Interleaved Fin Connectors

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Figure 1
The symmetric solution valid for an interleaved fin connector with a large number of fins. k denotes thermal conductivity.

Introduction

There has always been a need for mechanically flexible thermal interfaces. Some flexibility can be achieved with conventional grease layers but it is limited to movements in two directions. Many modern applications are more demanding. The problem of interfacing several components with a common heat sink is one example. Another examples are simple and dry slide contacts.

This article is a short introduction into the thermal aspects of interleaved fin connectors. Several other devices can be used for the same purpose but the advantage with the interleaved fin connector is that it combines a large flexibility with a simple design.

Basics

A perfectly flexible thermal connector must be able to absorb three linear and three angular movements. The interleaved fin connector has this potential. It is a simple device that consists of two interfaced parts, figure 1. It tolerates large movements in two directions and limited movements in the third direction and for rotation.

Although the device in itself is simple, it is not that easy to characterise thermally. There are many cases to consider, non-symmetrical fin positions, different fin thickness or material in the two parts, less than 100% fin overlapping etc. Numerical solutions can of coarse always be used but analytical solutions have the advantage of offering better overviews. An example of the latter is the equation in figure 1. It is the simplest of all possible solutions and it is valid for a fully symmetrical case with a large number of fins.


Figure 2
Typical temperature profiles in the fins.

Figure 2 shows typical temperature profiles in the fins. It can be noted that the temperature difference is nearly uniform which indicates that there are good approximations to make. This is also the case. For some more details on this matter, see the PDF document: Research report 91/9 Interleaved Fin Thermal Connectors for...


Figure 3
A simplified thermal resistance model for a single gap.

Figure 3 shows a simplified model for a single gap. It is surprisingly accurate, (<20% error). In addition it also maps all tendencies correctly. It is ideal for first level approaches because it is simple and because all deviations from the symmetrical case make accurate calculations impossible anyway.


Figure 4
Optimum length as function of the thermal conductivity for the gap material, b=1 mm, s=0.5 mm, fin material: aluminium. The simplified model sets the constant to 1.0 in stead of 0.881.

Optimum fin length

The simplified model in figure 3 shows that a large overlapping fin length, L, results in a large thermal resistance for the fins, Rb, but a small thermal resistance for the gap, Rs. For short fins, it is the other way around. The lowest possible total thermal resistance is found in between these two extremes. The expression is given in figure 4.

The optimum fin length is a function of the fin thickness, the gap width and the thermal conductivity of the materials. A fin thickness of 1 mm, a gap width of 0.5 mm and aluminium fins, were used for the diagram. It reveals that the optimum length is a strong function of the gap filler material. Air would in this case result in an optimum fin length on the 60 mm level, which obviously is excessive. The situation improves considerably if a gap filler is used. Another improvement option could be to decrease the fin thickness and the gap width. To achieve a thermal resistance on the same level as for thermal paste would however require a size reduction with a factor 10, which hardly is realistic.

There are some candidates for the gap filler material. Grease could be used but would require some kind of wrapping to stay in place. The modern two-composite materials that create conductive foams are probably a better alternative. They do not creep on surfaces and they have a relatively high thermal conductivity. Any kind of gap filler would in addition require fins with holes that allow the filler to float from one side of the fins to the other.

Gap filler material	Therm cond [W/mK]	Optimum length [mm]	Therm res [K/W]
Air	0.023	60	4.5
Paste	1.5	7.3	0.55

Table 1
Data for a 20x20 mm fin connector, b=1 mm, s=0.5 mm. Fin material aluminium.

Table 1 shows calculated data for a 20x20 mm fin connector. The design is definitely impossible if air fills the gaps. The thermal resistance that can be achieved with thermal paste is however sufficiently low to carry heat flows on the 10 W level, which is attractive.

Optimum fin thickness

Just as for heat sinks there is also an optimum fin thickness. Thin fins conduct heat less well than thick fins but for a given device width there will other hand be more of them. The general expression is very complicated but for the optimum length it simplifies to b=s. It is indeed surprising that this expression is so simple and in addition, is independent of the materials used.

The flexibility requirement for mechanical tolerances and thermal movements will in most cases set gap width to the order of a few tenths of a millimetre. To use a thin thickness of the same order is however hardly realistic. They would be too difficult to manufacture. It is therefore apparent that most applied interleaved fin designs will deviate considerably from the optimum design.


Figure 5
Optimum thermal resistance for a 20x20 mm connector. s=0.5 mm, gap filler:: k=1.5 W/mK. Fin material aluminium. The simplified model sets the constant to 4.0 in stead of 4.59.

Optimum thermal resistance

Figure 5 shows the expression for the optimum thermal resistance. It is quite simple and shows the best that can be made if the fin material is aluminium. For copper, which conducts heat twice as good, the values will be a square root of 2 lower. The correlation is only valid for absolutely centred fins. This is of coarse never the case but all deviations in this respect have a positive impact.

An actual design is always a compromise between several requirements. It can therefore never be made as good as the diagram shows. In all design situations it is nevertheless very helpful to have access to landmark data.

Discussion

A potentially large-scale application for interleaved fins is as interface between components and integral heat sinks. These kind of designs are now appearing frequently and it is indeed a problem to manage thermal connections between components of different height and a common heat sink. It is nevertheless apparent that interleaved fin connectors with air as gap filler, not can be used for this purpose.

There are however some applications where simple interleaved fin connectors are attractive. One example is as slide connectors for edge cooled devices. An example follows below.



Example

Problem
An edge-cooled device is connected to a cold wall with an interleaved fin connector. The width of the connector is 20 mm, the length is 220 mm. There are 4 fins with the height 5 mm and the width 2.77 mm. The material is aluminium and the fin overlapping is 90%. Calculate the temperature difference that can be expected if the heat dissipation is 15 W.

Solution 1
Use the referenced calculator. The thermal resistance is 0.58 K/W. The corresponding temperature difference is 8.7 K.

Solution 2
The gap width is 0,1 mm and there are 8 gaps. Use the simplified model to calculate each gap:
Rb=L/(kbx0.5xbxD)=0.9x5e-3/(210x0.5x2.77e-3x220e-3)=0.07 K/W
Rs=s/(ksxDxL)=0.1e-3/(0.023x220e-3x0.9x5e-3)=4.39

The total thermal resistance for the overlapping sections of the fins are:
Rslots=(2*Rb+Rs)/8=(2x0.07+4.39)/8=0.57 K/W

In addition there is a thermal resistance in the non overlapping section:
Rf=(l/(kbxbxd)x2/4=0.1x5e-3/(210x2.77e-3x220e-3)x2/4=0.001 K/W

The total thermal resistance is:
Rtot=0.57+0.001=0.57 k/W

The corresponding temperature difference is:
dT=(QxR)=15x0.57=8.6 K.