# Tag Archives: thermal resistance

## Optimizing Heat Sink Base Spreading Resistance to Enhance Thermal Performance

(This article was featured in an issue of Qpedia Thermal e-Magazine, an online publication dedicated to the thermal management of electronics. To get the current issue or to look through the archives, visit http://www.qats.com/Qpedia-Thermal-eMagazine.)

Heat sinks are routinely used in electronics cooling applications to keep critical components below a recommended maximum junction temperature. The total resistance to heat transfer from junction to air, Rja, can be expressed as a sum of the following resistance values as shown in Equation 1 and displayed in Figure 1.

Where, Rjc is the internal thermal resistance from junction to the case of the component. RTIM is the thermal resistance of the thermal interface material. Rf is the total thermal resistance through the fins. The final term in Equation 1 represents the resistance of the fluid, e.g. air, going through the heat sink where m is the mass flow rate and Cp is the heat capacity of the fluid. As Equation 2 shows, Rcond and Rconv are the conduction and convection resistance respectively through the heat sink fins respectively.

Fig. 1 – Resistance network of a typical heat sink in electronics cooling. [1]

Fig. 2 – Heat source on a heat sink base. [2]

Rs stands for the spreading resistance that is non-zero when the heat sink base is larger than the component. The next few sections show the full analytical solution for calculating spreading resistance, followed by an approximate simplified solution and the amount of error from the full solution and finally the use of these solutions to model and optimize a heat sink.

Lee et al. [2] derived an analytical solution for the spreading resistance. Figure 2 shows a cross-section of a circular heat source with radius a on the base with radius b and thickness t. The heat, q, originates from the source, spreads out over the base and dissipates into the fluid on the other side with heat transfer coefficient, h. For heat transfer through finned heat sinks, the effective heat transfer coefficient is related to thermal resistance of the fins, Rf as shown in Equation 3. For square heat source and plates, the values of a and b can be approximated by finding an effective radius as shown in equations 4 and 5.

Where,
h = heat transfer coefficient [W/m2K]
a = effective radius of the heater [m]
Aheater = area of the heater [m2]
b = effective radius of the heat sink base [m]
Abase = total area of the heat sink base [m2]

The derivation of the analytical solution starts with the Laplace equation for conduction heat transfer and applying the boundary conditions. Equation 6 shows the final analytical solution for spreading resistance. The values for the eigenvalue can be computed by using the Bessel function of the first kind at the outer edge of the plate, r=b as shown in Equation 7.

Where,
k = Thermal Conductivity of the plate or heat sink [W/mK]
J1 = Bessel function of the first kind
λn = Eigenvalue that can be computed using Equation (3) at r = b
t = thickness of the heat sink base [m]

Lee et al. [2] also offered an approximation as shown in Equation 8 along with the approximation for the eigenvalues as shown in Equation 9. This approximation eliminates the need for calculating complex formulas that involve the Bessel functions and can be computed by a simple calculator.

Approximation vs. Full Solution

Simons [3] compared the full solution (Equations 6 and 7) with the approximations shown in (Equations 8 and 9). The problem contained a 10 mm square heat source on a 2.5 mm thick plate with a conductivity of 25 W/mK, 20 mm width and varying length, L as shown in Figure 3. Figure 4 shows that the percentage error increases with length but stays relatively low. Less than 10% error is expected for lengths up to 50 mm; five times the length of the heater. This is acceptable for most engineering problems since analytical solutions are first-cut approximations that should later be verified through empirical testing and/or CFD simulations. However, the full analytical solution should be used if the heater-to-heat sink base area difference gets much larger or if a more accurate solution is desired.

Fig. 3 – Example problem for comparing analytical and approximate solutions for spreading resistance. [3]

Fig. 4 – Percent error between the analytical and the approximate solution of spreading resistance for the example shown in Figure 3. [3]

Optimizing Heat Sink Performance

The goal of any electronic cooling solution is to lower the component junction temperature, Tj. For a given Rjc and RTIM, the objective is to maximize heat sink performance by reducing the spreading resistance, Rs, and the fin resistance Rf.

