient -> RELATES -> ConvectiveHeatFluxAndTemperatureDifference
    HeatTransfer -> MAY_CHANGE -> InternalEnergy
  }

  SEMANTIC_EQUIVALENCE {
    "heat transfer" ~= heat WHEN formal_thermodynamic_context
    "joule" ~= "J"
    "heat flow rate" ~= heat_transfer_rate
    "thermal flux" ~= heat_flux WHEN heat_transfer_context

    heat != temperature
    heat != internal_energy
    heat != thermal_energy_state
    heat != heat_transfer_rate
    heat_flux != heat_transfer_rate
    sensible_heat != latent_heat
  }

  CONSTRAINTS {
    heat_is_energy_transfer_not_state_property = true
    dimensional_formula = M*L^2*T^-2
    SI_unit = J
    system_boundary_must_be_defined_for_formal_heat_transfer = true
    sign_convention_must_be_preserved = true
    heat_and_temperature_are_not_semantically_equivalent = true
    heat_and_internal_energy_are_not_semantically_equivalent = true
    heat_and_heat_transfer_rate_are_not_semantically_equivalent = true
    radiation_temperature_must_use_absolute_scale = true
    phase_change_context_must_be_preserved_for_latent_heat = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Heat

    COMMON_METHODS:
      calorimetry
      heat_flux_integration
      power_time_integration
      sensible_heat_inference
      latent_heat_inference
      energy_balance

    COMMON_INSTRUMENTS:
      calorimeter
      differential_scanning_calorimeter
      heat_flux_sensor
      heat_flow_meter
      temperature_sensors
      power_meter

    RECORD:
      numerical_value
      unit
      heat_transfer_direction
      sign_convention
      system_boundary
      initial_state
      final_state
      material
      mass
      phase
      temperature_initial
      temperature_final
      pressure_when_relevant
      transfer_mode
      time_interval
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_heat = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF mass_specific_heat_and_temperature_change_known
      AND applicable_sensible_heat_model
      THEN heat = mass*specific_heat*temperature_change

    IF mass_and_latent_heat_known
      AND applicable_phase_change_occurs
      THEN heat = mass*latent_heat

    IF heat_transfer_rate_known_as_function_of_time
      THEN heat = integral(heat_transfer_rate, time)

    IF constant_heat_transfer_rate_known AND time_interval_known
      THEN heat = heat_transfer_rate*time_interval

    IF heat_flux_field_known_over_surface_and_time
      THEN heat =
        integral_over_time(surface_integral(heat_flux dot dA))

    IF conductivity_geometry_and_temperature_difference_known
      AND one_dimensional_steady_conduction_model_applies
      THEN heat_transfer_rate =
        conductivity*area*temperature_difference/length

    IF convection_coefficient_area_and_temperature_difference_known
      THEN convective_heat_transfer_rate =
        coefficient*area*temperature_difference

    IF emissivity_area_and_absolute_temperatures_known
      AND radiation_model_applies
      THEN radiative_heat_transfer_rate =
        emissivity*sigma_SB*area*(T_surface^4 - T_surroundings^4)

    IF heat_and_work_known
      AND first_law_sign_convention_defined
      THEN infer_internal_energy_change
  }

  SYSTEM_BOUNDARY_MODEL {
    REQUIRE:
      system
      surroundings
      boundary
      heat_transfer_direction
      other_energy_transfer_modes

    OPEN_SYSTEM:
      may_include_mass_energy_transport

    CLOSED_SYSTEM:
      no_mass_crosses_boundary

    ISOLATED_SYSTEM:
      no_heat_work_or_mass_energy_transfer

    RULE:
      heat_transfer statement MUST identify_or_imply system_boundary
  }

  SIGN_MODEL {
    common_convention:
      Q_positive -> heat_into_system
      Q_negative -> heat_out_of_system

    alternative_convention:
      allowed_if_explicit

    RULE:
      never_combine_heat_values_with_different_sign_conventions_without_normalisation
  }

  UNCERTAINTY_MODEL {
    sources:
      mass_measurement
      temperature_measurement
      specific_heat_capacity
      latent_heat
      heat_loss
      calorimeter_constant
      heat_flux_sensor_calibration
      area
      time
      emissivity
      convection_coefficient
      thermal_conductivity
      model_assumptions

    PROPAGATION:
      derived_heat_uncertainty
      <- measurement_material_geometry_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    first_law_relationship_confidence: 1.00
    heat_transfer_model_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when system boundary, sign convention,
      material state, phase, transfer mode, temperature,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK system_boundary
    CHECK sign_convention
    CHECK heat_vs_internal_energy_distinction
    CHECK heat_vs_temperature_distinction
    CHECK heat_vs_heat_transfer_rate_distinction
    CHECK heat_flux_vs_total_rate_distinction
    CHECK sensible_vs_latent_heat_context
    CHECK material_and_phase_conditions
    CHECK absolute_temperature_for_radiation
    CHECK applicable_heat_transfer_model
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_system_boundary
      identify_sign_convention
      identify_transfer_direction
      identify_heat_type
      identify_transfer_mode
      attach_initial_and_final_states
      attach_material_mass_phase_and_temperature
      attach_pressure_when_relevant
      attach_time_interval
      normalize_to_joule
      preserve_original_value_and_unit
      attach_uncertainty
      update_heat_transfer_state

    ON thermal_state_change:
      update_temperature
      update_phase
      update_material_properties
      recompute_sensible_or_latent_heat_when_model_available
      preserve_previous_state

    ON transfer_mode_change:
      update_conduction_convection_or_radiation_model
      recompute_heat_rate
      integrate_heat_over_time_when_required
      preserve_transfer_provenance

    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: Heat
    canonical_symbol: Q
    canonical_dimension: M*L^2*T^-2
    canonical_SI_unit: J

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_system_boundary
      identify_sign_convention
      identify_transfer_direction
      identify_sensible_or_latent_context
      identify_conduction_convection_or_radiation
      identify_material_mass_phase_and_temperature
      identify_initial_and_final_states
      identify_heat_rate_or_flux_context
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_energy_transfer_relationships

    ambiguity_controls:
      distinguish_heat_from_temperature
      distinguish_heat_from_internal_energy
      distinguish_heat_from_stored_thermal_energy
      distinguish_heat_from_heat_transfer_rate
      distinguish_heat_flux_from_total_heat_rate
      distinguish_sensible_from_latent_heat
      distinguish_heat_into_system_from_heat_out_of_system
      preserve_system_boundary_sign_convention_and_process_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_thermal_heat_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      heat_internal_energy_distinction_model
      first_law_model
      sensible_heat_model
      latent_heat_model
      conduction_model
      convection_model
      radiation_model
      heat_transfer_rate_model
      heat_flux_model
      calorimetry_model
      system_boundary_model
      sign_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      heat_transfer_semantics_change
      first_law_or_sign_model_changes
      sensible_or_latent_heat_model_changes
      conduction_convection_or_radiation_model_changes
      measurement_model_changes
      system_boundary_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW