Question

A batch of material is dried under constant drying conditions. When drying is taking place from all the surfaces, the rate of drying during the constant rate period is:

• A. Directly proportional to the solid thickness
• B. Inversely proportional to the solid thickness
• C. Independent of solid thickness
• D. Inversely proportional to the square of solid thickness

Hint:

Drying period differences: - Constant Rate Period: Surface evaporation limits the process \( \rightarrow \) Controlled entirely by external gas film conditions \( \rightarrow \) Independent of solid thickness. - Falling Rate Period: Internal liquid diffusion limits the process \( \rightarrow \) Controlled by internal solid transport properties \( \rightarrow \) Strongly dependent on solid thickness.

Answer 1

The Correct Option is C

Concept: The rate of drying during industrial batch processing is categorized into two primary regimes: the Constant Rate Period and the Falling Rate Period. During the Constant Rate Period, the surface of the solid material remains fully saturated with liquid water. The drying process is entirely limited by external mass and heat transfer resistances across the gas boundary layer. The rate of moisture evaporation matches evaporation from a free liquid surface and is independent of internal moisture diffusion mechanisms within the solid matrix.

Step 1: Analyzing the equation governing the Constant Rate Period.
The constant drying rate per unit surface area, denoted as \( R_c \), is expressed mathematically using convective mass transfer coefficients: \[ R_c = \frac{-1}{A} \cdot \frac{dW}{dt} = k_y \cdot (Y_s - Y_g) = \frac{h \cdot (T_g - T_s)}{\lambda_s} \] Where:
• \( A \) represents the total exposed surface area available for evaporation.
• \( \frac{dW}{dt} \) is the absolute mass drying rate of water loss over time.
• \( k_y \) is the convective gas-phase mass transfer coefficient.
• \( Y_s \) and \( Y_g \) represent the absolute humidity at the wet surface boundary and in the bulk gas phase respectively.
• \( h \) is the convective heat transfer coefficient across the gas boundary film layer.
• \( T_g - T_s \) is the thermal driving potential between bulk air and the wet-bulb surface temperature.
• \( \lambda_s \) represents the latent heat of vaporization evaluated at temperature \( T_s \).

Step 2: Evaluating the role of solid physical thickness.
Looking at the governing equation for \( R_c \), the parameter factors influencing the drying rate include gas velocity, bulk humidity, air temperature, and exposed boundary area \( A \). Internal physical characteristics of the solid slab—such as its total thickness (\( x \)) or internal diffusion pathways—do not appear in the governing equation for this period. Because moisture moves to the surface fast enough to maintain a completely wet outer boundary layer, internal mass transfer resistance is negligible. Consequently, the core drying rate during this initial constant period remains completely independent of the solid thickness. In contrast, during the subsequent falling rate period, internal moisture diffusion limits the process, making the drying rate depend significantly on solid thickness.