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GATE 2024 CH – Question 43

Mass Transfer · Leaching, liquid-liquid extraction, drying, humidification and adsorption · 2 marks · Multiple choice

Alumina particles with an initial moisture content of 5 kg per kg dry solid are dried in a batch dryer. For the first two hours, the measured drying rate is constant at 2 kg m$^{-2}$ h$^{-1}$. Thereafter, in the falling-rate period, the rate decreases linearly with the moisture content. The equilibrium moisture content is 0.05 kg per kg dry solid and the drying area of the particles is 0.5 m$^2$ per kg dry solid. The total drying time, in h, to reduce the moisture content to half its initial value is

  1. 4.13
  2. 2.55
  3. 3.22
  4. 5.13

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Correct answer: (B) 2.55

Explanation

The drying rate per kg of dry solid is $2 \times 0.5 = 1$ kg per kg per hour. In the first 2 h the moisture falls by 2, from 5 to the critical value $X_c = 3$. The falling rate period (rate linear in $X - X^*$) runs from 3 to $X = 2.5$: $t = \frac{X_c - X^*}{R_c}\ln\frac{X_c - X^*}{X - X^*} = 2.95\ln\frac{2.95}{2.45} = 2.95 \times 0.1859 = 0.548$ h. The total time is $2 + 0.548 = 2.55$ h.