Negative sign in Fourier heat conduction equation indicatesa)Heat always flow is in the direction of positive temperature gradientb)Heat always flow in the direction of negative temperature gradientc)No heat flow is thered)Data is insufficientCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Fourier heat conduction equation:

The Fourier heat conduction equation describes the conduction of heat through a medium in the form of a differential equation, which is given by:

∂T/∂t = α(∂²T/∂x²)

where,
T = temperature of the medium
t = time
x = distance
α = thermal diffusivity of the medium

Negative sign:

The negative sign in the Fourier heat conduction equation indicates that heat always flows in the direction of the negative temperature gradient.

Explanation:

- The temperature gradient is defined as the rate of change of temperature with respect to distance. It is expressed as ΔT/Δx, where ΔT is the temperature difference across a distance Δx.
- The negative temperature gradient means that the temperature decreases with increasing distance. This means that the heat is flowing from the region of higher temperature to the region of lower temperature.
- The Fourier heat conduction equation describes the rate of change of temperature with respect to time and distance. The negative sign indicates that the temperature decreases with increasing distance, which means that the heat is flowing from the region of higher temperature to the region of lower temperature.
- Therefore, the negative sign in the Fourier heat conduction equation indicates that heat always flows in the direction of the negative temperature gradient.

Conclusion:

In summary, the negative sign in the Fourier heat conduction equation indicates that heat always flows in the direction of the negative temperature gradient, which means that it flows from the region of higher temperature to the region of lower temperature.

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