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Heat Transfer
Convection & Radiation
GATE 2008
Hard

For a 1m×2m×2m rectangular object, five faces are insulated. The sixth face PQRS (area 4 m²) is not insulated and interacts thermally with the ambient, with convective heat transfer coefficient 10 W/m².K. Ambient temperature is 30°C. Heat is uniformly generated inside the object at 100 W/m³. Assuming face PQRS is at uniform temperature, its steady state temperature is

  • A10°C
  • B20°C
  • C30°C
  • 40°C

Explanation

Volume=1×2×2=4 m³, so total heat generated=100×4=400 W. At steady state all generated heat leaves through face PQRS (area 4 m², the other five faces insulated): 400=h·A·(Ts-Tamb)=10×4×(Ts-30) ⟹ Ts-30=10 ⟹ Ts=40°C.

Source: GATE ME 2008 (2008)

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