Hot and cold fluids enter a parallel flow double t ube heat

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Hot and cold fluids enter a parallel flow double t ube heat exchanger at 100 °C and 15 °C, respectively. The heat capacity rates of hot and cold fluids are C_h = 2000 W/K and C_c = 1200 W/ K, respectively. If the outlet temperature of the cold fluid is 45 °C, the log mean temperature difference (LMTD) of the heat exchanger is _____ K (round off to two decimal places).

1. 5.771 °C or K
2. 517.71 °C or K
3. 157.71 °C or K
4. 57.71 °C or K

Correct Option: D

Hot fluid: (ṁ C_p)_h = 2000 W/K
T_{h_i} = 100 °C
Cold fluid: (ṁ C_p)_c = 1200 W/K
T_{c_i} = 15 °C, T_{c_o} = 45 °C
(ṁ C_p)_h (T_{h_i} - T_{h_o}) = (ṁ C_p)_c (T_{c_o} - T_{c_i})
⇒ 2000 × (100 - T_{h_o}) = 1200 (45 - 15)
⇒ T_{h_o = 82 °C
(∆T_i) = T_{h_i} - T_{c_i} = 100 - 15 = 85 °C
(∆T_o) = T_{h_o} - T_{c_o} = 82 - 45 = 37 °C}

(LMTD)_Parallel =	85° - 37°		= 57.71 °C or K
	ln	85
		37