# SI units for Heat transfer equation

by jeff1evesque
Tags: equation, heat, transfer, units
 P: 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
 HW Helper P: 5,346 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.
P: 312
 Quote by 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.
Oh I see it now, but what about the unit for seconds "s"?

PF Patron
HW Helper
P: 2,532

## SI units for Heat transfer equation

k is not the thermal resistivity, it's the inverse thermal diffusivity.
P: 312
 Quote by Mapes k is not the thermal resistivity, it's the inverse 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
 PF Patron HW Helper Sci Advisor P: 2,532 It doesn't matter if I'm sure. Check the literature; ask your teacher for a reference.

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