Question

The relationship between Heat Utilization Factor (HUF) and Coefficient of Performance (COP) of a grain dryer is expressed as ________.

• A. $\text{HUF} = 1 + \text{COP}$
• B. $\text{HUF} = 1 - \text{COP}$
• C. $\text{HUF} = \text{COP}$
• D. $\text{HUF} = 1 / \text{COP}$

Hint:

This relationship is derived from the conservation of energy: the total heat energy supplied is equal to the heat used for drying ($\text{HUF}$) plus the heat lost in the exhaust ($\text{COP}$). Therefore, their sum must equal $1$ ($\text{HUF} + \text{COP} = 1$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The thermal efficiency and performance of agricultural convective grain dryers are evaluated using parameters that describe how effectively heat is utilized to evaporate moisture from the grain.
Key Formula or Approach:
Let us analyze the temperature parameters of a typical grain drying process:
- $T_0$ is the ambient temperature.
- $T_1$ is the temperature of the drying air entering the dryer.
- $T_2$ is the temperature of the exhaust air leaving the dryer.
The thermodynamic parameters are defined as:
1. Heat Utilization Factor (HUF): The ratio of the temperature drop during drying to the total temperature rise of the heated air:
\[ \text{HUF} = \frac{T_1 - T_2}{T_1 - T_0} \] 2. Coefficient of Performance (COP): The ratio of the heat carried away by the exhaust air to the total heat supplied:
\[ \text{COP} = \frac{T_2 - T_0}{T_1 - T_0} \]

Step 2: Detailed Explanation:
Let us add HUF and COP together:
\[ \text{HUF} + \text{COP} = \frac{T_1 - T_2}{T_1 - T_0} + \frac{T_2 - T_0}{T_1 - T_0} \] \[ \text{HUF} + \text{COP} = \frac{T_1 - T_2 + T_2 - T_0}{T_1 - T_0} \] \[ \text{HUF} + \text{COP} = \frac{T_1 - T_0}{T_1 - T_0} = 1 \] Rearranging this relationship gives:
\[ \text{HUF} = 1 - \text{COP} \] This equation describes how the thermal energy supplied to the dryer is partitioned between moisture evaporation (HUF) and sensible heat losses in the exhaust air (COP).

Step 3: Final Answer:
The relationship between HUF and COP is expressed as $\text{HUF} = 1 - \text{COP}$.