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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
  • a)
    Quadratic
  • b)
    Exponential
  • c)
    Logarithmic
  • d)
    Linear
Correct answer is option 'C'. Can you explain this answer?
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One-dimensional steady state heat conduction takes place through a sol...
Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.






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Explanation:

In one-dimensional steady state heat conduction, the temperature distribution in the solid depends on the variation of cross-sectional area in the direction of heat transfer. Let's analyze each option to understand which one is correct.

Option A: Quadratic

A quadratic temperature distribution would imply that the temperature varies with the square of the distance. However, since the cross-sectional area varies linearly, this means that the distance is also varying linearly. Therefore, a quadratic temperature distribution is not possible in this case.

Option B: Exponential

An exponential temperature distribution would imply that the temperature varies exponentially with the distance. However, since the cross-sectional area varies linearly, this means that the distance is also varying linearly. Therefore, an exponential temperature distribution is not possible in this case.

Option C: Logarithmic

A logarithmic temperature distribution would imply that the temperature varies logarithmically with the distance. In this case, as the cross-sectional area varies linearly, the distance is also varying linearly. Therefore, a logarithmic temperature distribution is possible in this case.

Option D: Linear

A linear temperature distribution would imply that the temperature varies linearly with the distance. Since the cross-sectional area varies linearly, this means that the distance is also varying linearly. Therefore, a linear temperature distribution is possible in this case.

Conclusion:

The correct answer is option C: Logarithmic. The temperature distribution in the solid will follow a logarithmic variation with the distance due to the linear variation of the cross-sectional area in the direction of heat transfer.
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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 isa)Quadraticb)Exponentialc)Logarithmicd)LinearCorrect answer is option 'C'. Can you explain this answer?
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