Category Archives: Thermal Design

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

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.

Heat Sinks

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.

Analytical Solution of Spreading Resistance

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.

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.

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.


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.

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.
3. Simons, Robert

For more information about Advanced Thermal Solutions, Inc. (ATS) thermal management consulting and design services, visit or contact ATS at 781.769.2800 or

ATS and Future Facilities Hosting Workshop

ATS and Future Facilities have announced a hands-on workshop on Wednesday, Sept. 12 at the ATS headquarters (89 Access Rd. Norwood, MA). “A Comprehensive Approach to Thermal Design and Validation” will teach engineers how to tackle thermal challenges in modern electronics from concept to final validation. Click here to learn more and to register for this workshop. Sign up today because space is limited.

ATS and Future Facilities

ATS Collaborates on SAM Car Featured on the CNBC program ‘Jay Leno’s Garage’

On Jan. 6, 2000, champion race car driver Sam Schmidt crashed his vehicle at the Walt Disney World Speedway in Orlando, Fla. The accident severely injured his spinal cord, leaving him paralyzed from the neck down and with doctors telling him that he would never walk again, let alone get behind the wheel of a car.


ATS partnered with ARROW Electronics to devise a thermal solution for the computer system in the semi-autonomous car that allowed Sam Schmidt to get back behind the wheel. (Advanced Thermal Solutions, Inc.)

Colorado-based neurosurgeon Dr. Scott Falci had other ideas and enlisted the aid of several technology companies, including ARROW Electronics, the Air Force Research Laboratory (AFRL), and Ball Aerospace and Technologies Corp., to make his dream of helping Schmidt drive come to fruition 17 years after the accident.

The result was the SAM Car. Using infrared sensors, cameras, on-board GPS and other next-generation technologies, the team created a semi-autonomous vehicle that Schmidt could power by simply moving his head. Leaning right or left would steer the car, tilting his head back would cause the car to accelerate, and biting down on a special mouthpiece would cause the car to break.

Watch this CNBC video with Jay Leno to learn more and see the car in action:

Advanced Thermal Solutions, Inc. (ATS) was brought in by ARROW to assist with the challenge of providing thermal management for the car’s on-board computer system. ATS designed an enclosure that cooled both sides of the board without the need for a fan and protected it from dust and other debris.

ATS engineers Bahman Tavassoli, Vineet Barot, and Anatoly Pikovsky are proud to have collaborated with these other innovative pioneers to provide Mr. Schmidt with the ability to get back behind the wheel where he belongs.

For more information about Advanced Thermal Solutions, Inc. (ATS) thermal management consulting and design services, visit or contact ATS at 781.769.2800 or

Heat Sink Design: ATS Engineers Bring Ideas to Life

Marketing Communications Specialist Josh Perry sat down with Product Engineering Manager Greg Wong to discuss the process that Advanced Thermal Solutions, Inc. (ATS) engineers go through to create a heat sink and find a thermal solution for customers.

Watch the full conversation in the video below and scroll down to read the transcript of the interview.

JP: Greg, thanks again for joining us here in marketing to explain what it is that goes into designing a heat sink for a customer. So, how does that process begin?
GW: We usually start with a few basic parameters; we call them boundary conditions. So, we start with a few boundary conditions, basics like how much airflow we have, how much space constraint we have around a heat sink, and how much power we’re dissipating, as well as the ambient temperature of the air coming into the heat sink.

So, those are the real basic parts that we need to start out with and sometimes the customer has that information and they give it to us, and usually we double-check too, and then other times the customer has parts of the information, like they know what fan they want to use and they know what kind of chassis they’re putting it in and we take that information and we come up with some rough calculations so we can arrive at those things like air flow and stuff like that.

JP: When you get the data from the customer, how do you determine what the problem is, so that way you can move forward?
GW: We usually start out with an analytical analysis. So, we put pen to paper and we start out with basic principles of heat transfer and thermal resistance and stuff like that so we can understand if what we’re trying to achieve is even feasible and we can come up with some basic parameters just using that analytical analysis.

Like we can calculate what kind of heat sink thermal resistance we need or we can calculate how much air flow we need or, if we have several components in a row, we can calculate what the rough air temperature rise is going to be along that chain of parts. So, there’s a lot we can do when we get the basic information from the customer just on pen and paper.

