GATE 2021 CH – Question 57
In a batch drying experiment, a solid with a critical moisture content of 0.2 kg H₂O/kg dry solid is dried from an initial moisture content of 0.35 kg H₂O/kg dry solid to a final moisture content of 0.1 kg H₂O/kg dry solid in 5 h. In the constant rate regime, the rate of drying is 2 kg H₂O/(m² h). The entire falling rate regime is assumed to be uniformly linear. The equilibrium moisture content is assumed to be zero. The mass of the dry solid per unit area is _____ kg/m² (round off to nearest integer).
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Correct answer: 35
Explanation
Let $M_s/A=S$ kg/m². The constant-rate time is $t_c=S(X_i-X_c)/N_c=S(0.35-0.2)/2=0.075S$.
With zero equilibrium moisture and a linear falling rate, $N(X)=N_cX/X_c$. Integration from $X_c=0.2$ to $X_f=0.1$ gives
$$t_f=S\frac{X_c}{N_c}\ln\frac{X_c}{X_f}=0.1S\ln2.$$
Thus $5=S(0.075+0.1\ln2)$, giving $S=34.6465\ \mathrm{kg/m^2}$. **Answer: 35 kg/m².** Both drying regimes must be included.