# Understanding Thermal Resistance Calculations

Category:
• Indium Corporation
• Thermal Interface Materials
• Voiding

• I have previously discussed various reasons why thermal considerations in a device cannot be an afterthought. There are various methods for handling the thermal needs of a device before it becomes a problem. One of my well-known colleagues, Ross Wilcoxon, Principal Mechanical Engineer at Rockwell Collins, knows a great deal about these. His article, “a spreadsheet based matrix solution for a thermal resistance network: part 1” was highlighted in Electronics Cooling Fall 2010, and in it he discusses a method using Excel to do thermal resistance modeling.

My inquisitive nature couldn’t let the article stand on its own. I had to tack on a few more questions. Ross was accommodating enough to help me out.

[Amanda Hartnett] Why is it important to characterize the thermal resistance of each material used in a device?

[Ross Wilcoxon] It may not be - sometimes the best lesson learned from a resistance network analysis (or any modeling effort for that matter) is determining which things are really important to the final results (component temperatures, reliabilty, etc.) and which things aren't.  For example, if the aluminum chassis in a system plays a critical part in the overall thermal resistance and has a large temperature gradient, then it is pretty important to know what alloy it is so that you can better estimate its thermal conductivity.  On the other hand, if the chassis is pretty much uniform in temperature, then knowing exactly what its thermal conductivity is probably doesn't matter so much.

[Amanda Hartnett] What information is needed from the material vendors in order to complete a resistance network analysis?

[Ross Wilcoxon] Obviously, thermal conductivity is a good start and if you are doing a transient analysis (I plan to talk about that in part 3 of the series that I would like to do for Electronics Cooling), information on specific heat and density are pretty important.  For interface materials, the overall interface resistance is needed more than the thermal conductivity.  In many cases, it would be really nice to have data not only for nominal values but also some indication of uncertainty.  The resistances in a thermal network can be calculated using best or worst case numbers as easily as they can with nominal material properties.  It is pretty easy to switch between these values within the spreadsheet and it is a good way to get a feel for how important knowing the precise value really is by looking at how varying between best and worst values impact the overall temperatures.  Also, I have done a few spreadsheet based Monte Carlo simulations for getting my hands around the cumulative effects of uncertainty in things like thermal gap fillers and a thermal test stand.  For that type of analysis, you have to have some understanding of the uncertainty as well as the nominal values.

[Amanda Hartnett] Could a model like this be used to characterize the effect of degradation in a single layer?

[Ross Wilcoxon] I guess I'm not sure exactly what you mean on this.  If the effect of the single layer (I suppose you mean a thermal interface material) is accounted for in the thermal resistance calculation, sure - you can just apply a factor in the equation to account for something like voiding to say that the effective thermal conductivity of the interface material decreases by X% to assess how much that impacts the overall effect.  I suppose it just comes down to how complicated you get in converting material and geometry parameters into thermal resistance.

[Amanda Hartnett] In a typical cooling solution, have you found that one boundary was more critical than another?

[Ross Wilcoxon] In a lot of cases, the thermal battle is lost in the first mm of the thermal path (the interface between a component and whatever it is attached to - I bet you like that answer, huh?!) but in a lot of our systems the choke point is in the last mm (moving the heat from the system to the surroundings).  One of the big benefits of network resistance analysis is the fact that you can very easily adjust the resistances, including these boundary conditions, by just changing a couple cells in the spreadsheet. This can give a good feel for which parameters are the most critical and what needs to be better understood.  For example, in the next article for Electronics Cooling (assuming that I get it written), I plan to talk a bit about an analysis that I did for some of our equipment going into a missile pod along with equipment from a number of other suppliers.  At the time of the analysis, we didn't know certain details about things like the surface finish to which we were attaching our module, the specific alloys in the missile pod, etc.  Having a quick-look analysis tool helped us determine which unknowns were really critical for the thermal analysis and we could concentrate in chasing down that information.

-----------------------------------

Ross – Thank you for your time and for sharing your knowledge and experience!