CALCULATORS / HEAT TRANSFER AND TEMPERATURE

Lumped cooling time calculator

Lumped Newton cooling to an intermediate temperature; uniform body.

thermal-cooling-time.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	timeConstants	durations
	90	161.258
	72	129.007

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

cooling time budget161.26 s✓ passes

BASELINE INPUTS

mass0.5 kgheatCapacity900 J/(kg*K)conductance5 W/KinitialExcess60 KfinalExcess10 K

CALCULATED

timeConstant90 s

duration161.26 s

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Lumped cooling time
# Scope: Lumped Newton cooling to an intermediate temperature; uniform body.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

mass = 0.5 kg
heatCapacity = 900 J/(kg*K)
conductance = 5 W/K
initialExcess = 60 K
finalExcess = 10 K

timeConstant := mass*heatCapacity/conductance [s]
duration := timeConstant*log(initialExcess/finalExcess) [s]

check cooling time budget: duration <= 300.0 s

scenario alternative: mass = 0.4 kg

Calculated from your source · not saved

Baseline · Baseline

cooling time budget161.26 s ✓ passes

alternative · alternative

cooling time budget129.01 s ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

time constant: timeConstant = mass*heatCapacity/conductance [s]
duration: duration = timeConstant*log(initialExcess/finalExcess) [s]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

mass: 0.5 kg
heat capacity: 900 J/(kg*K)
conductance: 5 W/K
initial excess: 60 K
final excess: 10 K

Calculated

time constant: 90 s
duration: 161.258 s

Assumptions and limits

Lumped Newton cooling to an intermediate temperature; uniform body.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Lumped cooling time. Inputs: thermal mass; conductance; ambient; initial temperature. Outputs: cool-down curve; target time. Model scope: Lumped or low-dimensional thermal models with explicit properties. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: thermal mass, conductance, ambient, initial temperature
Outputs: cool-down curve, target time
Modes: calculate, compare, sweep
Drawing: Temperature and heat-flow plot

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS