What does the heat equation tell us about heat flow and energy balance?

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Discussion Overview

The discussion revolves around the heat equation and its implications for heat flow and energy balance in a specific context involving a wall and airflow. Participants explore the meaning of different terms in the equation and their physical significance.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents an equation related to heat flow and questions the interpretation of the left side, specifically regarding the meaning of the stored energy component.
  • Another participant asserts the principle of energy conservation, indicating that energy input equals energy output, but expresses uncertainty about the units involved in the equation.
  • A third participant confirms that the units on both sides of the equation are Watts, suggesting consistency in the energy balance.
  • A fourth participant references two equations, Q=MCpdT and Q=UAdT, to support the idea that heat flows and energy is conserved, but notes a potential discrepancy in units, suggesting they might be Joules instead.

Areas of Agreement / Disagreement

Participants generally agree on the principle of energy conservation, but there is uncertainty regarding the interpretation of specific terms in the equation and the consistency of units.

Contextual Notes

Participants express confusion about the units used in the equation and the implications of the terms, indicating a need for clarification on these aspects without resolving the underlying questions.

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I'm considering a wall, using this equation:

<br /> Q_P + \rho \cdot C_P \cdot \dot V\left( {T_O - T_R } \right) = U \cdot A\left( {T_R - T_O } \right)<br />

Where QP is added effect (an oven), \dot V is air-flow, and the rest should be self-explanatory. I'm just not sure what it tells me. The right side gives me the leakage of heat, but I'm not sure what the left side says. Could someone explain?
 
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Energy in = Energy out...

It looks like you have the input energy in the form of Qp and a stored energy component in the moving air stream. I'm still wondering about the units in that group though...
 
Well it's Watt on both sides...
 
Q=MCpdT
and Q=UAdT
so yeah heat flows, energy in=energy out.
But I think its Joules on either side.
 

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