Comparing the approaches of the finned surface and the porous body to heat transfer description in cooling systems of laser mirrors and chips

Аuthors

Shanin Y. I.

NII NPO "LUCH", Podolsk, Russia

e-mail: ShaninYuI@sialuch.ru

Abstract

The main task of the mirror consists in redirecting laser radiation while ensuring minimal distortion of the optical surface due to thermal expansion and bending. Laser mirrors cooling is a necessary condition when high coefficients of specular reflectance of the optical surface obtained by advanced technological methods are not enough to reduce to acceptable values the heat fluxes, penetrating the skeleton of the mirror. Various mathematical models have been pro- posed in the literature for the heat-stressed state describing of both uncooled and cooled mirrors. The article regards and compares two analytical mathematical models describing the tempera- ture field in the cooled mirror. The first approach considers the cooling system a structured set of edges of different geometry (stripes, wafers, spikes, etc.), enclosed between a substrate with a smooth surface and the basis of the mirror through which the cooler is pumped. The second mathematical model regards the cooling system as a porous body. The heat flux is supplied from the side of the substrate, the temperature field in the liquid and the cooling system skeleton are assumed one-dimensional along the thickness of the mirror and two-dimensional along its length. Analytic dependences for temperature fields and heat exchange characteristics were ob- tained. The dimensionless temperature fields and heat transfer characteristics were compared under identical loading conditions and boundary conditions. The comparison of results obtained using two computational models was performed for various cooling systems such as channel, wafer, brush for which experimental results on hydraulic resistance, heat transfer, and tempera- ture fields were obtained earlier. The performed comparison revealed that the finned surface ap- proach described more adequately the heat transfer in cooling systems with a structured set of fins with dimensions characteristic for mirrors. In the adduced heat-transfer, it is necessary to account for the heat transfer of the non-finned parts of the substrate and the mirror base. The po- rous body approach is also valid with porous bodies of more complex structures and it gives re- sults comparable with the finned surface approach results. Another object of the obtained results application may be cooled electronic equipment (chips). The chip overheating above certain critical temperature is impermissible. The requirements for mirrors cooling systems are much stricter than these for chips cooling, since the optical surface distortions exceeding laser radia- tion wavelength by more than 5–10% are not allowed.

Keywords:

laser mirror, cooling system, finned surface, porous body, heat transfer, tem- perature distribution.

References

1. Plakseev A.A., Kharitonov V.V. Heat transfer in channels with porous inserts during forced fluid flow. Journal of En- gineering Physics, 1989, vol. 56, no. 1, pp. 26–33. https://doi.org/10.1007/BF00870455

2. Subbotin V.I., Kharitonov V.V. Thermophysics of cooled laser mirrors. High Temperature, 1991, vol. 29, no. 2, pp. 290–302.

3. Apollonov V.V. Power optics. Quantum Electronics, 2014, vol. 44, no. 2, pp. 103–121.

4. Shanin Yu.I., Shanin O.I. Teplootdacha kompaktnykh sis- tem okhlazhdeniya lazernykh zerkal [Heat transfer of a compact cooling system of laser mirrors]. Teplovyye protsessy v tekhnike — Thermal processes in engineering, 2015, vol. 7, no. 4, pp. 166–171. In Russ.

5. Fedoseev V.N., Shanin O.I., Shanin Y.I., Afanasyev V.A. Heat-transfer in rectangular channels with heat-conducting walls in the case of unidirectional heating. High Tempera- ture, 1989, vol. 27, no. 6, pp. 898–904.

6. Shanin Yu.I., Fedoseev V.N., Shanin O.I. Heat transfer in multilayered direct-flow cooling systems with unilat- eral heating. High Temperature, 1991, vol. 29, no. 2, pp. 238–246.

7. Kern D.Q., Kraus A.D. Extended Surface Heat Transfer. New-York: McGraw-Hill Book Company, 1972. 805 p. (Rus. ed. Kern D., Kraus A. Razvityye poverkhnosti teploob- mena, Moscow, Energy, 1977. 464 p.)