Tools › Fluids and Heat Transfer › Convection › Electronics Cooling and Heat Sinks › Example
A 25 W TO-247 device on a 100 x 100 x 40 mm aluminium plate-fin heat sink in 40 °C air: sink resistance 1.546 °C/W by natural convection and radiation, junction 110.0 °C
| Tool | Electronics Cooling and Heat Sinks |
| Source | U.S. Department of Defense (1978). Reliability/Design Thermal Applications. MIL-HDBK-251, 19 January 1978, paragraphs 8.1 to 8.3 (thermal circuit, Figures 12, 14 and 28; Examples 8-4 to 8-9); Bar-Cohen, A., and Rohsenow, W. M. (1984). Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates. Journal of Heat Transfer, Vol. 106, pp. 116-123. |
| Level | Professional |
Problem
A TO-247 power device dissipating 25 W, with a junction-to-case resistance of 0.6 °C/W, a case-to-sink interface of 0.5 °C/W and a rated junction temperature of 150 °C, is mounted at the centre of an anodized aluminium heat sink 100 mm wide and 100 mm long with twelve fins 32 mm high and 2 mm thick on an 8 mm base (conductivity 200 W/(m K), emissivity 0.85). The fins are vertical in still air at 40 °C at sea level. Find the sink-to-ambient resistance, the sink, case and junction temperatures, the margin to the rating, the sink resistance the device requires, the spreading resistance of the base under the 16 x 21 mm footprint and the fin count that gives the lowest resistance.
Inputs to Enter
- Air 40 °C, altitude 0; one part: 25 W, junction to case 0.6 °C/W, case to sink 0.5 °C/W, maximum junction 150 °C, on the shared sink
- Spreading included, source 16 x 21 mm; cooling: natural convection and radiation, fins vertical
- Sink: width 100 mm, length 100 mm, fin height 32 mm, base 8 mm, 12 fins of 2 mm, conductivity 200 W/(m K), emissivity 0.85
Answers
- Fin spacing (100 - 12 x 2)/11 = 6.909 mm; Elenbaas number 51.39 at a rise of 38.64 °C; channel Nusselt number 1.271 (Bar-Cohen and Rohsenow; Elenbaas 1.262), channel coefficient 5.287 W/(m2 K), outer faces 5.912 W/(m2 K), fin efficiency 0.9905; optimum spacing of thin fins 7.003 mm
- Channel radiation: view factors 0.0329 (tip to end) and 0.0068 (end to end), channel-to-opening factor 0.1466, apparent emissivity of the openings 0.894
- Heat balance at the solved temperature: convection 18.10 W (base strips 1.553, inner fins 13.356, end fins 2.828, base edges 0.366), radiation 6.898 W (channels 3.602, outer surfaces 3.297), total 25.000 W
- Sink temperature 78.64 °C, sink-to-ambient resistance 1.546 °C/W at this power
- Base under the source (equivalent radii 10.34 and 56.42 mm): exact series 0.1554 °C/W average and 0.1852 °C/W at the centre; closed form of Lee and co-authors 0.1460 and 0.1813 °C/W (6.1 % and 2.1 % low)
- Case 95.0 °C, junction 40 + 25 x (0.6 + 0.5 + 0.1554 + 1.546) = 110.0 °C, margin +40.0 °C to 150 °C; the device needs a sink of 3.145 °C/W or better
- Fin-count sweep at the same power and fin thickness: lowest resistance 1.533 °C/W at 11 fins
Notes
The tool's default inputs are this sink; press Submit. The sink is illustrative (stated on the method page), not a published example. The method is checked by test_heat_sink_electronics_cooling.php (494 checks) against seven worked examples of MIL-HDBK-251 reproduced to the printed digits (the composite bar of p. 52 and Examples 8-4 to 8-9, pp. 59 to 106), its Tables IV, V and XV, the analytical limits of the channel relation, and an independent numpy / scipy implementation on the default, 20 seeded sinks, forced-convection and fan cases (References/Electronics-Cooling/checks/).