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 inlet and 50 °C 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:
Point |
P |
Q |
R |
Wall Temp (°C) |
50 |
80 |
90 |
Among the locations P, Q and R, the flow is thermally developed at
Concept:
For solving this question, draw temperature (T) versus x profile.
Flow will be thermally fully developed when slopes of both mean fluid temperature line (T_{m}) and wall temperature line (T_{s}) are same.
Calculation:
Slope of line \(PQ=\frac{80-50}{0.2}=150\)
Slope of line \(P'{Q}'=\frac{30-20}{0.2}=50\)
⇒ Flow is not thermally developed at P.
Slope of line \(QR=\frac{90-80}{0.2}=50\)
Slope of line \({Q}'{R}'=\frac{40-30}{0.2}=50\)
⇒ Flow is developed thermally at point Q and R.