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qid 8531 · math
Question: The temperature at the point $(x, y, z)$ in a substance with conductivity $K=6.5$ is $u(x, y, z)=2 y^2+2 z^2$. Find the rate of heat flow inward across the cylindrical surface $y^2+z^2=6$, $0 \leqslant x \leqslant 4$
- $800\pi$
- $1504\pi$
- $1248\pi$
- $1560\pi$
- $960\pi$
- $1104\pi$
- $1320\pi$
- $1400\pi$
- $1040\pi$
- $984\pi$
Our answer: C. $1248\pi$ Source quote machine-checked (exact quote)
How it was answered
Multi-step solver (maze), replayed by code
Current source
Wikipedia, "Thermal conduction" (Fourier's law)
https://en.wikipedia.org/wiki/Thermal_conduction
“the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows.”
Source quote machine-checked (exact quote)
Earlier version (superseded)
https://en.wikipedia.org/wiki/Thermal_conduction#Fourier
Source weak (http_get_200_text_and_question_terms)
Earlier version (superseded)
No public source has been found for this card yet (3 places checked internally).
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