# “All models are wrong, but some are useful” Part V

By Robin Bornoff

A variant on the original G. E. Box quote is:  “Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful”. For electronics cooling simulation that really depends on what your expectations are of the simulation. Many use CFD to provide an insight or understanding of the thermal behaviour of the system. Others expect a 99.5% accurate simulation of reality. On average, with a certain amount of care, or at least awareness of the issues already covered in this series, a simulation accuracy of ~+/-10% is common. The fifth and final modelling issue that requires some attention is the concept of environment boundary conditions.

When doing any 3D numerical modelling you consider a portion of space (and time sometimes) and get your software to predict what goes on inside (or during). There will always be an edge of your model, the limit at which you don’t model the ‘outside’.  At this boundary you have to set an assumption of what’s happening on the ‘other side’. This condition can often have a very dominant effect on the simulation of the stuff you are considering.  Such things are called… wait for it…. the clue was in the previous text……

Boundary Conditions

Consider the following modelling level:

Which explicitly contains representations of a PCB and the components on that PCB. To the right of the red model box is that which is not being modelled. However heat will pass out (and cold will pass in) the interface between modelled and not modelled. Defining where the heat passes to, or rather how difficult the heat passes out, is done by specifying a parameter, or two.

The most obvious one is temperature, the temperature just outside the 3D space being meshed and predicted. This is effectively an ambient temperature.  If the interface between model and outside (the boundary condition interface) is air to air then this is the temperature air will assume as it is blown or induced into the modelled space. In addition, for such air to air boundary conditions you may have to set whether the air is stagnant (by specifying gauge pressure = 0), or moving in or out (by specifying a velocity).

If there is solid at the interface then you still need to set a temperature of the air on the other side of the wall but instead of also setting pressure/speed one sets what is called a heat transfer coefficient (HTC) instead. An HTC is defined in terms of degC/Wm^2. I always think of it as the efficiency by which heat is removed from a surface, what degC temperature rise penalty is levied for a Watt going through an area 1 m squared. For the following conduction only package modelling level:

The boundary of the model will all be solid interfaces requiring heat transfer coefficients to be specified on top (to say represent the effect of a heatsink that you’re not explicitly modelling heatsinks are good at increasing HTC, that’s their raison d’etre) and bottom (how much Cu or vias under the package will dominate that HTC). Prediction of HTCs due to air is what CFD is best at really, I’ll come back to this issue in a subsequent blog.

If you get this boundary condition setting wrong, e.g. innacurate or badly specified, then this error will propagate back to the heat source temperature prediction. All heat has to go out the sides of the model, best to ensure the BCs (boundary conditions) set there are right then. To best assure accuracy the first thing is to chose the best point at which to truncate the model from what is meshed and solved to that which is outside and not.

If in doubt increase the size of the model a bit until it extends to a  point where you are confident of correctly specifying the BCs. Not sure of the HTC the heatsink will bequeath to the top of your component? Then model the heatsink and some of the air around it or be willing to accept that your package model will be bound by the HTC you specify.

In reality such BCs are most often assumed and the results of the simulation simply valid for that assumption. Spec sheets will often say “ensure ambient temperature does not exceed 55degC” (is that stagnant air or moving 😉 ) Clever FloTHERM model(ers) will invert the model definition to predict exactly what the maximum ambient temperature can be for a given power dissipation such that maximum limit temperatures are not exceeded. Nice.

Some clever person once said that the best model of the universe is the universe itself. To remove any uncertainty in settings BCs for such electronics cooling simulations your model space should be:

Yeh, OK, FloTHERM’s powerful, fast and robust, but modelling the entire world is a bit beyond even it. So, like it or lump it, you’ll always have to set these BCs (boundary conditions) at the interface between what you model and what you don’t. Either accept what such an assumption imposes or make your model a bit bigger.

2nd July, Ross-on-Wye

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This article first appeared on the Siemens Digital Industries Software blog at https://blogs.sw.siemens.com/simulating-the-real-world/2009/07/02/all-models-are-wrong-but-some-are-useful-part-v/