Question

In a heat exchanger, milk is to be heated from 5°C to 85°C with 80% regeneration and then finally in a heating section. The temperature of milk after regeneration would be

• A. 64°C
• B. 69°C
• C. 74°C
• D. 80°C

Hint:

Regeneration Calculation Shortcut: Temp after Regen = $\text{Inlet Temp} + [\text{Regen \%} \times (\text{Final Temp} - \text{Inlet Temp})] = 5 + [0.80 \times (85 - 5)] = 5 + 64 = \mathbf{69^\circ\text{C}}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Thermal regeneration efficiency in dairy pasteurizers: Regeneration efficiency ($R$) is defined as the fraction of the total required heating range ($\Delta T_{ ext{total}} = T_{ ext{final}} - T_{ ext{initial}}$) achieved by regenerative heat exchange from hot pasteurized milk to incoming cold raw milk.
Key Formula or Approach:
\[ \Delta T_{\text{total}} = T_{\text{final}} - T_{\text{inlet}} = 85^\circ\text{C} - 5^\circ\text{C} = 80^\circ\text{C} \]
\[ \text{Temperature Rise in Regenerator } (\Delta T_{\text{regen}}) = R \times \Delta T_{\text{total}} = 0.80 \times 80^\circ\text{C} = \mathbf{64^\circ\text{C}} \]
\[ T_{\text{after regen}} = T_{\text{inlet}} + \Delta T_{\text{regen}} = 5^\circ\text{C} + 64^\circ\text{C} = \mathbf{69^\circ\text{C}} \]

Step 2: Detailed Explanation:
Step-by-step thermodynamic calculation of regeneration temperature:
1. Total Desired Temperature Rise ($\Delta T_{\text{total}}$):
\[ \Delta T_{\text{total}} = T_{\text{pasteurization}} - T_{\text{raw milk inlet}} = 85^\circ\text{C} - 5^\circ\text{C} = 80^\circ\text{C} \]
2. Heat Energy Recovered by Regeneration ($80\%$):
\[ \Delta T_{\text{regen}} = 80\% \times 80^\circ\text{C} = 0.80 \times 80 = 64^\circ\text{C} \]
3. Temperature of Milk Leaving Regeneration Section ($T_{\text{after regen}}$):
\[ T_{\text{after regen}} = T_{\text{inlet}} + \Delta T_{\text{regen}} = 5^\circ\text{C} + 64^\circ\text{C} = \mathbf{69^\circ\text{C}} \]
4. (The hot section then only needs to supply additional heat from $69^\circ ext{C}$ to $85^\circ ext{C}$, yielding massive energy savings).

Step 3: Final Answer:
Therefore, the temperature of milk after regeneration would be 69°C, corresponding to option (B).