Heat Transfer and Cooling Techniques at Low Temperature

The first part of this chapter gives an introduction to heat transfer and cooling techniques at low temperature. We review the fundamental laws of heat transfer (conduction, convection and radiation) and give useful data specific to cryogenic conditions (thermal contact resistance, total emissivity of materials and heat transfer correlation in forced or boiling flow for example) used in the design of cooling systems. In the second part, we review the main cooling techniques at low temperature, with or without cryogen, from the simplest ones (bath cooling) to the ones involving the use of cryocoolers without forgetting the cooling flow techniques.Comment: 24 pages, contribution to the CAS-CERN Accelerator School: Superconductivity for Accelerators, Erice, Italy, 24 April - 4 May 2013, edited by R. Baile

Superfluid Helium Flow in Porous Media

Superfluid helium is primarily used in the field of applied superconductivity. Given the complexity of the magnet geometry and the scales involved, a real 3D simulation of heat transfer in such devices at the micro-channel scale is very difficult, even impossible. However, the repeatability or even periodicity of the structure suggests the possibility of a macro-scale description following a porous medium approach. Which macro-scale model may be used? This largely remains an open field while some answers have been proposed based on experimental or theoretical work

Investigation of suitability of the method of volume averaging for the study of heat transfer in superconducting accelerator magnet cooled by superfluid helium.

In the field of applied superconductivity, there is a growing need to better understand heat transfers in superconducting accelerator magnets. Depending on the engineering point of view looked at, either 0-D, 1-D, 2D or 3D modeling may be needed. Because of the size of these magnets, alone or coupled together, it is yet, impossible to study this numerically for computational reasons alone without simplification in the description of the geometry and the physics. The main idea of this study is to consider the interior of a superconducting accelerator magnet as a porous medium and to apply methods used in the field of por-ous media physics to obtain the equations that model heat transfers of a superconducting accelerator magnet in different configurations (steady-state, beam losses, quench, etc.) with minimal compromises to the physics and geometry. Since the interior of a superconducting magnet is made of coils, collars and yoke filled with liquid helium, creating channels that interconnect the helium inside the magnet, an upscaling method provides models that describe heat transfer at the magnet scale and are suitable for numerical studies. This paper presents concisely the method and an example of application for super-conducting accelerator magnet cooled by superfluid helium in the steady-state regime in considering the thermal point of view