A wood log (k = 0.17 W/m · K and a = 1.28 × 10-7 m²/s) is 7.5 cm in diameter and is initially at a uniform temperature of 15°C. It is exposed to hot gases at 500°C in a fireplace with a heat transfer coefficient of 13.6 W/m2 · K on the surface. If the ignition temperature of the wood is 420°C, determine how long it will be before the log ignites.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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A wood log (\(k = 0.17 \, \text{W/m} \cdot \text{K}\) and \(\alpha = 1.28 \times 10^{-7} \, \text{m}^2/\text{s}\)) is 7.5 cm in diameter and is initially at a uniform temperature of 15°C. It is exposed to hot gases at 500°C in a fireplace with a heat transfer coefficient of 13.6 \(\text{W/m}^2 \cdot \text{K}\) on the surface. If the ignition temperature of the wood is 420°C, determine how long it will be before the log ignites.
Transcribed Image Text:A wood log (\(k = 0.17 \, \text{W/m} \cdot \text{K}\) and \(\alpha = 1.28 \times 10^{-7} \, \text{m}^2/\text{s}\)) is 7.5 cm in diameter and is initially at a uniform temperature of 15°C. It is exposed to hot gases at 500°C in a fireplace with a heat transfer coefficient of 13.6 \(\text{W/m}^2 \cdot \text{K}\) on the surface. If the ignition temperature of the wood is 420°C, determine how long it will be before the log ignites.
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