Fourier's law of heat conduction: correct mathematical form Given Q (heat rate), A (area normal to heat flow), dT (temperature difference), dx (thickness along heat flow), and k (thermal conductivity). Select the correct expression for one-dimensional conduction through a slab.
Mechanical Engineering
Heat Transfer, Refrigeration and Air Conditioning
Difficulty: Easy
Choose an option
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AQ = k A (dT/dx)
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BQ = - k A (dT/dx)
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CQ = k A (dx/dT)
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DQ = - k A (dx/dT)
Answer
Correct Answer: Q = - k A (dT/dx)
Explanation
ConceptFourier's law (1-D): heat flows from hot to cold in the direction of decreasing temperature; the negative sign enforces this directionality.
Step-by-stepHeat flux qx = -k (dT/dx).Multiply by area A to get heat rate: Q = qx A = - k A (dT/dx).
Common pitfallOmitting the minus sign gives non-physical positive heat flow with positive temperature gradient.