Heat flux

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Heat flux or thermal flux is a flow of energy per unit of area per unit of time. In SI units, it is measured in [W·m^-2]. It has both a direction and a magnitude so it is a vectorial quantity. To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small.

Heat flux is often denoted $\overrightarrow{\phi_q}$ , the subscript q specifying heat flux, as opposed to mass or momentum flux. The most important appearance of heat flux in physics is in Fourier's law describing heat conduction.

Heat flux $\overrightarrow{\phi_q}$ through a surface.

[edit] Measuring heat flux

Main article: Heat flux sensor

The measurement of heat flux is most often done by measuring a temperature difference over a piece of material with known thermal conductivity. This method is analogous to a standard way to measure an electric current, where one measures the voltage drop over a known resistor.

[edit] Relevance to science and engineering

One of the tools in a scientist's or engineer's toolbox is the energy balance. Such a balance can be set up for any physical system, from chemical reactors to living organisms, and generally takes the following form

$\frac{\partial E_{in}}{\partial t} - \frac{\partial E_{out}}{\partial t} - \frac{\partial E_{accumulated}}{\partial t} = 0$

where the three $\frac{\partial E}{\partial t}$ terms stand for the time rate of change of respectively the total amount of incoming energy, the total amount of outgoing energy and the total amount of accumulated energy.

Now, if the only way the system exchanges energy with its surroundings is through heat transfer, the heat flux can be used to calculate the energy balance, since

$\frac{\partial E_{in}}{\partial t} - \frac{\partial E_{out}}{\partial t} = \oint_S \overrightarrow{\phi_q} \cdot \, \overrightarrow{dS}$

where we have integrated the heat flux $\overrightarrow{\phi_q}$ over the surface $S$ of the system.

In real-world applications of course one cannot know the heat flux at every point on the surface, but intelligent estimates to calculate the integral can be made, for example through Monte Carlo integration.