Rate of Heat Flow

Question

I was given a problem that asks me for the heat transfer power, also specifying that the heat transfer power is directly proportional to the difference in temperature. Does it refer to the rate of heat flow?

Answer 1

Yes, the name power alone suggests this. Power has units of energy per unit time, consequently heat transfer power is the transferred heat energy per unit time. This is often also called rate of heat flow.

Answer 2

To add to Noah's comment, it is also correct that this is proportional to the temperature difference. One can use an analogy with Ohm's law to see this. Ohm's law says $$I=V/R$$ If we relate a temperature difference between two points, T, as similar to a voltage difference between two points, and the thermal resistance between two points as the thermal resistivity (inverse of thermal conductivity) multiplied by a geometric factor, then we get: $$\dot q=T/R$$, where $\dot q$ is the heat flow rate.

Just to confirm, let's check the units. T is in Kelvin, K. Thermal conductivity is in $W/Km^2$. After taking the inverse of the thermal conductivity (which gives thermal resistivity) and multiplying a geometric factor through, the thermal resistance would be K/W. So $T/R$ would indeed give Watts, which is power.

This analogy is used in some calorimeter instrument designs.

Answer 3

Heat transfer power does refer to rate of heat flow, $\dot Q$, generally expressed as Joules/second or watts.

For heat transfer by conduction and convection, the rate of heat flow is directly proportional to temperature difference, governed by Fourier's Law of Conduction and Newton's Law of Cooling, respectively.

However, for heat transfer by radiation, it is directly proportional to the difference of the temperatures raised to the fourth power, governed by the Stefan-Boltzmann Law of Black body radiation.

Hope this helps.