SI units for Heat transfer equation

[jeff1evesque]

Homework Statement

I am trying to get the units to match up on both sides. $$\frac{\partial T}{\partial t} = \frac{\nabla ^{2} T}{k} = \frac{1}{K}(\frac{\partial ^2 T}{\partial x^2} + \frac{\partial ^2 T}{\partial y^2} + \frac{\partial ^2 T}{\partial z^2}})$$, where k is the thermal resistivity.

The Attempt at a Solution

By searching all over the web, I've found that thermal resistivity "k" has units of $$\frac{Kelvins}{W}$$.

Therefore,

$$\frac{\partial T}{\partial t} = \frac{Kelvins}{s} \neq (\frac{W}{Kelvins})*(\frac{Kelvins}{m^2})$$. Could someone help me correct the units.Thanks,JL

 

[LowlyPion]

This may be useful:
http://en.wikipedia.org/wiki/Thermal_resistivity

I think there needs to be a factor of m added to your statement.

 

[jeff1evesque]

This may be useful:
http://en.wikipedia.org/wiki/Thermal_resistivity

I think there needs to be a factor of m added to your statement.

Oh I see it now, but what about the unit for seconds "s"?

 

[Mapes]

k is not the thermal resistivity, it's the inverse http://en.wikipedia.org/wiki/Thermal_diffusivity" .

 

[jeff1evesque]

k is not the thermal resistivity, it's the inverse http://en.wikipedia.org/wiki/Thermal_diffusivity" .

Are you sure? I mean the units do infact check out if you are correct- but according to my class notes they've referred it to thermal resistivity.

Thanks a lot.

JL

 

[Mapes]

It doesn't matter if I'm sure. Check the literature; ask your teacher for a reference.