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Equation of thermal conduction in solids

This article explores the equation of thermal conduction in solids, focusing on the rate of change of heat energy within a volume. According to the principles outlined in LL7 Section 32, this rate is equal to the negative of the heat energy flux exiting through the boundary surface. By employing Gauss’s theorem, we derive a volume integral reflecting this relationship. We delve into how these concepts are crucial for understanding heat transfer in solid materials and the implications for engineering applications.

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Equation of thermal conduction in solids

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  1. Equation of thermal conduction in solids LL7 Section 32

  2. Solids

  3. Rate of change of heat energy in a volume = negative of heat energy flux q out of volume through the boundary surface = Negative volume integral of div qby Gauss’s theorem.

  4. Per unit volume…

  5. Because of second term…

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