Lumped capacitance: after ten hours one packing is still under its limit

Type the yard temperature hour by hour and each packing's limit. After 10 hours the lighter option reads 10.5 degrees and the heavier 6.6, so one is still inside.

Live result

At 10 hours, 1 of the options are still at or below their typed limit. Heavy pack

options compared2
next checked change15 hours

At that checked dwell, the set of options still within their limits changes.

Temperature trace and checked dwell

1. Light pack10.5 degrees
2. Heavy pack6.6 degrees

Try a scenario

Typed yard case

Unpowered yard dwell10hours

This is the one control tracked across the chart and sweep rail.

Sweep step

Use a whole number that divides 120 and places the dwell on the grid.

Packing options

2 / 5

Option 1

Option label

Starting temperaturedegrees

Typed limitdegrees

Heat capacitykJ/K

Effective conductanceW/K

Option 2

Option label

Starting temperaturedegrees

Typed limitdegrees

Heat capacitykJ/K

Effective conductanceW/K

Yard ambient log

1 / 121

Ambient row 1

Hourhours

Ambient temperaturedegrees

Tracked answer

Light pack

End reading: 10.5 degrees
Typed limit: 8 degrees
State: Above

Heavy pack

End reading: 6.6 degrees
Typed limit: 8 degrees
State: At or below

Option	End reading	Typed limit	State
Light pack	10.5 degrees	8 degrees	Above
Heavy pack	6.6 degrees	8 degrees	At or below

First checked crossings

Light pack: 10 hours
Heavy pack: 15 hours
First change above: 15 hours
First change below: 5 hours

The boundary is the typed lumped body, ambient log, and limits. Stratification, openings, sunlight, sensor position, phase change, and events outside the typed window are not represented.

Here is the maths

The formula, in words

For each constant ambient segment, multiply the gap from ambient by exp of minus conductance rate times elapsed hours, then add ambient. Conductance rate equals 3.6 times effective conductance divided by heat capacity.

T = T_a + (T_0 - T_a)\exp(-kt)

where $T$ is the reading at the end of the segment, $T_a$ the ambient temperature, $T_0$ the reading at its start, $k$ the conductance rate an hour, and $t$ the elapsed hours.

A worked example

Both options start at 2 degrees in a yard at 30 degrees, with a typed limit of 8 and effective conductance of 10 W/K.

For the light option, $k$ equals 3.6 times 10 divided by 1,000, or 0.036 per hour. After 10 hours its reading is 10.5 degrees.

For the heavy option, $k$ equals 0.018 per hour. After 10 hours its reading is 6.6 degrees, so only the heavy option remains inside.

What this does not model

The model treats each option as one temperature. It does not represent stratification, openings, direct sun, sensor position, phase change, or an untyped event.

Check it yourself

At zero dwell, each option equals its typed starting temperature. With zero conductance, its reading stays there through the full sweep.

Sources

Published lumped capacitance heat transfer mathematics.
Cold chain guidance on recording temperature excursions, described here without qualification tables or product limits.

Model version

1.0.0

The whole record prints. Your browser can save it as a PDF instead of printing it.

Every limit and temperature log shown here comes from your entries. This calculation qualifies no load, validates no packing, supplies no product or carrier limit, and is not a temperature record.

Unpowered yard temperature record