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An x-dependent prescribed heating excess keeps streamwise advection

Because T_r−T_∞=ΔT₀x/(1−γt)² grows with x, u∂T/∂x SURVIVES the similarity reduction as f′θ. The independent ΔT₀ has units K/m and must not be replaced by the stretching rate c.

Dimension I

Definition

What it is — and what it is not

What it is
  • S1Correction and justification — Because T_r−T_∞=ΔT₀x/(1−γt)² grows with x, u∂T/∂x SURVIVES the similarity reduction as f′θ. The independent ΔT₀ has units K/m and must not be replaced by the stretching rate c. [1.1]

Dimension II

In practice

How to deal with it

No practical guidance recorded yet.

Applies pattern

References

  1. Ishak, Nazar & Pop (2009), Meccanica

    • 1.1

      Similarity transformation and energy ODE — Because T_r−T_∞=ΔT₀x/(1−γt)² grows with x, u∂T/∂x SURVIVES the similarity reduction as f′θ. The independent ΔT₀ has units K/m and must not be replaced by the stretching rate c.

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