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Heat Transfer
Conduction
GATE 2019
Medium

One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is

  • ALinear
  • BQuadratic
  • Logarithmic
  • DExponential

Explanation

Steady 1-D conduction with no generation requires kA(x)dT/dx=constant. Since A(x) is linear in x, dT/dx=C/A(x) is inversely proportional to a linear function of x, and integrating 1/A(x) (linear in x) produces a logarithmic function of x. So T(x) is logarithmic.

Source: GATE ME 2019 Session 2 (Set 3) (2019)

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