Heat flow through very thick-walled cylinders should be calculated using the ___________ mean radius?
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Answer: B. Logarithmic
Explanation
Thick-walled cylindrical systems feature a radial area gradient that prevents the use of simple arithmetic mean radii. Logarithmic mean radius accounts correctly for the non-linear heat conduction area variation across thick walls. Fourier's law integration across cylindrical coordinates yields the logarithmic expression requiring this mean radius. Heat conduction through cylindrical walls is governed by radial area expansion from inner to outer radius. Logarithmic mean radius is defined as outer radius minus inner radius divided by the natural log of their ratio. Thin-walled cylinders allow approximating mean radius as arithmetic average without significant calculation errors.
Insulation layers on large industrial storage tanks and thick pipes require logarithmic mean calculations. Nuclear fuel rod cladding and high-pressure chemical reactor walls demand precise thick-cylinder heat transfer analysis. Thermal design software automatically applies logarithmic mean radii for high radius-ratio geometries. Arithmetic mean radius is suitable only for thin walls where radial area changes are negligible. Geometric mean radius is used in electrical capacitance and inductance calculations rather than heat conduction. Stating either arithmetic or geometric means are acceptable ignores the mathematical derivation of radial heat flow.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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