Knowledge card
Velocity Response to the Magnetic Field
Mathematical Modelling — Fluid Dynamics & Heat TransferNumerical analysis; boundary-layer similarity theory
Symbol
How the dimensionless velocity profile responds to magnetic forcing.
Dimension I
Definition
What it is — and what it is not
No definition recorded yet.
Dimension II
In practice
How to deal with it
- Observed results
- S1For every converged M-sweep, record f′(η), f″(0), the first η at which |f′| is below the far-field tolerance, and any profile crossing. Do not encode “velocity decreases with M” as a result until the computed branches establish it for the declared parameter set.
- Physical interpretation
- S2The direct magnetic contribution −(φ_σ/φ_ρ)Mf′ is braking wherever f′ > 0. A lower velocity profile is therefore the expected local response, but it is not a global monotonicity theorem for this coupled nonlinear BVP: buoyancy, slip, suction and branch changes can offset or reverse a pointwise trend.
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