18 lines
2.7 KiB
JSON
18 lines
2.7 KiB
JSON
{
|
||
"schemaVersion": "1.1",
|
||
"runId": "orch-1771288051-2d112738",
|
||
"agent": "tech-lead",
|
||
"status": "complete",
|
||
"result": "## Analytical Heat Sink Thermal Analysis\n\n### Given\n- 4 rectangular fins on 50mm × 50mm base\n- Fin height: 25mm, thickness: 1mm, span: 50mm\n- AL6061-T6: k = 167 W/m·K\n- h = 10 W/m²·K (natural convection), Q = 10W, T_amb = 25°C\n\n### Fin Efficiency\n- Fin parameter: m = √(2h/kt) = √(2×10 / 167×0.001) = √119.76 = 10.94 m⁻¹\n- Corrected fin length (accounts for tip): Lc = L + t/2 = 0.025 + 0.0005 = 0.0255 m\n- mLc = 10.94 × 0.0255 = 0.279\n- **η = tanh(mLc) / mLc = 0.2738 / 0.279 = 0.981 (98.1%)**\n\nThe high efficiency is expected — thin aluminum fins with modest convection yield a nearly isothermal fin.\n\n### Surface Areas\n- Per fin (including tip via corrected length): 2 × 0.0255 × 0.05 = 0.00255 m²\n- Total fin area (4 fins): 4 × 0.00255 = 0.01020 m²\n- Unfinned base area: 0.05² − 4×(0.001×0.05) = 0.0025 − 0.0002 = 0.0023 m²\n- Effective convective area: η·A_fin + A_unfinned = 0.981×0.01020 + 0.0023 = 0.01231 m²\n\n### Thermal Resistance\n- **R_conv = 1 / (h · A_eff) = 1 / (10 × 0.01231) = 8.12 °C/W**\n- Base conduction resistance neglected (base thickness not specified; for typical 2-5mm AL6061 base it would add < 0.01 °C/W — negligible)\n\n### Base Temperature\n- **T_base = T_amb + Q · R_total = 25 + 10 × 8.12 = 106.2°C**\n\n### Summary Table\n| Parameter | Value |\n|-----------|-------|\n| Fin efficiency (η) | 98.1% |\n| Thermal resistance (R) | 8.12 °C/W |\n| Base temperature | 106.2°C |\n| Max fin tip temperature | ~104.9°C (η≈0.981 means ~1.3°C gradient along fin) |\n\n### Notes\n- With only 4 fins the total convective area is small, resulting in high thermal resistance. For lower base temperature, increase fin count (e.g., 10-12 fins with ~3mm spacing would roughly halve R).\n- Natural convection h=10 W/m²·K is reasonable for vertical plates in still air. Actual h depends on orientation and fin spacing (chimney effect).\n- Base conduction spreading resistance is negligible for this geometry but should be checked if heat source is localized.",
|
||
"deliverable": {
|
||
"type": "analysis",
|
||
"title": "4-Fin Heat Sink Analytical Thermal Solution",
|
||
"path": null,
|
||
"summary": "Fin efficiency 98.1%, thermal resistance 8.12 °C/W, base temperature 106.2°C for 10W load with natural convection"
|
||
},
|
||
"artifacts": [],
|
||
"confidence": "high",
|
||
"notes": "Classical extended surface (fin) theory used with corrected fin length for tip convection. Base conduction resistance neglected (not specified). Results are for uniform h assumption; real natural convection h varies with fin spacing and orientation.",
|
||
"timestamp": "2026-02-16T19:27:00-05:00"
|
||
}
|