Model real cooling with engineering-ready rate outputs fast. Switch methods, units, and boundary conditions easily. Export a clean report for teams and quality checks.
Use this for quick checks and design comparisons. For critical designs, validate with measurements and detailed thermal analysis.
| Scenario | Ti | Tf | Ta | Time | Avg rate | Newton k | Lumped k |
|---|---|---|---|---|---|---|---|
| Sample | 120 °C | 60 °C | 25 °C | 15 min | 4.0 °C/min | 0.001109 1/s | 0.003000 1/s |
Average rate summarizes a window: (Ti−Tf)/Δt. For the sample 120→60 °C over 15 min, the magnitude is 4.0 °C/min. Instantaneous rate changes with time in exponential cooling, so use a query time to compare mid‑process behavior. Use consistent units: °C and K share difference magnitude, while °F differences scale by 9/5, which this tool converts automatically for comparisons.
When ambient is known, the Newton fit estimates k from measured temperatures. The time constant τ=1/k sets the response speed, and the half‑life is t50=τ·ln(2). With k=0.001109 1/s, τ≈902 s and t50≈625 s (10.4 min). If Tf is too close to Ta, small measurement noise can inflate k and τ.
If you can estimate h, area, mass, and Cp, the lumped model uses k=hA/(mCp). Natural convection in still air often falls near 5–25 W/(m²·K); forced air may reach 30–200; water cooling can exceed 200 and climb into thousands. Doubling h or area doubles k and cuts τ in half. Typical Cp values: metals 380–900, water about 4180 J/kg·K.
The lumped approach assumes the object is nearly uniform in temperature. A quick screen is Bi=hLc/ks. A common guideline is Bi<0.1. Using h=30 W/(m²·K), Lc=0.02 m, and ks=15 W/(m·K) gives Bi=0.04, supporting a uniform‑temperature approximation.
Thermal energy removed is Q=mCpΔT. For m=10 kg, Cp=500 J/(kg·K), and ΔT=60 K, Q=300,000 J. Over 900 s, average power is about 333 W. If the same drop must occur in 300 s, power rises to about 1,000 W.
Log temperature at a consistent interval, and avoid sensor lag by improving contact or using thin probes. Keep ambient stable; a 3 °C ambient drift can bias k. Export CSV to audit inputs and outputs, then share PDF results with assumptions, units, and the chosen model. For compliance, include calibration date, uncertainty.
Use the average rate for a simple summary over the entered interval. Use the Newton or convection rate at a query time when you need an instantaneous value for control, sizing, or comparison between different ambient conditions.
The fit requires (Ti−Ta)/(Tf−Ta) to be positive and nonzero. If Tf is at or beyond ambient, or ambient is entered incorrectly, the logarithm becomes invalid. Recheck Ta, units, and measurement timing.
Start with published ranges: still air 5–25 W/(m²·K), forced air 30–200, water 200–10,000+. Refine using tests or correlations for your geometry and flow. Treat h as the biggest uncertainty in convection predictions.
Bi=hLc/ks compares internal conduction resistance to surface convection. If Bi is below about 0.1, the object is often close to uniform temperature and the lumped model is more defensible. Higher Bi suggests internal gradients matter.
Yes. If Tf exceeds Ti, the signed average dT/dt becomes negative, indicating heating. The exponential models still describe approach toward ambient when the ambient is on the opposite side of the initial temperature.
Query time returns predicted temperature and rate partway through the process. Target temperature estimates the time needed to reach a specified temperature under the chosen model. These are useful for cycle-time planning and pass/fail thermal requirements.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.