Knowledge card

Standard Local Surface Nusselt Number

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

Symbol

N u_{x, s}

The standard local Nusselt number based on the actual fluid-side surface excess T_s−T∞, where T_s=T(x,0,t).

Main equation

(R e_{x}^{- ½} N u_{x, s} S2.1 = \frac{( \frac{φ _{k} + 4 R d}{3} ) ( - θ ^{'} ( 0 ))}{θ ( 0 )})

Dimension:1Maths:𝔹 equation(·) — A statement that two sides are equal, depending on another quantityDimensionally verifiedMathematically verifiedFully reduced to base quantities

In words:equals.

Open full derivation chain: 2 stepsDerivation

1
Open Step 1: Given / definition · Use the standard local surface definition Nu_{x,s}=xq_w/[k_f(T_s−T∞)]. Under the convective Rob…
Use the standard local surface definition Nu_{x,s}=xq_w/[k_f(T_s−T∞)]. Under the convective Robin condition, T_s−T∞=(T_r−T∞)θ(0), so the reference-normalised wall flux must be divided by θ(0).Given / definition
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$(\frac{( \frac{R e _{x}^{- ½} N u _{x, s}}{( \frac{φ _{k} + 4 R d}{3} ) ( - θ ^{'} ( 0 ))} ) _{[S1.1]}}{θ ( 0 )})_{[S1.2]}$
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Open Step 2: Parameter definition · Substitute the already reduced total wall flux and retain θ(0), which is an unknown shooting va…
Substitute the already reduced total wall flux and retain θ(0), which is an unknown shooting value for the Robin condition and cannot be silently set to one.Parameter definition
Open term-change ledger: 1 records
Open record 1: (φ_k+4Rd/3)(−θ′(0)) + θ(0) → (φ_k+4Rd/3)(−θ′(0))/θ(0)
Consumes:L0 $(φ_{k} + 4 R d /3) (- θ' (0))$ L0 $θ (0)$ Produces:L0 $(φ_{k} + 4 R d /3) (- θ' (0)) / θ (0)$ Since T_s−T∞=(T_r−T∞)θ(0), changing the denominator from the prescribed reference excess to the actual surface excess divides the reference-temperature proxy by θ(0).(φ_k+4Rd/3)(−θ′(0))/θ(0)
Level 0 · more available
Brief — named quantities
About levels
Why the levels load one at a time
Only level 0 travels with this article. The complete expansion is several megabytes, so deeper levels are fetched one at a time when you ask for them — and how deep it goes is not known until you get there.
To go deeper still, open any quantity in the reading as its own concept card — it carries its own derivation and its own depth ladder.
How many levels remain is not yet known — the depth is discovered one level at a time.
$(R e_{x}^{- ½} N u_{x, s} S2.1 = \frac{( \frac{φ _{k} + 4 R d}{3} ) ( - θ ^{'} ( 0 ))}{θ ( 0 )})$

Numerical solution · Standard Local Surface Nusselt Number

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Step-by-step unit check (2 steps)

Step 1 given
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Step 2 parameter_definition
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Reads as: Nu_{x,s}

“Nu_{x,s}” is analysed by expanding its full defining equation (its children and their relations), not as a bare symbol. Use Check this concept’s units above for the same result.

Mathematical Analysis

Object type, lawful operations, conditions, comparisons, and derivation-step checks.

Check one step at a time (2 steps)

Step 1 — given

Step 2 — parameter definition

Dimension I

Definition

What it is — and what it is not

What it is: S1The standard scaled surface group is the dimensionless total wall flux divided by the actual dimensionless surface excess θ(0).
S1.1essenceRe_x^{−½}Nu_{x,s} divided by (φ_k+4Rd/3)(−θ′(0)).
S1.2essence(Re_x^{−½}Nu_{x,s} / (φ_k+4Rd/3)(−θ′(0))) divided by θ(0).
Wisdoms: S2Standard surface result: Re_x^{−½}Nu_{x,s}=(φ_k+4Rd/3)(−θ′(0))/θ(0).
S2.1essenceRe_x^{−½}Nu_{x,s} set equal to (φ_k+4Rd/3)(−θ′(0))/θ(0).

Dimension II

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Standard Local Surface Nusselt Number

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