In certain HE, both the fluids have identical mass flow rate-spec

SOLUTION

Concept:

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

\(\epsilon = \frac{{{Q_{act}}}}{{{Q_{max}}}}\)

Qact = ṁh Cph (Th1 – Th2) = ṁc Ċpc (Tc2 – Tc1)

Fluid Capacity Rate, C : Ch = ṁh Cph, Cc = ṁc Cpc

Qmax = Ch (Th1 – Tc1) or Cc (Th1 – Tc1)

Qmax = Cmin (Th1 – Tc1)

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

Calculation:

Given:

T_h1 = 76°C, T_h2=47°C, T_c1 = 28°C, T_c2 = 55°C
C_h = C_c

\(\epsilon = \frac{{\left( {{T_{h1}} - {T_{h2}}} \right)}}{{\left( {{T_{h1}} - {T_{c1}}} \right)}} \)

\( \epsilon = \frac{{76 - 47}}{{76 - 28}} = \frac{{29}}{{48}} = 0.60 \simeq 0.58\)