In Fourier's law, qx = -k A (dT/dx), the heat transfer rate is proportional to which of the following?

In Fourier's law, qx = -k A (dT/dx), the heat transfer rate is proportional to which of the following?

• A. The negative temperature gradient, the cross-sectional area, and the thermal conductivity
• B. The positive temperature gradient and area
• C. The inverse of temperature
• D. The surface emissivity

Answer: (A)

Heat transfer by conduction is driven by how strong the temperature difference is, how much material is available for the transfer, and how well the material conducts heat. Fourier’s law says the rate of heat transfer in the x-direction is qx = -k A (dT/dx). The rate is proportional to the thermal conductivity k (how easily heat moves through the material), the cross-sectional area A (more area lets more heat pass), and the temperature gradient dT/dx (the steeper the gradient, the greater the driving force for heat flow). The minus sign indicates heat flows opposite to the direction of increasing temperature, so the gradient is effectively taken as negative for forward heat flow along +x. In magnitude, you can think of it as proportional to k A |dT/dx|. This is not about the inverse of temperature or about emissivity, which relates to radiation, not conduction.

Heat transfer by conduction is driven by how strong the temperature difference is, how much material is available for the transfer, and how well the material conducts heat. Fourier’s law says the rate of heat transfer in the x-direction is qx = -k A (dT/dx). The rate is proportional to the thermal conductivity k (how easily heat moves through the material), the cross-sectional area A (more area lets more heat pass), and the temperature gradient dT/dx (the steeper the gradient, the greater the driving force for heat flow). The minus sign indicates heat flows opposite to the direction of increasing temperature, so the gradient is effectively taken as negative for forward heat flow along +x. In magnitude, you can think of it as proportional to k A |dT/dx|. This is not about the inverse of temperature or about emissivity, which relates to radiation, not conduction.