The spreading resistance can be reduced by increasing base thickness. However, most electronics applications are limited by total heat sink height and thus any increase in base thickness leads to shorter fins which reduce the total area of the fins Afins. For a fixed heat transfer coefficient (the heat transfer coefficient is a function of fin design and air velocity and we can assume it is fixed for this exercise) a reduction in the fin area increases Rf as shown in Equation 2. Equation 10 shows this combined heat sink resistance, Rhs, as a function of the spreading and fin resistance.

Thus, for a given fin design, the thermal engineer must choose the appropriate heat sink base thickness to optimize heat sink performance. To illustrate this point, let’s take an example of an application with the parameters as shown in Table 1.

Table 1 – Example Heat Sink Application

Figure 5 shows a graph of the total thermal resistance of the heat sink, Rhs and spreading resistance, Rs as a function of base thickness for copper and aluminum material. (Note that the final term from Equations 1 and 10 is ignored because it is constant and does not contribute to the understanding of spreading resistance). The graph shows that spreading resistance improves monotonically with increased base thickness. However, the total thermal resistance has an optimal point between 2-4 mm base thicknesses. For base thicknesses less than 2 mm, there is a sharp increase in spreading resistance which leads to a higher overall thermal resistance.

Fig. 5 – Total and spreading resistance of the example shown in Table 1 for a 50 mm heat sink.

On the other hand, increasing the base thickness above 4 or 5 mm gives diminishing marginal returns; the improvement in spreading resistance is minimal compared to the increase in thermal resistance due to the reduced fin area. Additionally, the graph also shows that higher conductivity materials such as copper, improves thermal performance across the entire domain.

Conclusion

The heat spreading resistance is an important factor when designing a heat sink for cooling electronics components. The full analytical solution for calculating the spreading resistance, shown in Equations 6 and 7, can be substituted with the approximations shown in Equations 8 and 9 with minimal error. The error increases with increased difference between the heat sink base and heater size and the complete analytical model should be used if needed. The analytical model can be used to choose the right heat sink base thickness that optimizes heat sink performance as shown in Figure 5.

Techniques such as higher conductivity materials, embedded heat pipes, vapor chambers etc. are available if the spreading resistance is major obstacle in the cooling. Thermal engineers must balance the increased weight and cost of such techniques against the benefits for each application.

References
1. “Spreading Resistance of Single and Multiple Heat Sources,” Qpedia. September 2010
2. Seri Lee et al. “Constriction/Spreading Resistance Model for Electronics Packaging,” 1995.

For more information about Advanced Thermal Solutions, Inc. (ATS) thermal management consulting and design services, visit https://www.qats.com/consulting or contact ATS at 781.769.2800 or ats-hq@qats.com.

## What are the benefits of using Pin Fin Heat Sinks in thermal management of electronics

Engineers tasked with designing modern electronics face a number of issues. Expectations are for more functionality, more power, and more components in ever-smaller packages but also with quick turnaround for production and staying within tight budget parameters.

Thermal management is a critical aspect of the design process and, as demand for component-density and miniaturization continues to increase, engineers need cooling solutions that fit into small spaces, will not cause project cost overruns, and will provide the best heat transfer possible for today’s modern,  processors.

Heat sinks and convection cooling remain the go-to solutions for most systems and high-efficiency Pin Fin heat sinks are designed to meet the requirements of modern electronics cooling with little extra cost added. In particular, the pin fin heat sink geometry is designed to provide increased surface area for heat transfer, low thermal resistance from base to fins at high airflow (200-plus LFM), and work in environments where the direction of airflow is ambiguous.

Pin fin heat sinks from Advanced Thermal Solutions, Inc. (ATS). Pin fin heat sinks provide low thermal resistance at high LFM. (Advanced Thermal Solutions, Inc.)

How does the Pin Fin geometry work?

Barry Dagan, an engineer at Cool Innovations, Inc., wrote a piece for New Electronics in 2009 that explained how the pin fin structure uses the ambient airflow to enhance its thermal performance. [1]

“Any heat sink removes heat by ‘breaking’ the boundary layers of still air that are wrapped around its surface because still air is a very good thermal insulator,” Dagan explained. “The boundary layers are broken by accelerating the flow of air into the heat sink – either using fans and forced airflow or via the chimney effect. In either case, the faster the airstream, the more likely the boundary layers are to break and the more effective the heat sink will be.”

