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Heat Transfer
Conduction
GATE 2007
Medium

Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m³. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK. The location of maximum temperature within the plate from its left face is

  • A15 mm
  • B10 mm
  • 5 mm
  • D0 mm

Explanation

T(x)=−(qgen/2k)x²+C1x+C2 with T(0)=160 giving C2=160, and T(0.02)=120 solving to C1=2000 (with qgen=80×10⁶ W/m³, k=200 W/mK). Maximum temperature location: dT/dx=0 ⟹ x=C1·k/qgen=2000×200/(80×10⁶)=0.005 m=5 mm.

Source: GATE ME 2007 (2007)

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