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Knowledge card
Buoyancy Term
Mathematical Modelling — Fluid Dynamics & Heat TransferContinuum mechanics; boundary-layer similarity theory
Symbol
The thermal buoyancy term — the expansion-to-density ratio times the mixed-convection parameter times the temperature times the inclination factor.
About levels
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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.
In words:divided bytimestimestimes.
Open full derivation chain: 2 stepsDerivation
- 1
Open Step 1: Given / definition · The source relation this block transforms: gβ_hnf(T_r−T∞)θcosα.
The source relation this block transforms: gβ_hnf(T_r−T∞)θcosα.Given / definition Defining ruleThe starting relation of a derivation — the definition or established equation every later step transforms; it justifies no change itself.Level 0 · more availableBrief — named quantitiesAbout 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.
- ★
Open Step 2: Parameter definition · Divide by c²x/(1−γt)²: the raw coefficient is gβ_hnfΔT₀/c², identified as (φ_{ρβ}/φ_ρ)λ using λ…
Divide by c²x/(1−γt)²: the raw coefficient is gβ_hnfΔT₀/c², identified as (φ_{ρβ}/φ_ρ)λ using λ=Gr_x/Re_x²=gβ_fΔT₀/c².Parameter definition Defining ruleΠ ≔ (grouped physical quantities)Naming a recurring group of quantities as a single parameter (A ≔ γ/c, M ≔ σB₀²/(ρc), …), replacing the group by its name.Open term-change ledger: 1 records
Open record 1: g + β_hnf + Tr−T∞ → φ_{ρβ} + φ_ρ + λ
Consumes:L0gL0L0Produces:L0L0L0Dividing the buoyancy acceleration gβ_hnf(T_r−T∞) by the convective inertial scale c²x/(1−γt)² regroups its dimensional factors into the dimensionless coefficient (φ_β/φ_ρ)λ: the hybrid thermal expansion β_hnf becomes the expansion ratio φ_β, the density ratio φ_ρ carries the ρ_hnf-division of the momentum balance, and gβ_fΔT₀/c² is named λ = Gr_x/Re_x².Level 0 · more availableBrief — named quantitiesAbout 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.
Equation Workspace
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Calculator
Equation Workspace
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Equation workspace
Set the values you know, then calculate the remaining quantities in Buoyancy Term.
Domain Analysis
Unit status, dimensional trails, per-step checks, and custom unit expressions.
Domain Analysis
Unit status, dimensional trails, per-step checks, and custom unit expressions.
Step-by-step unit check (2 steps)
Step 1 given
Expand checked this step.Step 2 parameter_definition
Expand checked this step.
Try your own — the unit calculator
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Reads as: (φ_β/φ_ρ) λ θ cos α
“(φ_β/φ_ρ) λ θ cos α” 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.
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
Essence
S1The buoyancy term of the reduced ODE: (φ_β/φ_ρ)λ θ cos α.
- S1.1essenceφ_{ρβ} divided by φ_ρ.
- S1.2essenceThe product of (φ_{ρβ} / φ_ρ) and λ.
- S1.3essenceThe product of ((φ_{ρβ} / φ_ρ) · λ) and θ.
- S1.4essenceThe product of (((φ_{ρβ} / φ_ρ) · λ) · θ) and cos α.
Dimension I
Definition
What it is — and what it is not
- What it is
- S2The substituted buoyancy: gβ_hnf(T_r−T∞)θcosα.
- S2.1essenceThe product of g and β_hnf.
- S2.2essenceThe product of (g · β_hnf) and Tr−T∞.
- S2.3essenceThe product of ((g · β_hnf) · Tr−T∞) and θ.
- S2.4essenceThe product of (((g · β_hnf) · Tr−T∞) · θ) and cos α.
- S2The substituted buoyancy: gβ_hnf(T_r−T∞)θcosα.
Dimension II
In practice
How to deal with it
No practical guidance recorded yet.