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Thermal Networks: Tried and True, and FAST!
Thermal analysis has evolved so much in the last decade, with sophisticated software running on desktop (or even notebook) computers. I'm a big fan of the fancy software, but not
until I understand the basics about the problem at hand. (Been burned by that too many times!) For that, I use thermal network analyses. These have gotten easier to do, too, since personal
computing power can do the analysis fast. Personally I prefer spreadsheets, since I'm a lousy programmer... Here are some design problems I've looked at recently for which network
analysis was just the thing. They share some characteristics that make them a bit more confusing than usual.
- Multiple heat sources
- Heat flow direction not always known -- depends on resulting temperature levels
- No fans can be used to vent the enclosure
- Natural convection and thermal radiation are the dominant heat transfer modes
- Case temperatures on enclosure surfaces are subject to UL touch temperature limits
Schematic network construction is simplified as much as possible using the following guidelines:
- One or more heat sources have temperature limits; these are assigned numbered nodes
- Nodes correspond to a representative temperature of a uniform object. One of these objects can be the internal air; another is the enclosure. Of course, there will be spatial variations
in these; if these are important, a more sophisticated analysis should follow (software)
- Heat sources whose temperatures are of no concern (is there such a thing??) have their heat dissipation assigned directly to internal air
To evaluate the links between nodes, assign thermal path values based on component sizes and thermal mechanisms between the nodes (conduction, convection, radiation). These can be
written in resistance form. Keep in mind that you are looking for the dominant path between two node points; if natural convection is the path from case surface to ambient, the conduction
resistance of a layer of paint won't make a noticeable difference. However, the fact that there is paint at all might imply an emissivity change (see article on radiative heat transfer
coefficient). Specifying individual input cells this way makes it easy to do what-if scenarios – a key reason that you are doing the analysis in the first place! To solve the
network, use the matrix inversion method covered in an earlier newsletter. Now to the examples, and a brief discussion.. next page |
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For upcoming events see Seminars page. |
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Spreadsheet Tricks for Thermal Engineers
: Solving Thermal Networks Eliminate the ambient node, and treat its value as zero when you write up the equations for the
matrix. Then, add the ambient each temperature value. For fan on/off options, use an indicator with allowable values of zero and one. For example, choose a heat transfer coefficient based on
the fan indicator, "htc = IF(fanID=0, htc_NC, htc_FC)". For an optional component (for example, heat sink fins on a surface), use a very small length dimension instead of zero. That way,
when you calculate a resistance that involves dividing by an area, you'll eliminate a divide by zero (#DIV/0!) error. For complex networks, Excel's labels capability is phenomenally useful. Set
up a table of resistances for each component to every other component. For example 3, where many nodes are linked to the internal air and to the ambient, the table looked partially like this
table:
| |
node1 |
node2 |
node3 |
case |
Rinternal |
R1i |
R2i |
R3i |
Rc1 |
Rambient |
R1a |
9999 |
9999 |
Rca |
Rsource3 |
9999 |
R23 |
R23 |
9999 |
The large values (9999) are placeholders in case you ever want to change the linkages in the matrix – then you
don't have to rewrite the matrix coefficients later. Of course, you may know that there is no way that link will ever exist, so you can leave it out.
Using this table setup, the matrix coefficients can be written – and debugged – very easily, for example: =1/node1 Rinternal + 1/node2 Rinternal + 1/node3 Rinternal + 1/case Rinternal
… (etc.) and =1/case Rinternal + 1/case Rambient + 1/case Rsource3 … (etc.)
Yes, just like that, with spaces -- Excel figures out that you want the value at the intersection of the row and column having the labels you've typed in (sort-of) plain English. |
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