feature-kindAvailable
Heat Transfer
rho*Cp*dT/dt - div(k*grad(T)) = Q
Reference contract
| Field | Value | Description |
|---|---|---|
| area | Heat Transfer | — |
| boundaryFeatures | [{"assemblyRole":"none","displayName":"Temperature","entityDimensions":["boundary"],"fields":[{"default":"293.15[K]","name":"value","required":true,"unit":"K","valueType":"expression"}],"kind":"Temperature","multiple":true,"parentCategory":"physics","role":"exclusive"},{"assemblyRole":"none","displayName":"Heat Flux","entityDimensions":["boundary"],"fields":[{"default":"0[W/m^2]","name":"value","required":true,"unit":"W/m^2","valueType":"expression"}],"kind":"Heat Flux","multiple":true,"parentCategory":"physics","role":"contributing"}] | — |
| childCategories | ["physics.domain","physics.boundary"] | — |
| defaultMaterial | null | — |
| displayName | Heat Transfer | — |
| domainFeatures | [{"assemblyRole":"none","displayName":"Heat Source","entityDimensions":["domain"],"fields":[{"default":"0[W/m^3]","name":"value","required":true,"unit":"W/m^3","valueType":"expression"}],"kind":"Heat Source","multiple":true,"parentCategory":"physics","required":false}] | — |
| kind | Heat Transfer | — |
| materialSchema | [{"default":"1[W/(m*K)]","name":"thermalConductivity","rank":"scalar","required":true,"unit":"W/(m*K)"},{"default":"1[kg/m^3]","name":"density","rank":"scalar","required":true,"unit":"kg/m^3"},{"default":"1[J/(kg*K)]","name":"heatCapacity","rank":"scalar","required":true,"unit":"J/(kg*K)"}] | — |
| publishedFields | [{"components":1,"displayName":"Temperature","expression":"ht.T","name":"ht.T","plottable":true,"rank":"scalar","studies":["stationary","transient","sensitivity","optimization"],"unit":"K"},{"components":1,"displayName":"Thermal energy functional","expression":"energy","name":"ht.energy","plottable":true,"rank":"scalar","studies":["stationary","sensitivity","optimization"],"unit":"J"},{"components":1,"displayName":"Thermal compliance","expression":"2*energy","name":"ht.compliance","plottable":true,"rank":"scalar","studies":["stationary","sensitivity","optimization"],"unit":"J"}] | — |
| status | certified | — |
| studies | ["Stationary","Transient","Sensitivity","Optimization","Eigenvalue"] | — |
| studyCapabilities | [{"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":"Heat Transfer sensitivity is disabled until verified per-parameter backend derivative solves are registered."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Heat Transfer optimization is outside the September 2026 classroom support matrix."},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalue","reason":"Heat Transfer eigenvalue analysis has not completed the September 2026 classroom physical-validation gate."}] | — |
| tag | ht | — |
| visible | true | — |
rhoCpdT/dt - div(k*grad(T)) = Q
Contract
| Property | Value |
|---|---|
| area | Heat Transfer |
| boundaryFeatures | [{"assemblyRole":"none","displayName":"Temperature","entityDimensions":["boundary"],"fields":[{"default":"293.15[K]","name":"value","required":true,"unit":"K","valueType":"expression"}],"kind":"Temperature","multiple":true,"parentCategory":"physics","role":"exclusive"},{"assemblyRole":"none","displayName":"Heat Flux","entityDimensions":["boundary"],"fields":[{"default":"0[W/m^2]","name":"value","required":true,"unit":"W/m^2","valueType":"expression"}],"kind":"Heat Flux","multiple":true,"paren... |
| childCategories | ["physics.domain","physics.boundary"] |
| defaultMaterial | null |
| displayName | Heat Transfer |
| domainFeatures | [{"assemblyRole":"none","displayName":"Heat Source","entityDimensions":["domain"],"fields":[{"default":"0[W/m^3]","name":"value","required":true,"unit":"W/m^3","valueType":"expression"}],"kind":"Heat Source","multiple":true,"parentCategory":"physics","required":false}] |
| kind | Heat Transfer |
| materialSchema | [{"default":"1[W/(m*K)]","name":"thermalConductivity","rank":"scalar","required":true,"unit":"W/(m*K)"},{"default":"1[kg/m^3]","name":"density","rank":"scalar","required":true,"unit":"kg/m^3"},{"default":"1[J/(kg*K)]","name":"heatCapacity","rank":"scalar","required":true,"unit":"J/(kg*K)"}] |
| publishedFields | [{"components":1,"displayName":"Temperature","expression":"ht.T","name":"ht.T","plottable":true,"rank":"scalar","studies":["stationary","transient","sensitivity","optimization"],"unit":"K"},{"components":1,"displayName":"Thermal energy functional","expression":"energy","name":"ht.energy","plottable":true,"rank":"scalar","studies":["stationary","sensitivity","optimization"],"unit":"J"},{"components":1,"displayName":"Thermal compliance","expression":"2*energy","name":"ht.compliance","plottable"... |
| status | certified |
| studies | ["Stationary","Transient","Sensitivity","Optimization","Eigenvalue"] |
| studyCapabilities | [{"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":"Heat Tran... |
| tag | ht |
| visible | true |