To reach magnetic fields higher than the ones produced with commercial superconducting magnets, copper alloy coils are developed in high magnetic field facilities. These magnetic fields are made available in a few facilities worldwide. At the high field facility in Grenoble, a DC electrical power of 24 MW permits to reach a steady field of 37 T in a 34 mm diameter bore. An upgrade to 30 MW is foreseen to be operational in 2022.

A high field magnet can be considered as an archetype of a compact heat exchanger with extreme characteristics: heat fluxes up to 10 MW.m^-2 are managed by monophasic water flows with velocities up to 30 m.s^-1 in channels with hydraulic diameters ranging from 200 to 1800 µm. A pressure loss of 20 bars is developed along the associated hydraulic lengths. The resulting heat transfer coefficient at the copper alloy coil wall reaches h=10^5 W.m^-2.K^-1.

In 2018, 15 GWh of energy were injected in the high field magnets in Grenoble. Currently this energy is integrally transformed in waste warm water rejected in the nearby river. One project of the laboratory is to inject these lost calories in the urban heating network of Grenoble. The outlet magnet temperature reaches today 40°C at its maximum and is lower than the temperature needed by the network (~85°C). To enhance the economic model and environmental performances of the waste heat recovery system one solution is to increase the outlet magnet temperature to minimize the electricity costs of the heat pumps. For this purpose, we need:

• to increase h (W.m^-2.K^-1) in the magnet microchannels to avoid overheating of the coils,

• to diminish the water flowrate through the magnet (300 l.s^-1 today).

The characteristics of these machines will be presented as well as the open thermo-hydrodynamics questions related to this project of waste heat recovery. This work is supported by the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02).