Question

In a parallel flow heat exchanger with equal heat capacities of hot and cold fluids and taking infinite length of heat exchanger, the value of effectiveness of heat exchanger is

• A. 0.25
• B. 1.0
• C. 0.5
• D. 0.75

Answer 1

The correct option is C 0.5

Parallel flow heat echanger for infinite length.

$\dot{m_n}{c}_{pn}=\dot{m_c}.c_{pc}$

Energy balance:
$\dot{m_n}.c_{pn}(T_{hi}-T_{hc})=\dot{m_c}.c_{pc}(T_{ce}-T_{ci})$

$T_{hi}-T=T-T_{ci}$

$T=\left(\frac{T_{hi}+T_{ci}}{2}\right)$

$effectiveness(\in )=\frac{C_{min}(T_{hi}-T)}{C_{min}(T_{hi}-T_{ci})}=\frac{T_{hi}-\left(\frac{T_{hi}+T_{ci}}{2}\right)}{T_{hi}-T_{ci}}$

$=\frac{2T_{hi}-T_{hi}-T_{ci}}{2(T_{hi}-T_{ci})}$

$\in =\frac{(T_{hi}-T_{ci})}{T_{hi}-T_{ci}}=0.5$