Aerogel-Infused Fabric Thermal Conductivity Modeler

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 9 inputs are read from the form on every keystroke: Aerogel Volume Fraction, Fibre Volume Fraction, Fabric Thickness, Aerogel Pore Size, Air Mean Free Path, Aerogel Skeleton Conductivity, Fibre Conductivity, Radiative Contribution and Structure Factor.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Effective Conductivity together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Aerogel Phase Conductivity, Suppressed Gas Conduction, Knudsen Number, Thermal Resistance and Insulation Value — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Effective Conductivity shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Composition and Phase Properties. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Effective Conductivity in the dark results panel — that is the headline figure, expressed in W/m·K.
4. Check the supporting rows underneath (Aerogel Phase Conductivity, Suppressed Gas Conduction, Knudsen Number, Thermal Resistance and Insulation Value) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Effective Conductivity before a trial is booked, so machine time and material in Acoustic, Thermal & Metamaterial Textiles are committed against a calculated figure rather than an estimate.
• Costing and quotation — Effective Conductivity is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Aerogel Volume Fraction) shows how much of the gap in Effective Conductivity each variable explains.
• Teaching and study — the accepted ranges bracket normal Acoustic, Thermal & Metamaterial Textiles practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Setting aerogel and fibre fractions above 100% between them drives the air fraction negative and the result stops meaning anything — the model does not police it, so check the two add up sensibly. The structure factor is fitted, not measured: it hides all the morphology the two-bound blend cannot represent, and it must be recovered from guarded hot-plate data on the actual composite. Compression matters more than any of this — an aerogel batt at half thickness under a pack strap is a different insulator, and the model assumes the quoted thickness holds in use.
• Every input is bounded to the range normal practice occupies (Aerogel Volume Fraction 0 to 90 %, Fibre Volume Fraction 1 to 80 % and Fabric Thickness 0.2 to 50 mm, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask