Dissipation due to heat conduction

[pere.balazs]

What is the dissipation due to heat conduction?

$$D = -k \frac{\vec q\cdot\nabla T}{T}$$

where q is the heat flux, k is the
coefficient of heat conduction and T is the absolut temperature.

What is the physical meaning of this?

 

[Mapes]

This is a peculiar term. According to Fourier's law of conduction,

$$\vec{q}\equiv -k\nabla T\mathrm{,}$$

so

$$-k \frac{\vec q\cdot\nabla T}{T}=k^2\frac{\nabla ^2 T}{T}$$

with units of W² m^-4 K^-1. In kinetic theory, this would correspond to $Tk\dot{\sigma}$, where $\dot{\sigma}$ is the volumetric rate of entropy creation. To my knowledge, this term isn't used for anything useful; are you certain about it?

 

[astrokreng]

The dissipation due to heat conduction refers to the process of heat energy being transferred from a region of higher temperature to a region of lower temperature through the movement of particles. This dissipation is quantified by the D term in the equation, which takes into account the heat flux, or the rate of heat transfer, as well as the temperature gradient, or the difference in temperature between the two regions. The coefficient of heat conduction, k, represents the material's ability to conduct heat and influences the rate of dissipation. The physical meaning of this equation is that it describes the mechanism by which heat is transferred through a material, and how much energy is dissipated in the process.