# SI units for Heat transfer equation

1. ### jeff1evesque

312
1. The problem statement, all variables and given/known data
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.

3. 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

5,328
3. ### jeff1evesque

312
Oh I see it now, but what about the unit for seconds "s"?

Last edited: Jul 9, 2009

2,532
5. ### jeff1evesque

312
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

6. ### Mapes

2,532
It doesn't matter if I'm sure. Check the literature; ask your teacher for a reference.