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Mechanical Engineering QUESTION #2416
Question 1
The general 1D heat conduction (diffusion) equation with internal heat generation \(\dot{q}\) (W/m³) is:
  • \(\frac{\partial^2 T}{\partial x^2} + \frac{\dot{q}}{k} = \frac{1}{\alpha}\frac{\partial T}{\partial t}\) where \(\alpha = k/(\rho c)\)✔️
  • \(\frac{\partial^2 T}{\partial x^2} = \frac{k}{\rho c}\frac{\partial T}{\partial t}\)
  • \(\frac{\partial T}{\partial t} = k\frac{\partial^2 T}{\partial x^2}\)
  • \(\frac{\partial^2 T}{\partial x^2} = \frac{\dot{q}}{k}\)
Correct Answer Explanation
The 1D heat diffusion equation: \(\frac{\partial^2 T}{\partial x^2}+\frac{\dot{q}}{k}=\frac{1}{\alpha}\frac{\partial T}{\partial t}\), where \(\alpha=k/(\rho c)\) (m²/s) is the thermal diffusivity.