Two models are used for the calculations: the point-dipole model of a magnet [1–3] (model 1) and the exact cylindrical magnet model [4, 5] (model 2).
The cylindrical magnet model contains a double integral; therefore, calculation is very slow.
The results of both models coincide when and both equal 1.6.
= pipe length,
= outer diameter of the pipe,
= thickness of the pipe wall,
= radius of the magnet,
= height of the magnet,
= volume of the magnet,
= remnant field.
, terminal velocity,
, drag coefficient for infinite pipe (point-dipole models),
, , inner and outer radius of pipe,
volume of magnet,
= conductivity of metallic pipe,
, drag force.
, drag force for finite pipe (point-dipole model).
, drag coefficient for infinite pipe (point-dipole model).
The velocity was found as the solution of the equation of motion by an iterative method:
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