Constant-Rate Drying Period Time
Computes how long the constant-rate period of a tray drying run lasts, t = m_s × (X₁ − X_c) ÷ (A × N_c), that is, the mass of water to be evaporated divided by the surface evaporation rate. Moisture contents are on a dry basis, in kilograms of water per kilogram of dry solid, and N_c is the evaporation flux measured while the surface is still fully wet, in kg per square metre per hour. While this period lasts the surface behaves like an open pool and the rate does not depend on the material, only on the air; it ends at the critical moisture X_c, when internal water can no longer reach the surface as fast as it evaporates. Enter the dry solid mass, the initial and critical moisture contents, the exposed area and the constant evaporation rate.
Result
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Constant-Rate Drying Period Time in Tray Dryers
The drying curve of a solid on a tray has two stretches, and they get computed separately. The first one is the constant-rate period, and it is the cheap one: while the surface stays fully wet, water leaves at the speed it would leave an open pool, and nothing about the material matters — only the air does. Whoever sizes a tray dryer, schedules a batch cycle or works through a unit operations problem set starts here, because this time tells how much of the cycle the air controls and how much is left for the hard part.
The water to evaporate in this stretch is m_s × (X₁ − X_c), with moisture on a dry basis; the surface evaporation flow is A × N_c. The time is one divided by the other. With the default values — 50 kg of dry solid, moisture falling from 0.35 to 0.12 kg/kg, 2.5 m² exposed and a rate of 1.2 kg/m²·h — that is 11.5 kg of water leaving at 3 kg/h, or 3.833 h. To check against the textbook, enter 21.5 kg of solid, 1 m² of area, X₁ of 0.38, X_c of 0.195 and N_c of 1.51: the page returns 2.634 h, the answer of the classic tray drying example.
The model assumes N_c really is constant, which requires steady air temperature, humidity and velocity throughout the stretch — in an uncontrolled batch oven that slips. Area A is the surface actually exposed to the air: if the tray dries from both faces the figure doubles, and entering only the top face is a common slip. Moisture has to be on a dry basis, kilograms of water per kilogram of dry solid. Critical moisture X_c is no material constant either: it shifts with bed thickness and with the drying rate itself, running higher the more aggressive the air. This page covers only this stretch, with no falling-rate period and no initial warm-up.
Frequently asked questions
How do I convert wet-basis moisture to dry basis?
Is this the total drying time?
Where does the constant rate N_c come from?
Related Tools
Falling-Rate Drying Period Time
Computes the duration of the falling-rate drying period under the model where the rate drops linearly with free moisture starting at the critical moisture: t = m_s × X_c ÷ (A × N_c) × ln(X_c ÷ X₂). Moisture contents go in as free moisture on a dry basis, that is, with the equilibrium moisture already subtracted, which is why X₂ can never be zero — drying down to equilibrium would take infinite time, exactly what the logarithm says. Compared with the constant-rate period this is the expensive stretch: every kilogram of water removed costs far more time than in the previous stretch, because internal transport now sets the pace. Enter the dry solid mass, the critical moisture, the final free moisture, the exposed area and the constant rate at the critical moisture.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.