Question

If there is no change in the temperatures of liquid and the tube wall for turbulent flow through the tube, flow velocity is doubled and tube diameter is halved, then the heat transfer coefficient will become remain the original value.

• A. Same
• B. Half
• C. Four times
• D. Two times

Hint:

h \(\propto\) V\(^{0.8}\) D\(^{0.2}\).
Doubling V and halving D gives 2\(\times\) h.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Heat transfer coefficient depends on flow parameters.
The Dittus-Boelter equation relates these parameters.

Step 2: Key Formula or Approach:
Nu \(\propto\) Re\(^{0.8}\) Pr\(^{0.4}\), and h \(\propto\) Nu/D.
Re \(\propto\) VD.

Step 3: Detailed Explanation:
V is doubled (2V), D is halved (D/2).
Re \(\propto\) (2V)(D/2) = V D (same as original).
Nu \(\propto\) Re\(^{0.8}\) = same.
h \(\propto\) Nu D \(\propto\) 1 (D/2) = 2 times.
Thus, the heat transfer coefficient becomes two times.

Step 4: Final Answer:
The heat transfer coefficient will become two times.
Hence, the correct option is (D).