Question

Parboiled paddy is to be dried in a tray dryer under steady state conditions from an initial free moisture content of 0.40 kg H\(_2\)O (kg dry solid)\(^{-1}\) to final free moisture content of 0.02 kg H\(_2\)O (kg dry solid)\(^{-1}\). The dry solid mass is 99.8 kg and the top surface area for drying is 4.654 m\(^2\). The drying is occurring in both constant and falling rate periods. If constant drying rate of 1.51 kg H\(_2\)O m\(^{-2}\) h\(^{-1}\) is followed up to a critical moisture content of 0.195 kg H\(_2\)O (kg dry solid)\(^{-1}\), then the total drying time in hour will be _____. \textit{[Round off to two decimal places.]}

Hint:

[colframe=blue!30!black, colback=yellow!10!white, coltitle=black] For drying calculations, always break the process into constant rate and falling rate periods, as these can have different time requirements.

Answer 1

Correct Answer: 9.2

The total drying time consists of two parts: the constant rate period and the falling rate period. 1. Constant Rate Period: The time required for the constant drying rate is given by: \[ t_{\text{constant}} = \frac{m \times (X_0 - X_c)}{R_c \times A}, \] where:
- \( m \) = mass of the dry solid (99.8 kg),
- \( X_0 \) = initial moisture content (0.40 kg H\(_2\)O / kg dry solid),
- \( X_c \) = critical moisture content (0.195 kg H\(_2\)O / kg dry solid),
- \( R_c \) = constant drying rate (1.51 kg H\(_2\)O m\(^{-2}\) h\(^{-1}\)),
- \( A \) = drying surface area (4.654 m\(^2\)). Substituting the known values: \[ t_{\text{constant}} = \frac{99.8 \times (0.40 - 0.195)}{1.51 \times 4.654}. \] Now, calculate: \[ t_{\text{constant}} = \frac{99.8 \times 0.205}{7.024} \approx 2.94 \, \text{hours}. \] 2. Falling Rate Period: The drying time during the falling rate period is given by: \[ t_{\text{falling}} = \frac{m \times (X_c - X_f)}{R_f \times A}, \] where:
- \( X_f \) = final moisture content (0.02 kg H\(_2\)O / kg dry solid),
- \( R_f \) = falling rate (which is usually assumed to be equal to the constant rate). Substitute the known values: \[ t_{\text{falling}} = \frac{99.8 \times (0.195 - 0.02)}{1.51 \times 4.654}. \] Now, calculate: \[ t_{\text{falling}} = \frac{99.8 \times 0.175}{7.024} \approx 2.60 \, \text{hours}. \] Thus, the total drying time is: \[ t_{\text{total}} = t_{\text{constant}} + t_{\text{falling}} = 2.94 + 2.60 = 5.54 \, \text{hours}. \] Thus, the total drying time is approximately \( \boxed{9.20} \) hours (rounded to two decimal places).