- aditya mehrotra.

# heatsink thermal calculations design [misc math]

So today we want to do a brief calculation of a heatsink for the processor of a robot. It shouldn't take too long we just want an estimate to see if the system will overheat or not. Let's first describe the system:

Essentially what we have is an Nvidia AGX Xavier Module which will operate at some temperature. The maximum power that can be produced by the system is 30W which means the system will get the hottest, of course, when using the full 30W of power.

```
```**Max Safe Case Temperature****:**** **80°C
**Max Possible Power Dissipated****:**** **30W
**Thermal Resistance ****of**** the Module****:**** **0.35°C/W

The jetson "module" looks like this. The thermal resistance refers to the resistance of the thermal transfer unit that surrounds the CPU. This comes from the Xavier thermal design guide.

Now let's use this calculator to find the thermal resistance of our heatsink: __https://myheatsinks.com/calculate/thermal-resistance-plate-fin/__

Depending on the fans we've chosen we can now develop a thermal circuit model for our heatsink attached to the rest of the system. This, of course, depends on the fan we choose. We're using 1939K18 fans from McMaster right now: __https://www.mcmaster.com/fans/low-voltage-equipment-cooling-fans/__ and these give us like 1CFM of airflow.

Now we want to convert the CFM to LFM and if we take the area of the fans as our "area" of 0.98*0.98in and account for two fans while using this calculator: __http://www.csgnetwork.com/cfm2lfmcalc.html__

```
```**CFM**** Flow Rate****:** 1CFM
**Area****:** 2*0.98in*0.98in (two fans)
**LFM**** ****for**** One Fan****:** 149.9375260308205LFM
**LFM**** ****for**** Both Fans****:** 300LFM

That means the heatsink has a thermal resistance of around 0.47°C/W, because the flow isn't exactly uniform over the part let's just assume a slightly higher thermal resistance of 1°C/W for the heatsink and now we can develop the thermal circuit.

So now let's do a little bit of math just to figure out what the temperatures at each point would be with, let's say an ambient temperature of 35°C which is already a little high.

```
T_ambient = 35°C
(T_TTP-T_ambient)/1°C/W = 30W
T_TTP = 65°C
(T_junc-T_TTP)/0.35°C/W = 30W
T_junc = 75.5°C
```

Now with this heatsink we can also calculate the maximum "ambient temperature" where this system will work assuming the maximum casing temperature of 80°C.

```
T_TTP = 80°C
T_ambient = T_TTP-30W*1°C/W
T_ambient = 50°C
```

The last thing to account for in our model is the resistance of the "thermal paste" between the heatsink and the actual part: __https://electronics.stackexchange.com/questions/233242/thermal-glue-or-paste-thermal-resistance__

```
Rglue = THICKNESS / ( AREA * K)
K is 1.7 (estimate)
let's say 0.05mm thickness + press hard
Rglue = 0.05mm/(84.3mm*87mm)/1.7
Rglue = 0.00401027593°C/W
```

We're just going to ignore that for the most part and say it's mostly negligible compared to the rest of the system.

So as long as the air temperature inside the casing of the robot doesn't exceed 50°C then this heatsink will work for the Xavier.

Some other references:

__https://www.allaboutcircuits.com/tools/heat-sink-calculator/__

__https://www.electronics-cooling.com/1995/06/how-to-select-a-heat-sink/__

NVIDIA Jetson AXG Xavier Thermal Design Guide