The flow rates of hot and cold water streams running through a parallel flow heat exchanger are 0.2 Kg/sec and 0.5 Kg/sec respectively. The inlet temperatures on hot and cold sides are 75°C and 20°C respectively. The exit temperature of hot water is 45°C. Calculate LMTD of heat exchanger.
29.12°C
Energy balance gives \(T_{c,o}=20+\frac{0.2}{0.5}(75-45)=32^\circ\mathrm C\). For parallel flow, endpoint temperature differences are \(\Delta T_1=75-20=55^\circ\mathrm C\) and \(\Delta T_2=45-32=13^\circ\mathrm C\). Thus \(\Delta T_{lm}=\frac{55-13}{\ln(55/13)}\approx29.12^\circ\mathrm C\).
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