Transient Heat Problem

This section presents the Heat Equation and the associated test cases:

The temperature is a constraint to make electro-magnets :

For resistive magnet : the Joule’s Effect disspates a part of electric energy to heat. This heat increases the temperature of matters and can melt or broke it, like in this photo :

For proper functioning, it need to cooling resistive magnet with cooling water : the laboratory have cooling system with two cycles, the first cycles take water to the Drac river and free water to Isère river. The hydrography of location of LNCMI is exceptional. The water of first cycle is cooling with heat exchanger. The fist cycle cooling the water of second cycle which demineralized to prevent electrolise of copper of electromagnet.

The water of second cycle is in direct contact of electromagnet : * For Helix : the water pass between the helix. * For Bitter : the water pass by holes provided for this purpose.

For superconudctor magnet : the superconductor matters loses its property of non-resistance for great temperature. For HTS (High temperature superconductor), this temperature is \(77 \, K\). To reach this temperature, the experimenters use nitrogen liquid (liquefaction temperature \(77 \, K\)) and helium liquid (liquefaction temperature\(4 K\)).