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Difficulty: MediumHeat Transfer: Conduction

A technician is mounting a sensitive metal control panel to a high-temperature industrial furnace using solid steel standoff bolts. To minimize the rate of heat conducted directly through these bolts to the control panel, which design modification is most effective?

  1. Use longer standoff bolts with a smaller cross-sectional area.Answer
  2. B
    Polish the exterior of the bolts to a highly reflective finish to bounce the heat back into the furnace.
  3. C
    Choose a bolt material with a lower specific heat capacity so that the metal requires more energy to heat up.
  4. D
    Shorten and widen the bolts so the increased metal mass can physically block the transfer of thermal energy.

Answer

Use longer standoff bolts with a smaller cross-sectional area.
The rate of conductive heat transfer through a solid object depends heavily on its geometry. It is directly proportional to the cross-sectional area and inversely proportional to the length. By using longer bolts with a smaller cross-sectional area, you increase the thermal resistance of the connection, which significantly reduces the amount of heat that reaches the control panel.

Step-by-Step Solution

1
Identify the primary mechanism of heat transfer in the scenario.
The heat is traveling through solid steel bolts that directly connect a hot object to a cooler one, which means the mechanism is thermal conduction.
Understanding the heat transfer mode is necessary to apply the correct physical principles.
2
Recall the factors that affect the rate of thermal conduction.
According to Fourier's Law of Thermal Conduction, the rate of heat transfer (Q/tQ/t) is directly proportional to the cross-sectional area (AA) and inversely proportional to the length (LL) of the conductor.
This relationship determines how geometric changes will impact heat flow.
3
Determine the geometric changes required to minimize the heat transfer rate.
To decrease the heat transfer rate, the thermal resistance must be increased by minimizing the cross-sectional area (making the bolts thinner) and maximizing the length (making the bolts longer).
A smaller pathway over a longer distance restricts the flow of thermal energy through the solid.

Key Concept

Fourier's Law of Thermal Conduction
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Topics

Heat Transfer: Conduction

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