He added, “The round, aerodynamic pin design reduces resistance to surrounding airstreams that enter the pin array, while simultaneously increasing air turbulence. The omnidirectional pin configuration, which allows air to enter and exit the heat sink in any direction, exposes the heat sink to the fastest possible air speed.”

In an earlier article for EE Times, Dagan also noted that the pin fin geometry “allows for a high degree of customization.” Engineers can make adjustments to the overall height, pin height, base thickness, footprint, pin diameter, and pin density to find an optimal cooling solution for their particular project. [2]

“Pin fins can also be catered for situations where both footprint and height are restricted,” Dagan wrote. “For example, the pin fin technology enables the design of heat sinks with a footprint of half an inch squared and a total height as low as 0.15 in.”

A study conducted by Younghwan Joo and Sung Jin Kim that was published in the International Journal of Heat and Mass Transfer indicated that the heat dissipation per mass of optimized pin fin heat sinks was greater than optimized plate-fin heat sinks in most applications. [3]

Pin Fin heat sinks on a PCB. (Advanced Thermal Solutions, Inc.)

In a comparison of heat sinks conducted at Advanced Thermal Solutions, Inc. (ATS) and published in Qpedia Thermal eMagazine, a 33-mm tall elliptical pin fin heat sink under forced convection had the lowest thermal resistance of the 10 heat sinks that were tested. [4]

The ATS family of pin fin heat sinks, made from extruded aluminum, range in sizes from 10 mm by 10 mm to 60 mm by 60 mm. Heights range from 2-25 mm. Through testing in ATS wind tunnels, the pin fin heat sinks demonstrated thermal resistance as low as 2.5°C/W and added little weight to the board. [5]

How are pin fin heat sinks attached to a board?

Pin fin heat sinks are versatile and can be attached to a variety of component packages, including BGA, QFP, LCC, LGA, CLCC, TSOP, DIP, LQFP, and many others. Because pin fin heat sinks are lightweight, standard thermal tape or epoxy can be used to securely attach them to components.

In addition, pin fin heat sinks work with mechanical attachments such as z-clips and ATS maxiGRIPTM or superGRIPTM, which are two-component attachment systems that provide secure hold without damaging the PCB and only minimal addition to the component footprint.

Pin fin heat sinks attached to a PCB with ATS maxiGRIP heat sink attachment system. (Advanced Thermal Solutions, Inc.)

How do pin fin heat sinks provide cost savings?

In his article for EE Times, Dagan explained, “Pin fin technology provides cost-effective heat sink solutions for medium and high-volume applications due to low associated tooling charges and minimal waste of raw materials.” [2]

For example, the ATS family of standard and custom pin fin heat sinks are all available for less than \$2.00, with the vast majority of heat sinks available for less than a dollar. This means that engineers can find high-efficiency heat sinks and save money in the budget, which can be put to other design considerations, such as higher-powered fans to increase airflow, better heat sinks attachments, or additional chips and other board components. [5]

This is particularly beneficial for the growing maker market, which is working on new technology or enhancing current technology but generally with far smaller budgets than traditional OEM.

A 2012 article from The Economist, entitled “A Third Industrial Revolution,” discussed the impact of additive manufacturing techniques and how it was now possible to make parts through processes like 3-D printing that are cheaper and faster than traditional methods. According to the article, this will not just affect large manufacturers but also trickles down to a community of makers and smaller companies, what the article labeled “social manufacturing.” [6]

The article added, “As manufacturing goes digital, a third great change is now gathering pace. It will allow things to be made economically in much smaller numbers, more flexibly and with a much lower input of labour, thanks to new materials, completely new processes such as 3D printing, easy-to-use robots and new collaborative manufacturing services available online. The wheel is almost coming full circle, turning away from mass manufacturing and towards much more individualised production.”

Pin fin heat sinks provide cost-effective cooling solutions for small manufacturers and the maker market. (Advanced Thermal Solutions, Inc.)

