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Question

Difficulty: MediumHeat Transfer: Conduction

A metal fabricator is designing a custom hand tool to manipulate red-hot steel parts in a forge. To ensure the handle stays safe to touch, the designer must minimize the rate of conductive heat transfer from the hot jaws along the tool's solid shaft. Which of the following shaft designs will most effectively restrict this heat conduction?

  1. A long shaft with a reduced cross-sectional area, made from a material with low thermal conductivity.Answer
  2. B
    A thick, massive shaft designed to absorb the thermal energy before it reaches the handle.
  3. C
    A short, wide shaft designed to rapidly dissipate the heat into the surrounding air.
  4. D
    A standard shaft coated with a highly reflective metallic finish to bounce the heat back toward the jaws.

Answer

The most effective design is a long shaft with a reduced cross-sectional area, made from a material with low thermal conductivity.
The rate of heat conduction through a solid object is directly proportional to its cross-sectional area and inversely proportional to its length. Therefore, a longer, thinner shaft made of an insulating material provides the greatest physical resistance to conductive heat flow.

Step-by-Step Solution

1
Identify the primary mechanism of heat transfer being restricted.
The problem specifies minimizing 'conductive heat transfer' through a solid shaft.
Different modes of heat transfer (conduction, convection, radiation) require different mitigation strategies.
2
Recall the factors that affect the rate of thermal conduction in a solid.
Conduction rate depends on the material's thermal conductivity, the cross-sectional area (thickness), and the length of the pathway.
Fourier's law of heat conduction dictates how physical dimensions influence heat flow.
3
Determine how to modify these factors to minimize conduction.
To restrict heat flow, the length must be increased (longer path), the cross-sectional area must be decreased (narrower path), and a material with low conductivity must be used.
Heat conduction is directly proportional to area and inversely proportional to length.

Key Concept

Factors Affecting Thermal Conduction
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Topics

Heat Transfer: Conduction

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