What is the formula for conductive heat transfer?

• A. k x A x ΔT / L
• B. k x A (ΔT/Δx)
• C. Q = hAΔT
• D. σA T^4

Answer: (B)

Heat conduction is governed by Fourier’s law: the rate of heat transfer through a material is proportional to how well the material conducts heat, the area through which heat flows, and the temperature gradient across the material. In one dimension, this is written as Q = k A (ΔT/Δx). Here k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference across a thickness Δx, and the ratio ΔT/Δx represents the temperature gradient driving the heat flow. This shows that increasing the material’s ability to conduct heat (k), increasing the area (A), or steepening the temperature gradient (ΔT/Δx) increases the heat transfer rate.

The other forms correspond to different situations: Q = hAΔT describes convection, and σA T^4 describes radiation. The form with L is the same idea but just uses a different symbol for the distance; the version that explicitly uses the temperature gradient ΔT/Δx is the standard way to express conduction in a finite-difference sense, which is why it’s the best choice here.