Cold water flowing at 0.1 kg/s is heated from 20°C to 70°C

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Cold water flowing at 0.1 kg/s is heated from 20°C to 70°C in a counter flow type heat exchange by a hot water stream flowing at 0.1 kg/s and entering at 90°C. The specific heat of water is 4200 J/(kgK) and density is 1000 kg/m³ . If the overall heat transfer coefficient U for the heat exchange is 2000 W/(m² K), the required heat exchange area (in m² ) is

1. 0.052
2. 0.525
3. 0.151
4. 0.202

Correct Option: B

C_h = C_c = 0.1 × 4200 = 420 J/s
C_c (T_c1 – T_c2) = C_h (T_h1 – T_h2) (70 – 20) = 90° T_h2
LMTD = θ₁ = θ₂ (∵ θ₁ = θ₂)
C_c (T_c2 – T_c1) = UA(LMTD)
or A = 0.525 m².