Knowledge card
Far-field Residual
Mathematical Modelling — Fluid Dynamics & Heat TransferNumerical analysis; boundary-layer similarity theory
Symbol
The miss vector R(s) = (f′(η_max; s), θ(η_max; s)): how far the integrated profiles are from the required far-field decay. A root of R is a solution of the BVP.
In words:plus.
Equation Workspace
Set known values, calculate unknowns, inspect dependencies, and run numerical solves.
Calculator
Equation Workspace
Set known values, calculate unknowns, inspect dependencies, and run numerical solves.
Equation workspace
Set the values you know, then calculate the remaining quantities in Far-field Residual.
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.
Try your own — the unit calculator
Ever wondered whether a formula “adds up”? This tool answers one plain question: do the units match? Pick a couple of quantities (distance, time, a speed…), join them with ×, ÷, +, or =, and press Run. It works out the resulting unit — for example distance ÷ time gives a speed, LT⁻¹ (metres per second) — and flags anything that can’t be right, like adding a length to a time.
Reads as: R(s)
“R(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.
Mathematical Analysis
Object type, lawful operations, conditions, comparisons, and derivation-step checks.
Dimension I
Definition
What it is — and what it is not
- What it is
- S1R(s) = (f′(η_max; s), θ(η_max; s)) — both components must vanish because the true far field decays to zero.
Dimension II
In practice
How to deal with it
No practical guidance recorded yet.