A study, also from 2012, from MAKE magazine and Intel surveyed the maker community to get data about the (self-proclaimed) hobbyists, builders, tinkerers, and engineers. Out of the total respondents, 79 percent said that they worked in hardware and software, with electronics in second place at more than 60 percent. Thirty-four percent of respondents said that they were involved in making products for income and 19 percent of the total said that they paid for projects with outside funding. [7]

Crowdfunding can only take a project so far and for makers trying to earn money from designs, it is crucial to find cost-effective solutions both to ensure a project comes in under budget and to maximize profits from the sale of the design.

Pin fin heat sinks can be added at low-cost and provide the necessary thermal performance to push a design process along. For the maker market and its (at times) limited resources, high-efficiency pin fin heat sinks provide thermal performance on a budget with the versatility to fit into a variety of systems and designs.

For more information about Advanced Thermal Solutions, Inc. (ATS) thermal management consulting and design services, visit www.qats.com or contact ATS at 781.769.2800 or ats-hq@qats.com.

## The Ultimate Heat Pipe Guide: Selection for Performance

### What are Heat Pipes?

Heat Pipes have been called Heat Superconductors! In this engineering article we’ll talk about what a heat pipe, how they are made, compare them with heat sinks, and talk about performance in various thermal management applications.

Figure 1 Schematic View of a Heat Pipe [1]

Heat pipes are transport mechanisms that can carry heat fluxes ranging from 10 W/cm2 to 20 KW/cm2 at a very fast speed. Essentially, they can be considered as heat super conductors. Heat pipes can be used either as a means to transport heat from one location to another, or as a means to isothermalize the temperature distribution.

The first heat pipe was tested at Los Alamos National Laboratory in 1963. Since then, heat pipes have been used in such diverse applications as laptop computers, spacecraft, plastic injection molders, medical devices, and lighting systems. The operation of a heat pipe is described in Figure 1.

### Sections of A Heat Pipe

A heat pipe has three sections: the evaporator, the adiabatic, and the condenser. The interior of the pipe is covered with a wick, and the pipe is partially filled with a liquid such as water. When the evaporator section (Le) is exposed to a heat source, the liquid inside vaporizes and the pressure in that section increases. The increased pressure causes the vapor to flow at a fast speed toward the condenser section of the heat pipe (Lc). The vapor in the condenser section loses heat to the integral heat sink and is converted back to liquid by the transfer of the latent heat of vaporization to the condenser. The liquid is then pumped back to the evaporator through the wick capillary action. The middle section of the heat pipe (La), the adiabatic portion, has a very small temperature difference.

Figure 2 Pressure Drop Distribution in a Heat Pipe [1]

Figure 2 shows the pressure drop distribution inside a heat pipe. In order for the capillary force to drive the vapor, the capillary pressure of the wick should exceed the pressure difference between the vapor and the liquid at the evaporator. The graph also shows that if the heat pipe is operated against the force of gravity, the liquid undergoes a larger pressure drop. The result is less pumping of the wick with reduced heat transfer. The amount of heat transfer decrease depends on the particular heat pipe.

### Structure of a heat pipe

1. Metallic pipe: The metal can be aluminum, copper or stainless steel. It must be compatible with the working fluid to prevent chemical reactions, such as oxidation.
2. Working fluid: Several types of fluids have been used to date. These include methane, water, ammonia, and sodium. Choice of fluid also depends on the operating temperature range.
3. Wick: The wick structure comes in different shapes and materials. Figure 3 shows the profiles of common wick types: axial groove, fine fiber, screen mesh, and sintering. Each wick has its own characteristics. For example, the axial groove has good conductivity, poor flow against gravity, and low thermal resistance.
Conversely, a sintering wick has excellent flow in the opposite direction of gravity, but has high thermal resistance.

Figure 3 Different Wick Structures – From top to bottom: Sintered powder, fine fiber, wrapped screen, axial groove

Table 1 shows experimental data for the operating temperature and heat transfer for three different types of heat pipes [1].

