Question

In certain heat exchanger, both the fluids have identical mass flow rate-specific heat product. The hot fluid enters at 76°C and leaves at 47°C and the cold fluid entering at 28°C leaves at 57°C. The effectiveness of the heat exchanger is
1. 0.16
2. 0.60
3. 0.72
4. 1.00

Answer 1

Correct Answer - Option 2 : 0.60

Concepts:

Effectiveness of the heat exchanger: 

The effectiveness (ϵ) of a heat exchanger is defined as the ratio of the actual heat transfer to the maximum possible heat transfer.

Actual heat transfer = Q = m_hc_ph(t_h1 − t_h2) = m_cc_pc(t_c2 − t_c1) 

where m_hc_ph = C_h = hot fluid capacity rate; m_cc_pc = C_c = Cold fluid capacity rate.

Maximum possible heat transfer = C_min(t_h1 - t_c1); where C_min is minimum of (Ch, Cc)

\(\varepsilon = \frac{{{C_h}\left( {{t_{h1}} - {t_{h2}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}} = \frac{{{C_c}\left( {{t_{c2}} - {t_{c1}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}}\)

Calculation:

Given:

th1 = 76°C; th2 = 47°C; tc2 = 57°C ; tc1 = 28°C; Ch = Cc

\(\varepsilon = \frac{{{C_h}\left( {{t_{h1}} - {t_{h2}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}} = \frac{{{C_c}\left( {{t_{c2}} - {t_{c1}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}}\)

\(\varepsilon = \frac{{\left( {76 - 47} \right)}}{{\left( {76 - 28} \right)}} = 0.60\)