Question

Milk enters into the heating section (heat exchanger) of a high temperature short time pasteurization plant at a temperature of ${45}^{0}C$ and leaves at ${72}^{0}C$. Hot water at a temperature of ${95}^{0}C$ enters counters currently into the heat exchanger and leaves at ${77}^{0}C$. The effectiveness of the heat exchanger is

• A. 0.84
• B. 0.18
• C. 0.54
• D. 0.36

Answer 1

The correct option is C 0.54



Energy balance:
Heat released by hot water = Heat received by cool milk

$\left(\dot{m}{C}_p{)}_{water}\right(T_{hi}-T_{he})=(\dot{m}{C}_p{)}_{milk}(T_{cc}-T_{ci})$

$C_{milk}(72-45)=C_{water}(95-77)$

$27\times C_{milk}=18\times C_{water}$

$C_{min}=C_{milk}$

$\text{Effectiveness =}\frac{\left(\dot{m}{C}_P{)}_{milk}\right(T_{cc}-T_{ci})}{\left(\dot{m}{C}_P{)}_{milk}\right(T_{cc}-T_{ci})}$

$=\frac{C_{min}(72-45)}{C_{min}(92-45)}=\frac{27}{50}=0.54$