Physical Transformation AtlasPTA
Pathway · p-bb4081c0b9 · demonstrated

Heat exchanger

Temperature gradientHeat conductionHeat flowUseful heat

Heat conducts through a wall from the hot stream to the cold one.

Epistemic state of the route

known constituent relations
3 / 3 established or replicated · weakest constituent established
constituent maturity floor
K4 · experimentally observed
search for this exact route
A recorded pathway or a reviewed search records a demonstration of this composition.
recorded pathway
Heat exchanger · commercial
composition maturity
K8 · commercial technology
recorded-pathway overlap
this route is the recorded pathway Heat exchanger
route-level evidence
1 source for the complete composition · 1 cited by the constituent steps
boundaries and interfaces
BOUNDARY compatible · no region transition

Explorematrix context · physics checks · performance · steps · route evidence · constituent evidence · cite

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

No coupling family recorded for this route's phenomena.

Measured or reported performance

Summary figures only; no datum-level record yet. Each figure below is a reviewed summary, not a single measurement.

notes
effectiveness 0.6–0.95 for counterflow designs; no thermodynamic ceiling on heat delivered, only on its temperature

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

  • Carnot limit · formula-bound · hard, filtered out by its applicability
    η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c

Steps

  1. 01
    thermal → thermal
    q = −κ · ∇T · thermal conductivity κ [W/(m K)]
    refs [1]
  2. 02
    Heat conduction —produces→ Heat flowestablishedclaim record
    thermal → thermal
    refs [1]
  3. 03
    Heat flow —converts into→ Useful heatestablishedclaim record
    thermal → thermal
    • heat delivered at a temperature above the point of use
    refs [1]

Evidence for the complete composition · 1

  1. [1]
    A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)
    Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record

Evidence for the constituent relations · 1

  1. [1]
    A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)
    Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record

Cite this route

Physical Transformation Atlas (2026). route p-bb4081c0b9: Heat exchanger. Dataset revision rbfbfcbb70e57 (hash of the canonical data). https://physical-transformation-atlas.wldud5192.workers.dev/path/bb4081c0b9

Ids and matrix addresses are stable across revisions; the revision hash identifies the exact canonical files the record was compiled from and is meta.data_hash in every /api export. Reuse terms: see the license field in any export.