Batch heating and cooling time
Time to heat or cool a batch vessel from one temperature to another, using steam, cooling water or another medium, with the temperature–time curve.
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How this calculator works
When you heat or cool a batch — a tank, a reactor or a vessel — the temperature changes fastest at the start and slows as the liquid approaches the medium temperature. The time to reach a target temperature depends on the liquid's thermal mass (mass × specific heat) and the rate of heat transfer (U × A × driving force). For an isothermal medium such as condensing steam or a boiling refrigerant, the driving force decays exponentially: t = (M·Cp)/(U·A) × ln[(Ti−Tm)/(Tf−Tm)]. For a non-isothermal medium such as cooling water, the medium's own temperature changes through the exchanger, so the effective driving force is reduced by a factor K = 1 − exp(−UA/ṁCpm).
Example: 5,000 kg of water at 25 °C heated to 80 °C with steam at 150 °C through a coil with U = 500 W/m²·K and A = 10 m². Time constant = M·Cp/(U·A) = 5,000 × 4.18 / (500 × 10 / 1000) = 4,180 s (70 min). Heating time = 4,180 × ln[(25−150)/(80−150)] = 4,180 × ln(125/70) = 4,180 × 0.580 = 2,424 s (40 min). The initial duty is 5 × (150−25) = 625 kW and the final duty is 5 × (150−80) = 350 kW.
Limits: assumes perfect mixing in the vessel (uniform batch temperature), constant U and constant fluid properties. Real tanks have temperature gradients unless agitated; U can change with temperature (especially for viscous liquids); and the medium flow may vary. For accurate results on viscous or non-Newtonian fluids, use a stepwise simulation. References: Kern, Process Heat Transfer; Perry's Chemical Engineers' Handbook, Section 11.