Heat Transfer

[Chocolatecat]

In the equation for heat transfer rate, q=-kA (delta T/ delta x). Given that plastic with the same dimension as a metal has a low conductivity than the metal and the heat transfer rate in the materials would be different. Why was the coefficient 'k' thermal conductivity of a material added to the equation to make them equal?


We would discover that this proportionality is true when switching the material (for example, from metal to plastic).
We would also discover, though, that for equal values of A, x,

and T, the plastic's qx value would be lower than the metal's. This implies that by adding a coefficient that represents a measure of the material behavior, the proportionality may be transformed into equality. Therefore, we write qx=-k(delta T/delta x)

 

[rb1957]

is there a question there ?

"k" is the constant of proportionality, different for different materials.
q is directly proportional to A and the thermal gradient (dT/dx).
The two materials will have different values of k.

do you have any background in science ? are you playing with ChatGPT ??

 

[3DDave]

It's been a while since thermo, but those equations appear to not make sense. If Area is involved then the result is (Q/t), not q.

The usual way out is a dimensional analysis of the units.

Broadly, "k" is introduced to change a proportion to an equation.

I spent time earlier on a write-up, but wiped it out over the mismatches in the equations, so I don't know what it is specifically to be about.

 

[LittleInch]

This makes no sense.

What is "x"?

 

[3DDave]

"x" is the thickness of material.

 

[MintJulep]

This is always confusing because:

Power / Area of surface / Length of thickness

Dimensionally that "simplifies" to Power/Length, but that simplification obscures the meaning.

 

[IRstuff]

k is the thermal conductivity of the material in question, given in units of W/m-K, normalized to an area of 1 m².

Therefore, Q = k*(area/thickness)*delta_T, where thickness is the distance through the material that the heat must traverse, and delta_T is the temperature difference across that distance.

So, increasing the area increases the flow - check
increasing the thickness reduces the flow - check
increasing the temperature difference increases the flow - check