Table 1: Heat Pipes with Different Structures and Operating Conditions [1]

Certain factors can limit the maximum heat transfer rate from a heat pipe. These are classified as follows:

1. Capillary Limit: Heat transfer is limited by the pumping action of the wick
2. Sonic Limit: When the vapor reaches the speed of sound, further increase in the heat transfer rate can only be achieved when the evaporator temperature increases
3. Boiling Limit: High heat fluxes can cause dry out.
4. Entrainment Limit: High speed vapor can impede the return of the liquid to the condenser

A heat pipe has an effective thermal conductivity much larger than that of a very good metal conductor, such as copper. Figure 4 shows a copper-water heat pipe and a copper pipe dipped into an 80oC water bath. Both pipes were initially at 20oC temperature. The heat pipe temperature reaches the water temperature in about 25 seconds, while the copper rod reaches just 30oC after 200 seconds. However, in an actual application when a heat pipe is soldered or epoxied to the base of a heat sink, the effective thermal conductivity of the heat pipe may be drastically reduced due to the extra thermal resistances added by the bonding. A rule of thumb for the effective thermal conductivity of a heat pipe is 4000 W/mK.

Figure 4. Experiment Comparing Speed of Heat Transfer Between a Heat Pipe and a Copper Pipe [1].

Heat pipe manufacturers generally provide data sheets showing the relationship between the temperature difference and the heat input. Figure 5 shows the temperature difference between the two ends of a heat pipe as a function of power [2].

Figure 5. Temperature Difference Between the Evaporator and the Condenser in a Heat Pipe [2]

### Types of heat pipes

There are many heat pipe shapes in the market, but the most common are either round or flat. Round heat pipes can be used for transferring heat from one point to another. They can be applied in tightly spaced electronic components, such as in a laptop. Heat is transferred to a different location that provides enough space to use a proper heat sink or other cooling solution. Figure 6 shows some of the common round heat pipes available in the market.

Figure 6. Typical Round Heat Pipes in the Market.

Flat heat pipes (vapor chambers) work conceptually the same as round heat pipes. Figure 7 shows a flat pipe design, they can be used as heat spreaders. When the heat source is much smaller than the heat sink base, a flat heat pipe can be embedded in the base of the heat sink, or it can be attached to the base to spread the heat more uniformly on the base of the heat sink. Figure 8 shows some common flat heat pipes.

Figure 7. Conceptual Design Schematic of a Flat Heat Pipe

Commonly Used Flat Heat Pipes

Figure 8. Commonly-used Flat Heat Pipes

Although a vapor chamber might be helpful in minimizing spreading resistance, it may not perform as well as a plate made from a very high conductor, such as diamond. A determining factor is the thickness of the base plate. Figure 9 shows the spreading resistance for 80 x 80 x 5 mm base plate of different materials with a 10 x 10 mm heat source. The vapor chamber has a spreading resistance that is better than copper, but worse than diamond. However the price of the diamond might not justify its application. Figure 9 also includes the spreading resistance from the ATS Forced Thermal Spreader (FTS), which is equal to that of diamond at a much lower cost. The FTS uses a combination of mini and micro channels to minimize the spreading resistance by circulating the liquid inside the spreader.

Thermal Spreading Resistances for Different Materials

### Importance of an Heat Pipe

Heat pipes have a very important role in the thermal management arena. With projected lifespans of 129,000-260,000 hours (as claimed by their manufacturers), they will continue to be an integral part of some new thermal systems. However, with such problems as dry out, acceleration, leakage, vapor lock and reliable performance in ETSI or NEBS types of environments, heat pipes should be tested prior to use and after unsatisfactory examination of other cooling methods have been explored.

Have you got a question on heat pipes or their application? How about an interest in bringing ATS’s team of experienced thermal engineers into one of your projects?  Reach us by visiting or email us at ats-hq@qats.com or give us a call at 781-769-2800

References:
1. Faghri, A. Heat Pipe Science and Technology Taylor & Francis, 1995.
2. Thermacore Internation, Inc., www.thermacore.com.
3. Xiong, D., Azar, K., Tavossoli, B., Experimental Study on a Hybrid

## The New Qpedia Thermal eMagazine is Out

Qpedia Thermal eMagazine, Volume 7, Issue 4, has just been released and can be downloaded at: http://www.qats.com/Qpedia-Thermal-eMagazine/Back-Issues.

