Water (c = 4.18 kJ/kgK) at 80°C enters a counter flow

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Water (c = 4.18 kJ/kgK) at 80°C enters a counter flow heat exchanger with a mass flow rate of 0.5 kg/s. Air (c = 1 kJ/kgK) enter at 30°C with a mass flow rate 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is

1. 40
2. 20
3. 10
4. 5

Correct Option: C

ε =	C_h	×	(t_h1 - t_h2)
	C_min		(t_h1 - t_c1)

∴ 0.8 =	4.18 × 0.5	×	(80 - t_h2)
	2.09 × 1		(80 - 30)

⇒ t_h2 = 40°C
m_hc_ph (t_h1 – t_h2) = m_c c_cp (t_c2 – t_c1)
∴ 0.5 × 4.18 × 40 = 2.09 × 1 × (t_c2 – 30)
⇒ t_c2 = 70°C
&thet;₁ = θ₂ = 10°C
∴ LMTD = 10°C