GATE ME 2019 Set 1 — Question 42
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Heat Transfer → Convection → Flat Plate & Pipe Correlations
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Question
The wall of a constant diameter pipe of length 1 m is heated uniformly with flux by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to at the inlet and at the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow thermally develops after some distance from the inlet. The following measurements are made:
Among the locations P, Q and R, the flow is thermally developed at
| Point | P | Q | R |
|---|---|---|---|
| Wall Temp () | 50 | 80 | 90 |
Correct answer
(C) Q and R only
Solution
1.Analyze Bulk Temperature ():
For a constant wall heat flux , the bulk temperature of the fluid increases linearly along the length of the pipe..
2.Calculate at points P, Q, and R:
- At P (): .
- At Q (): .
- At R (): .
In the thermally developed region with constant heat flux, the heat transfer coefficient is constant. Since , the temperature difference must be constant.
- At P: .
- At Q: .
- At R: .
The temperature difference is constant at points Q and R (), but different at P. Therefore, the flow is thermally developed at Q and R only.
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