How to ball park calculate thermal resistance of a square pl

[jalbers@bsu.edu]

I want to be able to get a ball park estimation of the thermal
resistance of various shapes (square plate, circular plate, ...) made
out of various materials (aluminum, copper, ...)

I know that Rthermal = deltaT/Power and that Rthermal = 1/(h*A) where
h is the transfer or convection coefficient.

According to an online source h can be approximated as 0.00221 *
(delta T/L)^0.25 where L is the direction of natural convection
(vertical). Units (W/in^2/degrees C).

This is great but as far as I can tell there is no provision in these
formulas for the type of material or its thickness. I am looking for
a ballpark formula to be able to calculate thermal resistance that
involves the thermal conductivity of the material.

I found some really neat calculators on this site:
http://www.novelconceptsinc.com/calculators.htm but these may not be
available in the future.

Any help would be greatly appreciated. Thanks

 

[John Larkin]

On Wed, 8 Jul 2009 08:04:17 -0700 (PDT), "jalbers@bsu.edu"
<jalbers@bsu.edu> wrote:

I want to be able to get a ball park estimation of the thermal
resistance of various shapes (square plate, circular plate, ...) made
out of various materials (aluminum, copper, ...)

I know that Rthermal = deltaT/Power and that Rthermal = 1/(h*A) where
h is the transfer or convection coefficient.

According to an online source h can be approximated as 0.00221 *
(delta T/L)^0.25 where L is the direction of natural convection
(vertical). Units (W/in^2/degrees C).

This is great but as far as I can tell there is no provision in these
formulas for the type of material or its thickness. I am looking for
a ballpark formula to be able to calculate thermal resistance that
involves the thermal conductivity of the material.

I found some really neat calculators on this site:
http://www.novelconceptsinc.com/calculators.htm but these may not be
available in the future.

Any help would be greatly appreciated. Thanks

If you attach a heat source to a plate, theta will depend on the size
of the source. The smaller the device contact area, the higher theta.

Given that, theta will drop as thickness increases and for materials
with higher thermal conductivity, and flatten out as the sheet
approaches isothermal (ie, no local hot spot around the source.)

Your equation above probably assumes an isothermal sheet, namely the
heat source being uniform all over the sheet.

Here's one experiment:

ftp://jjlarkin.lmi.net/Infinite_Sheet.jpg

Note the hot spot in the center. An infinite sheet wouldn't heat sink
this transistor much better. Thicker, or copper, would help a lot. A
bigger transistor, like a TO247, would have lower theta too.

This thermal stuff is complex enough that it's usually easier to
experiment than to calculate. Add forced air and the calculations get
much, much worse.

John

 

[George Herold]

On Jul 8, 11:04 am, "jalb...@bsu.edu" <jalb...@bsu.edu> wrote:

I want to be able to get a ball park estimation of the thermal
resistance of various shapes (square plate, circular plate, ...) made
out of various materials (aluminum, copper, ...)

I know that Rthermal = deltaT/Power and that Rthermal = 1/(h*A) where
h is the transfer or convection coefficient.

According to an online source h can be approximated as 0.00221 *
(delta T/L)^0.25 where L is the direction of natural convection
(vertical).  Units (W/in^2/degrees C).

This is great but as far as I can tell there is no provision in these
formulas for the type of material or its thickness.  I am looking for
a ballpark formula to be able to calculate thermal resistance that
involves the thermal conductivity of the material.

I found some really neat calculators on this site:http://www.novelconceptsinc.com/calculators.htmbut these may not be
available in the future.

Any help would be greatly appreciated.  Thanks

Thermal resistance of a piece of metal can be estimated just like the
electrical resistance.

R(sub T) = 1/rho* Length / Area, where rho is the thermal conductivity
(W/(m*K)), The length is measure along the direction of heat flow and
the area perpendicular.

rho is different for different materials.

If you want to know how well the piece of metal couples to the air,
then that is a lot harder.

You can also estimate the thermal heat capacity in the same way... and
then estimate the thermal time constant of the piece of material.

George H.