Discussion
The heat flux in the 'X' direction (9X) is proportional to the magnitude of temperature change across a unit distance in 'X' direction. If 'K' is thermal conductivity of the material, then the heat flux can be expressed as :
Answer: B
The heat flux is -K(dT/dx), Fourier's law of heat conduction.
The quantity printed '9X' is the heat flux \(q_{x}\). Fourier's law states
\[ q_{x} = -K \frac{dT}{dx} \]
The flux is proportional to the temperature gradient, with the thermal conductivity K as the constant, and the minus sign shows that heat flows from hot to cold, down the gradient.
Dividing the gradient by K would make a better conductor carry less heat, which is backwards; leaving K out ignores the material; and the fourth expression is not even dimensionally a gradient.
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