Q1: For turbulent flow in a tube, the heat transfer co-efficient is obtained from the Dittus-Boelter correlation. If the tube diameter is halved and the flow rate is doubled, then the heat transfer co-efficient will change by a factor of

ANS:C - 6.1

The Dittus-Boelter correlation relates the Nusselt number (𝑁𝑢Nu) to the Reynolds number (𝑅𝑒Re) and Prandtl number (𝑃𝑟Pr) for turbulent flow inside a tube. It is expressed as: 𝑁𝑢=0.023×𝑅𝑒0.8×𝑃𝑟0.3Nu=0.023×Re0.8×Pr0.3 When the tube diameter is halved and the flow rate is doubled, the Reynolds number and Prandtl number will change. The Reynolds number (𝑅𝑒Re) is given by: 𝑅𝑒=𝜌×𝑣×𝐷𝜇Re=μρ×v×D​ where:

• 𝜌ρ is the fluid density
• 𝑣v is the velocity of the fluid
• 𝐷D is the diameter of the tube
• 𝜇μ is the dynamic viscosity of the fluid

When the tube diameter is halved and the flow rate is doubled:

• The velocity (𝑣v) will be doubled.
• The diameter (𝐷D) will be halved.

The Reynolds number is proportional to the velocity and diameter. So, the Reynolds number will remain constant after these changes. Since the Nusselt number (𝑁𝑢Nu) is directly proportional to the heat transfer coefficient, and the Reynolds number doesn't change in this scenario, the heat transfer coefficient will also remain constant. Therefore, the factor by which the heat transfer coefficient changes is 1. So, the correct answer is 1.