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SI units for Heat transfer equation 
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#1
Jul909, 03:22 PM

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


#2
Jul909, 03:33 PM

HW Helper
P: 5,341

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. 


#3
Jul909, 03:40 PM

P: 312




#4
Jul909, 04:01 PM

Sci Advisor
HW Helper
PF Gold
P: 2,532

SI units for Heat transfer equation
k is not the thermal resistivity, it's the inverse thermal diffusivity.



#5
Jul909, 04:16 PM

P: 312

Thanks a lot. JL 


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