The overall heat transfer co-efficient for a shell and tube heat exchanger for clean surfaces is U₀ = 400 W/m².K. The fouling factor after one year of operation is found to be h_d0 = 2000 W/m².K. The overall heat transfer co-efficient at this time is

ANS:C - 333W/m².K

To find the overall heat transfer coefficient (𝑈U) after one year of operation, we can use the concept of overall heat transfer resistance: 1𝑈=1𝑈0+1ℎ𝑑0U1​=U0​1​+hd0​1​ Where:

• 𝑈0U0​ is the overall heat transfer coefficient for clean surfaces,
• ℎ𝑑0hd0​ is the fouling factor after one year of operation.

Given: 𝑈0=400 W/m2.KU0​=400W/m2.K ℎ𝑑0=2000 W/m2.Khd0​=2000W/m2.K Substituting the given values into the equation: 1𝑈=1400+12000U1​=4001​+20001​ 1𝑈=1400+12000=52000+12000=62000=1333.33 W/m2.KU1​=4001​+20001​=20005​+20001​=20006​=333.331​W/m2.K 𝑈=333.33 W/m2.KU=333.33W/m2.K Therefore, the overall heat transfer coefficient after one year of operation is approximately 333 W/m2.K333W/m2.K. Hence, the closest option is 333 W/m²·K.