# Thermal Design and Analysis of Electronics – Part II

### TAZ Project- Let us live to our vision, challenge us, charge us with our passion…

In part I, package level analysis and thermal design along with the important topic of Thermal Interface Materials were discussed. Now continuing on our heat flux path route, the next stop is on board level thermal design and analysis. In order for us to understand the possibilities in handling such a task I shall present some cooling solutions applied on board level thermal design, which shall allow the heat flux to continue its route while minimizing the temperature difference from the point of where it left the component (and its TIM) to that of where it leaves the board.

### board level Thermal modeling

#### Thermal modeling of a Printed Circuit Board (PCB)

The PCB is formed by thick layers of a low conductive material (such as FR4), with what could be considered as thin layers of which some percentage of the layer is copper (power, signals, ground).

PCB layers description

As it should be remembered that thermal resistance between two surfaces is essentially the temperature difference between two isothermal surfaces divided by the heat that ﬂows between them, local temperature differences in close proximity to the package top/bottom are not the goal of the analysis (and should be regarded as inaccurate no matter how refined is the mesh), but the global picture of the flux should match the physics, there is no added value in a detailed PCB thermal model (unless for rare cases of which the heating of signals is to be explored) which would prove quite prohibitive from a numerical standpoint.

As a consequence the PCB is modeled as orthotropic material, with in-plane and normal-to-plane thermal conduction:

PCB thermal analysis orthotropic conduction model

#### Bolted joints and ruggedized cover

As explained in Part I, when cooling of highly thermal dissipative components dominated by conduction through the PCB does not suffice, thermal management dictates the addition of another dominating heat flow path mechanism. This is often conducted by the addition a heat spreader which shall be bolted to the PCB. From a thermal design perspective, the more bolts we use, the lower is the contact thermal resistance between bolted joints. Nonetheless, many bolts mean a lot of drill holes in the PCB and less space to be populated by components. A tradeoff is to be made such that the pressure applied by nearby bolts on highly dissipative and/or sensitive components TIMs would be as to allow the TIM to compress in a predictive manner. An uncompressed TIM compares to an air gap.
Furthermore, it should be remembered that bolted joints do not compare with galvanic contact. It is customary to define a parameter which ascertains a satisfactory contact resistance such as the inverse of the thermal resistance per unit area – h (a value of 3000W/(m^2 K) would be quite conservative). In a thermal management dedicated code, a thermal resistance could be calculated and applied on the contact surface according to the area of contact, otherwise, for a general FEM/FVM code a thermal conduction could be applied to a thin volume representing the contact.

Conduction-based ruggedized cover

In the above picture, a conduction-based ruggedized cover is presented, a cooling methodology which is generally applied for harsh environmental conditions (airborne/sea). Highly dissipative or sensitive components are attached via TIM to the cover which serves as a heat spreader, while the heat flows through the spreader (generally made of Aluminum or Copper) to the sides of the cover where wedge-locks apply pressure to attach the sides of the cover to a chassis (or base-plate in general).
This methodology is termed conduction-based ruggedized cover, as the mode of conduction is dominating the heat transfer process.
Since the attachment of the cover to the chassis is not galvanic, a contact resistance between the ruggedized cover and the chassis is added to the simulation as the two thin colored volume object with conductivity derived from the wedge-locks contact thermal resistance supplied by vendor/experiment (a complete setup of an experiment for attachment contact resistance by wedge-locks estimation would be shared on private request).

attachment contact resistance by wedge-locks estimation

### Board Level Cooling Solutions

As for TIMs which are a cooling solution applied on the package level thermal design, there are instances of which thermal management dictates the use of board level cooling solutions so to allow the heat flux to continue its route while minimizing the temperature difference from to the point of where it left the component (or TIM) to that of where it leaves the board. Such instances occur when heat dissipation density is high and the addition of a cooling solution may diminish the hotspot by spreading or by thermal shortage.
In the following paragraphs, some recommended cooling solutions shall be presented. As there exists an abundance of cooling solutions, I shall only present those I found to be the most cost-effective and easy to apply. As for the thermal management engineer exploration of new cooling methodologies is always advised, it should be noted that it also advised to keep the cooling solution as simple as possible while still achieving the goal of tightening the thermal design margin of safety. New and exotic cooling solutions should be approached with caution because they often present new technologies which may contain hidden failure modes that are sometimes not so well understood.

