ReferenceAvailable
Heat Transfer
Three-dimensional stationary and transient heat conduction.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"HeatTransferCoupledAdapter","certification":"Certified scalar conductivity and capacity operators assembled as a monolithic graph residual.","checkpointing":true,"dynamic_state_schema":false,"execution_backend":"telion-v2-shared-execution","gradient_channels":["heat.materials","heat.coordinates","heat.inputs"],"history_depth":2,"history_jacobian_owner":"HeatTransferCoupledAdapter","jacobian_owner":"HeatTransferCoupledAdapter","nonlinear_solver":"CoupledNewtonSession","output_vjp_owner":"HeatTransferCoupledAdapter","requires_spatial_mesh":true,"residual_owner":"HeatTransferCoupledAdapter","runtime":"telion-coupled-graph","state_fields":["ht.T"],"supported_integrators":["BDF1","BDF2"]} | — |
| differentiable_runtime | {"certification":"HeatTransferScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["thermalConductivity"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["ht.T"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["ht.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["ht.compliance"],"value_kind":"scalar-global"}],"residual_owner":"HeatTransfer.element_residual","state_fields":["T"],"supported_objective_symbols":{"coordinate":["ht.T","ht.energy","ht.compliance"],"material":["ht.T","ht.energy","ht.compliance"],"topology":["ht.T","ht.energy","ht.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | rho*Cp*dT/dt - div(k*grad(T)) = Q | — |
| frequency_domain_runtime | null | — |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","transient"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"Scalar elliptic adjoint solve supports temperature expression objectives and material-coefficient sensitivities.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"ht.T","complexValued":false,"componentDescriptions":["Temperature"],"componentNames":["T"],"componentSymbols":["ht.T"],"components":1,"description":"Absolute temperature field.","differentiability":"exact-ad","displayName":"Temperature","finiteElementSpace":"H1-P1","initialValue":"293.15[K]","location":"node","name":"T","namingPolicy":"fixed","quantityId":"ht.T","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"HeatTransfer.element_residual"},"symbolPattern":null,"unit":"K"}] | — |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: exact affine Dirichlet temperature field on a tetrahedral block"},{"certified":true,"differentiability":"exact-ad","kind":"transient","reason":"september-2026-classroom verified contract: analytical sine-mode spatial convergence and second-order variable-step temporal convergence"},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Optimization is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalue","reason":"Eigenvalue is unavailable for this physics interface."}] | — |
| transient_runtime | {"capacity_properties":["density","heatCapacity"],"certification":"HeatTransferScalarCapacityBdfRuntime","checkpointing":true,"design_properties":["thermalConductivity","density","heatCapacity"],"design_property_conditions":{},"design_vjp_owner":"HeatTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates","parameter","material","input","capacity","initial"],"gradient_vjp_owner":"HeatTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"HeatTransientTopologyRuntime","observation_vjp_owner":"HeatTransientTopologyRuntime","residual_linearization_owner":"HeatTransientTopologyRuntime","runtime":"scalar-capacity-bdf","state_fields":["T"],"state_reconstruction_owner":"HeatTransientTopologyRuntime","supported_integrators":["BDF1","BDF2"],"supported_observation_symbols":["ht.T"],"time_derivative_orders":{"T":1},"topology_gradient":true,"transpose_solve_owner":"HeatTransientTopologyRuntime"} | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(ht.T)), thermalConductivity*grad(ht.T)) - test(ht.T)*heatSource","name":"ht.conduction","test_field":"ht.T"}] | — |
| category | Heat Transfer | — |
| description | Three-dimensional stationary and transient heat conduction. | — |
| dimensions | [3] | — |
| display_name | Heat Transfer | — |
| kind | Heat Transfer | — |
| namespace | ht | — |
| status | certified | — |
| visible | true | — |
Three-dimensional stationary and transient heat conduction.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"HeatTransferCoupledAdapter","certification":"Certified scalar conductivity and capacity operators assembled as a monolithic graph residual.","checkpointing":true,"dynamic_state_schema":false,"execution_backend":"telion-v2-shared-execution","gradient_channels":["heat.materials","heat.coordinates","heat.inputs"],"history_depth":2,"history_jacobian_owner":"HeatTransferCoupledAdapter","jacobian_owner":"HeatTransfer... |
| differentiable_runtime | {"certification":"HeatTransferScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["thermalConductivity"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum... |
| dynamic_outputs | [] |
| equation_summary | rho*Cp*dT/dt - div(k*grad(T)) = Q |
| frequency_domain_runtime | null |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","transient"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"Scalar elliptic adjoint solve supports temperature expression objectives and material-coefficient sensitivities.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"ht.T","complexValued":false,"componentDescriptions":["Temperature"],"componentNames":["T"],"componentSymbols":["ht.T"],"components":1,"description":"Absolute temperature field.","differentiability":"exact-ad","displayName":"Temperature","finiteElementSpace":"H1-P1","initialValu... |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: exact affine Dirichlet temperature field on a tetrahedral block"},{"certified":true,"differentiability":"exact-ad","kind":"transient","reason":"september-2026-classroom verified contract: analytical sine-mode spatial convergence and second-order variable-step temporal convergence"},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivi... |
| transient_runtime | {"capacity_properties":["density","heatCapacity"],"certification":"HeatTransferScalarCapacityBdfRuntime","checkpointing":true,"design_properties":["thermalConductivity","density","heatCapacity"],"design_property_conditions":{},"design_vjp_owner":"HeatTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates","parameter","material","input","capacity","initial"],"gradient_vjp_owner":"HeatTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_... |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(ht.T)), thermalConductivity*grad(ht.T)) - test(ht.T)*heatSource","name":"ht.conduction","test_field":"ht.T"}] |
| category | Heat Transfer |
| description | Three-dimensional stationary and transient heat conduction. |
| dimensions | [3] |
| display_name | Heat Transfer |
| kind | Heat Transfer |
| namespace | ht |
| status | certified |
| visible | true |