Thread: analogy to fouriers law

I recently started a module on heat transfer at my university. and pretty much the first thing we learned was fouriers law.

so for one dimensional heat conduction

q = kA dt/dx

where the heat transfer rate is proportional to the area and the temperature difference but inversely proportional to the thickness of the material.

And this got me thinking, if we consider the temperature difference to be a potential difference and the rate of heat transfer to be a current, we can view the term kA/dx as a resistance term.
I = V/R

and then i thought, that this form of an equation probably occurs in many areas of science.

Does anyone know of a similar example in another aspect of science.?

Originally Posted by organic god

I recently started a module on heat transfer at my university. and pretty much the first thing we learned was fouriers law.

so for one dimensional heat conduction

q = kA dt/dx

where the heat transfer rate is proportional to the area and the temperature difference but inversely proportional to the thickness of the material.

And this got me thinking, if we consider the temperature difference to be a potential difference and the rate of heat transfer to be a current, we can view the term kA/dx as a resistance term.
I = V/R

and then i thought, that this form of an equation probably occurs in many areas of science.

What you are finding out is that any system of first-order ordinary differential equations with constant coefficients can be modeled as a simple RLC circuit. That is precisely the principle behind the old analog computers.

The spring, mass, dashpot systems studied by mechanical engineers are modeled in just this way.

Does anyone know of a similar example in another aspect of science.?[/quote]

In fluid flow in a pipe, the flow (current) is directly proportional to the pressure drop (potential difference) and inversely proportional to the length of the pipe (resistance). However the resistance also varies with the flow velocity squared so the relation isn't quite as simple as with thermal and electrical conduction.