Non-similarity solution approximation to the thermal hydraulic quenchback in superconductors

Using an approximation to the conduction fluid equations, a solution is given using the direct method of integration of a differential equation. This solution establishes a possible increasing relation between the quench velocity and the length of the conductor. Using the direct integration approach in the one-dimensional differential equations, a restrictive fluid velocity expression is obtained which satisfies the initial and boundary conditions. This expression brings about a finish time which is nonincreasing with the length of the conductor. In particular, if a thermohydraulic quenchback mechanism is established in a magnet, the expression suggests that the normal zone will grow faster for longer magnets in a quench event.<>