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The wall of a constant diameter pipe of length 1 m is heated uniformly with flux q” 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 0°C at the i nlet and 50°C at the exi t. 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 at:
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- R only
- P and Q only
- P, Q and R
- Q and R only
Correct Option: D
I n case of uni for m heat flux, bulk mean t emperat ur e var ies linearly.
The difference bet ween bulk mean temperature and wall temperature is constant in thermally developed region so bulk tempeature,
T(x) = A + Bx
At x = 0, T = 0°C
⇒ A = 0°C
At x = 1, T = 50°C
⇒ B = 50°C
∴ T(x) = 50x
Here,
So, Q and R in thermally developed region.
