Cooling Time Calculator (Newton’s Law of Cooling)
Use Newton’s law of cooling to estimate how long a hot body takes to cool to a target temperature, or what temperature it reaches after a given time.
- τ = m × c ÷ (h × A) = 52,330 s
- t = −τ × ln[(T₁ − Ta) ÷ (T₀ − Ta)] = 13.89 h (833.3 min)
Newton’s Law of Cooling
τ = m × c ÷ (h × A)
t = −τ × ln[(T − Ta) ÷ (T₀ − Ta)]
m is the mass, c the specific heat, h the heat transfer coefficient, A the cooling surface area and τ the time constant. The method assumes the body is at one uniform temperature (well mixed liquid or a small solid) and that h stays constant.
Worked example
500 kg of water (c = 4186) in a tank with 4 m² of surface and h = 10 W/m²·K has τ ≈ 14.5 h. Cooling from 90 °C to 50 °C in 25 °C air takes about 13.9 h.
Frequently Asked Questions
When does Newton’s law of cooling apply?
When the body temperature is uniform and the heat transfer coefficient is roughly constant, such as a stirred tank or a small part.
What h value should I use?
About 5 to 10 W/m²·K for still air, 10 to 100 for forced air and much higher for liquids. Radiation adds to h at high temperature.
Can I use it for heating too?
Yes. The same exponential applies when a body warms towards a hotter surrounding temperature.
Learn more on the blog
Thermocouple and RTD installation precautions
A practical, field focused guide on instrumentationblog.in that explains the theory behind this calculator and how engineers apply it on real plants.
Read Full Article