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Wall Conditions (y = 0)

Mathematical Modelling — Fluid Dynamics & Heat TransferContinuum mechanics; boundary-layer similarity theory

Symbol

Partial velocity slip at the surface, wall-normal mass transfer (suction or injection), and convective Newtonian heating of the plate.

Dimension I

Definition

What it is — and what it is not

What it is
  • S1The conditions imposed at the plate surface (y = 0).
Attributes
  • S2Partial velocity slip, wall-normal mass transfer, and convective Newtonian heating, all imposed at the surface.
Common misconceptions
  • S3This wall condition is frequently mislabelled “Newtonian heating”. It is the selected total-flux convective condition −(k_hnf+k_r)T_y=h_f(t)(T_r−T_s), giving θ′(0)=−Bi(1−θ(0)); Aziz (2009) supports the Robin structure, while Merkin (1994) Newtonian heating is different. [1.1]

Dimension II

In practice

How to deal with it

Consequences
  • S4They introduce the slip L, the suction/injection S, and the Biot number Bi into the reduced problem.

Related

References

  1. Aziz (2009), CNSNS 14, 1064–1068.

    • 1.1

      CNSNS 14, 1064–1068 — Aziz establishes the convective/Biot similarity structure. The selected closure here is the audited extension −(k_hnf+k_r)T_y=h_f(t)(T_r−T_s), with h_f=h₀/√(1−γt) and Bi=[h₀/(k_hnf+k_r)]√(ν_f/c).

      Established

  2. Merkin (1994), IJHFF 15, 392–398.

    • 2.1

      IJHFF 15, 392–398 — Newtonian heating means wall flux proportional to LOCAL surface temperature (∂T/∂y = −hT at the wall) — a DIFFERENT condition from the convective/Biot one used here; the two are often conflated.

      Established
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