Question

If R is the radiation loss to the atmosphere, t1 and t2 are temperatures of inlet and outlet air respectively, then thermal efficiency of spray dryer would be expressed as

• A. [(R - 1) 100) (t2 - t1)] [t1 - t0]
• B. [(1 - R) 100) (t1 - t2)] [t1 - t0]
• C. [t1 - t0] [(1 - R) 100) (t1 - t2)]
• D. [t0 - t1] [(1 - R) 100) (t2 - t1)]

Hint:

Spray Dryer Efficiency Formula: Thermal Efficiency = $\frac{(1 - R)(t_1 - t_2)}{t_1 - t_0}$ (Drop in temperature corrected for radiation divided by total temperature span above ambient).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Thermal efficiency formulations for industrial spray dryers: overall thermal efficiency accounts for heat utilized in moisture evaporation relative to total heat supplied above ambient temperature ($t_0$), corrected for fractional casing radiation loss ($R$).
Key Formula or Approach:
\[ \mathbf{\eta_{\text{thermal}}} = \frac{\text{Actual Heat Used for Evaporation}}{\text{Total Heat Input from Ambient}} = \frac{\mathbf{(1 - R/100) \cdot (t_1 - t_2)}}{\mathbf{t_1 - t_0}} \]

Step 2: Detailed Explanation:
In thermal engineering and energy balance calculations of milk spray dryers:
1. Inlet Drying Air Temperature ($t_1$): Typically $180^\circ - 220^\circ ext{C}$.
2. Outlet Exhaust Air Temperature ($t_2$): Typically $80^\circ - 95^\circ ext{C}$.
3. Ambient Reference Temperature ($t_0$): Typically $20^\circ - 25^\circ ext{C}$.
4. Ideal Thermal Efficiency without Heat Losses:
\[ \eta_{\text{ideal}} = \frac{t_1 - t_2}{t_1 - t_0} \]
5. Correcting for Radiation and Convection Losses ($R$ %):
- If radiation loss through the dryer walls is $R\%$, the fraction of energy retained in the drying chamber is $(1 - R/100)$.
- Multiplying the sensible air temperature drop $(t_1 - t_2)$ by this retention factor yields the standard engineering expression:
\[ \mathbf{\eta_{\text{thermal}} = \frac{\left[ \frac{1 - R}{100} \right] (t_1 - t_2)}{t_1 - t_0}} \]

Step 3: Final Answer:
Hence, thermal efficiency is expressed as [(1 - R) 100) (t1 - t2)] [t1 - t0], matching option (B).