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Mechanical Engineering QUESTION #2415
Question 1
Fourier's Law of heat conduction in one dimension states that the heat flux density \(q''_x\) (W/m²) is:
  • \(q''_x = +k\frac{dT}{dx}\) (proportional to temperature gradient)
  • \(q''_x = -k\frac{dT}{dx}\) (negative sign — heat flows from hot to cold)✔️
  • \(q''_x = k\frac{d^2T}{dx^2}\)
  • \(q''_x = \frac{k \cdot A \cdot \Delta T}{L^2}\)
Correct Answer Explanation
Fourier's Law: \(q''_x=-k\frac{dT}{dx}\) where \(k\) (W/m·K) is thermal conductivity. The negative sign ensures that heat flows from hot to cold.