Knowledge card
Temperature Response to the Magnetic Field
Mathematical Modelling — Fluid Dynamics & Heat TransferNumerical analysis; boundary-layer similarity theory
Symbol
How the dimensionless temperature 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 parameter sweep, record θ(η), −θ′(0), thermal thickness at the declared tolerance, profile crossings and the energy-equation residual. The sign of ∂θ/∂M must be obtained numerically; M does not occur directly in the energy ODE.
- Physical interpretation
- S2Any temperature response to M is indirect, transmitted through the coupled velocity f. “Hotter but slower” is a plausible convection-suppression mechanism only after the computed θ profiles confirm it. It must not be attributed to Joule heating, because σB²u² is absent from this problem’s energy equation.
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