# Slotted heater, regenerator and cooler liner for a 2 in hot spool (Ø48.00 / Ø40.00)

> How do I put a real heater, regenerator and cooler inside a single tri-clamp hot tube?

- Category: Hardware › Stirling & thermoacoustic
- Kind: Hardware
- Basis: Design values; slot heat transfer and friction from the laminar rectangular-duct values (Shah & London) and the cycle model on the engine pages
- Page: https://xemstudio.com/objects/stirling-slotted-regenerator-liner/ · JSON: https://xemstudio.com/api/geometry?object=stirling-slotted-regenerator-liner · Plain text: https://xemstudio.com/objects/stirling-slotted-regenerator-liner/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

**Exact dimensions.** Every file is drawn at true size with no printing tolerance. The holes and pins that meet another part are listed below under Mating features, with the fit each joint needs; open those by your printer's or process's clearance before making the part.

## Notes

- The displacer runs in the liner's Ø40.00 bore. The gas does not go round the displacer: it goes out through the liner, along 120 slots 0.5 wide and 3 deep cut in its outside under the flame (the heater), through the annular screen stack on its Ø42 neck (the regenerator), along the same slots under the water jacket (the cooler) and in through 16 ports at the cold end.
- The slots' fin tips are Ø48.00, a press fit in the finished bore, so the heat crosses from the spool wall into the fins. Heater 50 mm, regenerator 40 mm, cooler 45 mm.
- Slot gas volume: heater 9.0 mL, cooler 8.1 mL. Wetted area: about 42 cm² in each of heater and cooler, against about 75 cm² of plain bore.
- Fitting: the screen stack goes on the neck first, then the liner is pressed (or shrunk) into the hot spool until its feet touch the floor; the cold end then sits 1.95 mm inside the face, where the Type B gasket's lip holds it.

## Mating features (exact size; open press / slide / run / socket by your process clearance, leave designed and clamp as drawn)

| feature | exact | mates with | fit | files |
|---|---|---|---|---|
| cold ring OD | Ø48.00, z 1.95–5 | hot-spool finished bore | slide | all |
| fin tips | Ø48.00, 120 slots 0.5 wide, z 9–54 and 94–144 | hot-spool finished bore (the heat path) | press | all |
| regenerator neck | Ø42.00 × 40 | screen stack bore | slide | all |
| bore | Ø40.00 × 145.45 | displacer land Ø40.00 | run | all |
| cold end face | annulus Ø40–Ø48 at z 1.95 | Type B gasket lip (holds the liner) | designed | all |
| feet | 3 × 4 wide, to z 149.4 | hot-spool floor | designed | all |

## Sizes

| zone | z from the spool face | size |
|---|---|---|
| cold ring | 1.95–5 | Ø48.00 (slide) |
| plenum + ports | 5–9 | Ø44, 16 × Ø3 at z 7 |
| cooler slots | 9–54 | 120 × 0.5 × 3, tips Ø48.00 |
| regenerator neck | 54–94 | Ø42.00 |
| heater slots | 94–144 | 120 × 0.5 × 3, tips Ø48.00 |
| hot plenum | 144–147.4 | Ø44 |
| feet | 147.4–149.4 | 3 × 4 wide |
| bore |  | Ø40.00 (displacer land: run) |

## Where the files are

- Academic Press (R. K. Shah, A. L. London): [Laminar Flow Forced Convection in Ducts (1978): fRe of rectangular ducts](https://doi.org/10.1016/C2013-0-06152-X) — book — book; correlation cited (verify at link)
- Ohio University (I. Urieli): [Stirling cycle machine analysis (after Urieli & Berchowitz, Stirling Cycle Engine Analysis, 1984): Schmidt and simple analyses, wire-screen regenerator friction fr = 54 + 1.43 Re^0.78 and St = 0.46 Re^−0.4 / Pr](https://www.ohio.edu/mechanical/stirling/) — web — university course pages (verify at link)
- NASA (W. R. Martini): [Stirling Engine Design Manual, 2nd edition, NASA CR-168088 (1983): decoupled second-order losses (shuttle, conduction, flow friction, regenerator)](https://ntrs.nasa.gov/citations/19830022057) — PDF — US government report
- Cambridge University Press (J. R. Senft): [Mechanical Efficiency of Heat Engines (2007): shaft work = E·W − (1/E − E)·W_forced](https://doi.org/10.1017/CBO9780511546105) — book — book; formula cited (verify at link)
- Long Earth Society: [Engine builds](https://longearthsociety.com/engineering/) — web, video — LES site

## Free STEP/STL (1 parts, CC BY 4.0, Xem Studio)

Index: https://xemstudio.com/files/hardware/stirling-slotted-regenerator-liner/index.json

- liner-2in-slotted-48-40: [STEP](https://xemstudio.com/files/hardware/stirling-slotted-regenerator-liner/liner-2in-slotted-48-40.step) · [STL](https://xemstudio.com/files/hardware/stirling-slotted-regenerator-liner/liner-2in-slotted-48-40.stl) — slotted heater / regenerator / cooler liner for the Ø48.00 hot spool: bore Ø40.00 × 145.45; cold ring Ø48.00; plenum Ø44 with 16 × Ø3 ports; cooler and heater: 120 slots 0.5 wide from the Ø48.00 tips to the Ø42.00 root (45 and 50 long); regenerator neck Ø42.00 × 40; three 4 mm feet

## Questions

**Why slots and not the plain annular gap?**

A plain 0.5 mm gap on a Ø48 bore has about a fifth of the wetted area; with air at a charge the cooler then runs far above the water temperature.

**What does the press fit do?**

It is the heat path from the spool wall into the fins. The engine numbers assume 5000 W/(m²·K) at the fin tips.

## Fits with

- [2 in × 152.4 mm closed-end hot spool, bore finished Ø48.00](https://xemstudio.com/objects/tri-clamp-closed-hot-spool-bored/)
- [Annular regenerator screen stack, Ø48 / Ø42 × 40 (50 mesh × 0.22 mm wire)](https://xemstudio.com/objects/stirling-annular-screen-stack/)
- [Clearance-seal displacer for a Ø40 liner: Ø40.00 running land, Ø38.50 body, 106 long](https://xemstudio.com/objects/stirling-clearance-seal-displacer/)
- [Build list: Tri-clamp horizontal gamma generator, 2 in, chargeable](https://xemstudio.com/objects/list-tri-clamp-horizontal-gamma/)
- [Build list: Tri-clamp charged beta, 2 in](https://xemstudio.com/objects/list-tri-clamp-charged-beta/)