Project ForgeThe wall of a constant-diameter pipe of length 1 m is heated uniformly with flux q" by a heater coil. The inlet flow is hydrodynamically fully developed; the fluid is incompressible, laminar, and steady. Bulk temperature is 0°C at the inlet and 50°C at the exit. Wall temperatures are measured at three equally-spaced locations P (0.4m), Q (0.6m), and R (0.8m) from the inlet: 50°C, 80°C, 90°C respectively. Among P, Q and R, the flow is thermally developed at
- AP, Q and R
- BP and Q only
- Q and R only
- DR only
Explanation
With constant wall flux, bulk temperature rises linearly: Tb(x)=50x (x in m, 0 to 1). At P (x=0.4): Tb=20, wall−bulk=50−20=30. At Q (x=0.6): Tb=30, wall−bulk=80−30=50. At R (x=0.8): Tb=40, wall−bulk=90−40=50. Flow is thermally developed once (Twall−Tbulk) becomes constant along x — true at Q and R (both 50°C), but not yet at P (only 30°C).
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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