Calculating Heat Conduction Time for a Wooden Cylinder on a Hot Plate

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SUMMARY

The discussion focuses on calculating the heat conduction time for a wooden cylinder placed on a hot plate, starting at 298K and reaching a temperature of 523K. The heat transfer is analyzed under the assumption of perfectly insulated sides, except for the contact point with the hot plate. The key challenge identified is determining the total heat required, given that different sections of the cylinder will reach varying temperatures. The conversation also prompts consideration of alternative materials beyond wood.

PREREQUISITES
  • Understanding of heat conduction principles
  • Familiarity with Fourier's law of heat conduction
  • Knowledge of thermal properties of materials, specifically wood
  • Basic thermodynamics concepts
NEXT STEPS
  • Research Fourier's law of heat conduction in detail
  • Learn about the thermal conductivity of various materials
  • Explore numerical methods for solving heat conduction problems
  • Investigate the impact of insulation on heat transfer rates
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Students in physics or engineering disciplines, thermal engineers, and anyone interested in heat transfer analysis and material science.

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If a wooden cylinder at 298K with perfectly insulated sides (other than the one in contact with the hot plate) where placed with one end on a hot plate until any point on the cylinder reached a temperature of 523K and the power of the hot plate is known and it all goes into the wood. How long would it take?

I created this question for an essay which is intended to go beyond the syllabus so my textbook does not cover this topic. I know that the temperature will first be reached at the part of the cylinder which is in contact with the hot plate, however I don't know the total amount of heat required because each part of the cylinder will reach a different temperature.
 
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What would you do if it wasn't wood?
 

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