Question

Apple slices are dried from a moisture content of 65% (dry basis) to 10% (dry basis) in a hybrid solar dryer under falling rate period. The apple slices have a drying rate constant of \( \frac{1}{104} \) minute\(^{-1}\). Considering an equilibrium moisture content of 2% (dry basis), the time required for drying is _________ minutes. (Rounded off to 2 decimal places)

Hint:

Use the falling rate period drying equation to estimate the drying time based on the moisture content and drying rate constant.

Answer 1

The drying process follows the falling rate period, and the time required to reduce the moisture content can be calculated using the formula for drying in this period: \[ {Time} = \frac{1}{k} \cdot \ln \left( \frac{X_1 - X_e}{X_2 - X_e} \right) \] where:
\(k\) is the drying rate constant, given as \( \frac{1}{10^4} \) minute\(^{-1}\).
\(X_1\) is the initial moisture content (65% dry basis), so \(X_1 = 0.65\).
\(X_2\) is the final moisture content (10% dry basis), so \(X_2 = 0.10\).
\(X_e\) is the equilibrium moisture content (2% dry basis), so \(X_e = 0.02\).
Now, substitute these values into the formula: \[ {Time} = \frac{1}{\frac{1}{10^4}} \cdot \ln \left( \frac{0.65 - 0.02}{0.10 - 0.02} \right) \] \[ {Time} = 10^4 \cdot \ln \left( \frac{0.63}{0.08} \right) \] \[ {Time} = 10^4 \cdot \ln (7.875) \] \[ {Time} = 10^4 \cdot 2.764 \] \[ {Time} = 214 \, {minutes} \] Thus, the time required for drying is 214 minutes.