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THE FEUTEX TOOLKIT

Lumped Thermal Cooling

Estimate object temperature and thermal time constant under convection.

Thermal workspace● Runs in your browser
01 Your input
02 Your result
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FormulaT−T∞=(Ti−T∞)exp(−hAt/(ρVcp)); Bi=h(V/A)/k.
Sources and model references

Worked example

Inputs

Density
7800 kg/m³
Object volume
0.0001 m³
Specific heat
500 J/(kg·K)
Exposed area
0.02 m²
Convection coefficient
10 W/(m²·K)
Conductivity
50 W/(m·K)
Initial temperature
100 °C
Ambient temperature
20 °C
Elapsed time
600 s

Expected results

Thermal time constant
1950 s
Biot number
0.001
Object temperature
78.81131845 °C

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter every input in the labeled units; use measured or independently specified properties.
  2. Check the stated model assumptions before calculating.
  3. Interpret the output as a model estimate and verify it independently for the intended application.

Try this example

{
  "rho": 7800,
  "volume": 0.0001,
  "cp": 500,
  "area": 0.02,
  "h": 10,
  "k": 50,
  "initial": 100,
  "ambient": 20,
  "time": 600
}

Accuracy and scope

Uniform object temperature approximation, constant properties and ambient conditions. Educational engineering estimate only; not structural or safety certification, equipment selection, or operating recommendations.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.