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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.

Difficulty: Easy

Q = k A (dT/dx)
Q = - k A (dT/dx)
Q = k A (dx/dT)
Q = - k A (dx/dT)

Correct Answer: Q = - k A (dT/dx)

Explanation:

Concept
Fourier's law (1-D): heat flows from hot to cold in the direction of decreasing temperature; the negative sign enforces this directionality.

Step-by-step
Heat flux q_x = -k (dT/dx).Multiply by area A to get heat rate: Q = q_x A = - k A (dT/dx).

Common pitfall
Omitting the minus sign gives non-physical positive heat flow with positive temperature gradient.

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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.

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