#### Heat pipes

A heat pipe is a hollow tube enclosed structure, containing a working fluid (usually water for copper structure) that transfer heat as it evaporates and a wick that brings the fluid back to its starting point when it condenses. As the entire thermal cycle is conducted without outside interference, a heat pipe is considered a passive liquid cooling device.
A typical heat pipe consists of a partially evacuated (such that its pressure is slightly below standard atmosphere), its inside wall aligned with a capillary wick structure (porous ceramic for example) and a small amount of fluid to vaporize in the process. When heat is applied to the hot end, the fluid within the pipe vaporizes and by that generates a force that drives the vapor to the cold end of the tube, where the removal of A heat pipe should operate in any orientation due to the wick’s capillary action, but performance is often degraded when i’s forced to work against gravity and the heat input end is higher than the output and the liquid in the wick is forced to move up the tube.

Heat pipe design and thermal cycle

One of the biggest problems (and one that I get the most questions about in my lectures) concerning heat pipes is reliability. Many thermal designers are concerned that degraded performance shall appear as close as within a few months of operation. This scenario is unaccepted as the slow increase in operation temperature is usually unnoticed until malfunctions or complete failure occur.
The greatest cause for heat pipe degraded performance is contamination that affects the vapor pressure inside the tube. To avoid such occurrence as much as possible care must be taken to the process of sealing the heat pipe by the manufacturer (such as electron beam welding, utilization of clean rooms for heat pipe assembly and a “burn-in” test of at least 50 hours) even more than the nominal characteristics supplied.
In most cooling solution configurations incorporating heat pipes they serve as thermal shortage, but heat pipes may also be used for in-plane heat spreading when applied by attaching two or a network of them in parallel. An extremely ingenious utilization of such a network is presented in the following presentation by Airtop:

Airtop Natural Airflow Introduction

#### Vapor chamber

A vapor chamber is essentially a planar heat pipe and as such could be defined as a heat pipe device. Its thermal process is also described by the same general thermodynamic cycle, but its role is rather as a heat spreading cooling solution to be placed above high density dissipative component for diminishing a hotspot.

Vapor chamber description

A vapor chamber, much like heat pipes, is easy to apply and is optimally constructed to utilize heat pipe thermal cycle for planar heat spreading.

Vapor chamber utilization for heat spreading purposes

Nonetheless, as vapor chambers are not cheap, the thermal engineer should always consider the realization of vapor chamber operation by the attachment of a series of flat heat pipes, which might not be as effective in diminishing the hotspot but shall certainly be cost-effective.

#### Aluminum cover with embedded pyrolytic graphite

Carbon is one of the most common atoms on earth. Carbon atoms have four valence electrons and can create bonds with up to four other atoms. This bonding to other elements or to other carbon atoms, allows a great variety of materials to be formed.
One of these materials (perhaps the most known and popular besides diamond) is graphite,  formed of a layered structure with strong covalent bonds within the layers, and weak Van-der-Vaals bonds connecting the layers (as opposed to diamond which has only strong covalent bonds – anyone who held a pencil against a diamond should value the difference in structure 😉 ). The thermal conductivity is in the magnitude of 1 000 W/(m∙K) in the plane but only around 5 W/(m∙K) through the thickness, making it a good heat spreader.
The cooling solution presented considers embedding thin graphite plate in an aluminum ruggedized cover, while avoiding air voids which shall hamper its thermal performance by attaching the interfaces by a specific chemical process.

Such a procedure conducted by CPS is presented in the following figure:

AlSiC with embedded graphite cooling solution

#### Thermo-Electric Coolers (TECs)

TECs create heat flux through the Peltier effect. TEC consists of several NP pellets connected electrically in series and thermally in parallel between two ceramic plates.   with the application of DC current of proper polarity, heat is pumped from one plate to the other plate making the first cooler.
I couldn’t leave TECs outside the review as they are mandatory for situations where a passive cooling solution choice will not suffice (as achieving a component junction temperature below that of the boundary conditions), but TECs are extremely low on power efficiency, a fact that could prove quite problematic if power budget is important and furthermore they sometimes tend to hamper the overall MTBF of the board.

TEC description

The third and final part shall deal with system-level thermal management considerations along with an in depth discussion about turbulence modelling for electronic equipment (a subject I am ever so fond of 😉 ) and my personal experience review of different thermal management dedicated and general purpose commercial software packages.