Featured articles in this issue include:

Dropwise Condensation in Vapor Chambers
Considerable attention has been devoted in the past to the evaporation process taking place in a vapor chamber. However, increased heat fluxes at the condensation end have prompted efforts to improve the condensation performance of the vapor chambers. This article presents a review of a novel method for improving the thermal performance of a vapor chamber condensing section by using special surfaces promoting dropwise condensation.

Heat Sink Manufacturing Using Metal Injection Molding

Using Metal Injection Molding It is only in the last few years that metal injection molding (MIM) has gained a foothold in the thermal community and its salient advantages have become more evident. The MIM process allows intricate features to be added into the heat sink design to boost thermal performance and its production process is very scalable compared with machining. Injection molding enables complex parts to be formed as easily as simple geometries, thereby allowing increased design freedom.Â  This article explore the merits of copper material in the MIM process.

Industry Developments: Thermoelectric Modules and Coolers

Thermoelectric modules (TEMs) are rugged, reliable and quiet devices that serve as heat pumps. The real heat-moving components inside TEMs are thermoelectric coolers or TECs. These are solid-state heat pumps and are designed for applications where temperature stabilization, temperature cycling, or cooling below ambient, are required. Today, TEMs are used in electro-optics applications, such as the cooling and stabilizing of laser diodes, IR detectors, cameras (charge coupled device), microprocessors, blood analyzers and optical switches. This article explores some of the latest developments in these devices.

Technology Review: Reducing Thermal Spreading Resistance in Heat Sinks

In this issue our spotlight is on reducing spreading resistance in heat sinks. There is much discussion about how this phenomenon can be achieved, and these patents show some of the salient features that are the focus of different inventors.

Cooling News featuring the latest product releases and buzz from around the electronics cooling industry.

Not a Qpedia subscriber? Subscribe Now for free at: http://www.qats.com/Qpedia-Thermal-eMagazine/Subscribe-to-Qpedia and see why over 18,000 engineers read Qpedia.

## New maxiFLOW DC-DC Brick Heat Sinks Ideal for Military-COTS Applications

ATS has recently launched a new product line of maxiFLOW heat sinks, specially designed to cool DC-DC converters. The new line of heat sinks can be used with Vicor’s DC-DC converter Bricks, including their military-COTS applications.

Vicor’s Maxi, Mini, and Micro series DC-DC converters are relied upon by over eight thousand OEMs for their proven performance, broad coverage of input and output voltages, ease of mechanical mounting and thermal management flexibility. These converter modules use advanced power processing, control, and packaging technologies to provide the performance, flexibility, and ruggedness expected in a Military COTS product. High frequency ZCS/ZVS switching, advanced power semiconductor packaging, and thermal management provide high-power density with low noise and high efficiency.

maxiFLOW Heat Sink for Half Brick DC-DC Converters

ATS’ patented maxiFLOW technology cools millions of BGAs and other PCB components. The same technology is now available for cooling eighth, quarter, half and full brick modules, such as the Micro, Mini, and Maxi series from Vicor. Unlike other converter heat sinks, the patented maxiFLOW heat sink design reduces air pressure drop and provides greater surface area, increasing thermal performance by 30-200%.

Vicor’s Micro, Mini, and Maxi DC-DC Converters

Vicor’s offering of full, half, and quarter-brick modules feature a patented low noise design with the highest reliability and power density available. Fully encapsulated, Maxi, Mini and Micro series DC-DC converters utilize a proprietary spin fill process that assures complete, void free encapsulation making them suitable for the harshest environments. Two grades (H & M) are available with temperatures to -55°C operating and -65°C storage. H & M-Grade modules are qualified to the stringent environmental tests of MIL-STD-810 and MIL-STD-202 and undergo 100% Environment Stress Screening.

By combining technology from industry leaders Vicor and ATS, it can be ensured that DC-DC converters will have superior performance in the harshest environments, which is vital for military and aerospace applications.