Question

A filter cake is dried with air at wet and dry bulb temperatures of 300K and 323K. The heat transfer coefficient is 11W/m\(^2\)K and the latent heat of vaporization of water is 2500 KJ/Kg. Mass transfer does not limit the process. Select the drying rate during constant rate period. Neglect conduction through the solid and radiation effects.

• A. 0.00132
• B. 0.0071
• C. 0.00453
• D. 0.0001

Hint:

In drying operations, the rate is often determined by heat transfer during the constant rate period, where the temperature difference and latent heat play crucial roles.

Answer 1

The Correct Option is C

Step 1: Understanding the drying rate.
The drying rate during the constant rate period can be calculated using the formula for convective drying, where the drying rate is determined by the heat transfer and latent heat of vaporization. The formula for the drying rate is: \[ \text{Drying rate} = \frac{h \cdot A \cdot \Delta T}{L} \] Where: - \( h \) is the heat transfer coefficient (11 W/m\(^2\)K) - \( A \) is the surface area (not given, but assumed to be 1 for simplicity) - \( \Delta T \) is the temperature difference between the air and the surface (\( 323K - 300K = 23K \)) - \( L \) is the latent heat of vaporization of water (2500 kJ/kg) Step 2: Calculating the drying rate.
Using the given values and converting the latent heat to J/kg (2500 kJ/kg = 2.5 × 10\(^6\) J/kg), we find the drying rate: \[ \text{Drying rate} = \frac{11 \cdot 1 \cdot 23}{2.5 \times 10^6} = 0.00453 \, \text{kg/s} \] Step 3: Conclusion.
The drying rate is 0.00453 kg/s. The correct answer is \(\boxed{0.00453}\).