In a parallel flow heat exchanger operating under steady

In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at 1 kg/s with cp = 4 kJ/kgK, enters the heat exchanger at 102°C while the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m²K and the corresponding heat transfer surface area is 5 m². Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2ε = 1 – expt(–2NTU). The exit temperature (in °C) for the cold fluid is

t_h₁ = 102 °C
t_c₂ = 15 °C

NTU =	UA	=	1 × 10³ × 5
	C_min		1 × 4 × 10³

ε =	1 - exp(-2NTU)
	2

=	1 - exp(-2.5)	= 0.458
	2

∴ 0.458 =	t_c₁ - t_c₂	=	t_c₁ - 15
	t_h₁ - t_h₂		102 - 15

or t_c₁ = 0.458 × (102 – 15) + 15 = 54.846° C ≈ 55°C
Alternately
C = M_c C_c = M_hC_h = 1 × 4 kJ/kg K

∴ C =	M_c C_c	= 1
	M_hC_h

NTU =	U.A.	=	1 × 5	=	5
	C_min		4		4

From the relation

ε =	1 - e^{-( 2 × 5 / 4 )}	= 0.46
	2

Now , ε =	t_c₂ - 15	= 0.46
	102 - 15

∴ 0.46 = t_c₂
or t_c₂ = 54.9