JP: What’s the next step beyond analytical?
GW: Well, we can do some lab testing or a lot of times we also use CFD simulations and, if our customer has a model they can supply us, we can plug that into the CFD simulations and we can come up with an initial heat sink design and we can put that into the simulations as well and then we set those up and run them.

The great thing, having done these analytical analyses beforehand, we know what to expect from CFD simulations. So that way, if the simulations don’t run quite right, we already have an understanding of the problem, we know what to expect, because CFD is not 100 percent reliable.

I mean, you can go and plug all this stuff in there but you really have to understand the problem to know if the CFD is giving you a good result. So, oftentimes that’s the next stage of the process and from there we can actually produce low-volume prototypes right here in Norwood (Mass.), in our factory. We have CNC machines and manual milling machines, lathes, all that kind of stuff, and we can produce the prototypes and test them out here in our labs.

JP: How much of a benefit is it to be able to create a prototype and to be able to turn one around quickly like that?
GW: Oh, it’s great. I mean, if we had to wait to get parts from China it will take weeks to get. We can turn them around here in a few days and the great thing about that is we can test them in our labs and, you know, when it comes to getting results nothing beats the testing.

I mean, you can do analytical analysis, you can do CFD simulations, but when you actually test the part in a situation that is similar to what the actual thing is going to be that’s where the real meat comes down.

Heat Sink Design

ATS engineers take customer data and using analytical modeling and CFD simulations can design the right cooling solution to meet the customer’s specific thermal needs. (Advanced Thermal Solutions, Inc.)

JP: So, we test the prototypes before sending them out to the customer? We do the testing here or do we send it to them first?
GW: It all depends on what the customer requires. Sometimes the customer has a chassis that we really can’t simulate in our labs, so we might send the prototype heat sinks to the customer and the customer will actually put them into their system to test them out.

Other times, a customer might have a concept and they don’t actually have a product yet, so we’ll mock something up in our labs and we’ll test it and it all just depends what the customer needs and also how complex the problem is.

If it’s a simple heat sink and pretty simple airflow, we might not need to test that because we understand that pretty well, but the more complex the chassis is and how the airflow bends and stuff like that, the greater benefits we get out of lab testing.

JP: Well, I appreciate it Greg. Thank you for taking us through the process of making a heat sink and solving thermal problems for our customers.
GW: Sure Josh. We love seeing new thermal challenges and coming up with ways of keeping stuff cool.

For more information about Advanced Thermal Solutions, Inc. thermal management consulting and design services, visit or contact ATS at 781.769.2800 or

What Cost Reduction Strategies Make New Product Introductions Faster?

Getting to markets faster and in the most cost-effective way is the primary goal of today’s product development process. Choosing a thermal design engineering partner that understands that goal makes a company’s product realization process simpler and faster. There are number of strategies a company’s project engineers can use to save time and money in the design of an electronics cooling solution. Two of the most efficient methods are Virtual Engineering Demos (VED) and Thermal Load Boards (TLB).

VEDs make it possible for project engineers to remotely see an instrument, how it operates, ask questions about how it works, and, if the project is included in the demo, get data in real time about a design. In this method, a live demo is setup at a thermal design engineering partner’s laboratory. Whether the project is a PCB, a system, or another product type, it can be included in the VED and be run through the lab set-up.

Greg Wong

ATS engineer Greg Wong gives a live, online demonstration from the ATS research lab to a potential customer. (John O’Day/Advanced Thermal Solutions, Inc.)

Candlestick Sensor

ATS engineer Greg Wong sets up to demonstrate the ATVS-2020, Candlestick Sensors and StageVIEW Data Acquisition Software (DAQ) for measuring and analyzing temperature for an electronics board in this VED. (Advanced Thermal Solutions, Inc.)

VED in Lab

Equipment setup and live camera feeds are all part of a VED setup. (Advanced Thermal Solutions, Inc.)

As the project is analyzed, data is shown on the engineering partner’s computer screen, which is in turn broadcast in real time to the project engineers via a live video feed. The video feed simultaneously shows the demo and the software’s operation, while allowing bi-directional conversation between the engineering partner and the project engineers in one or more locations.


Screenshot showing data being recorded in stageVIEW. This information is available to the remote team. (Advanced Thermal Solutions, Inc.)

The advantages of this strategy to project engineers are:

• Quick evaluation of a design to determine if there is a need for new equipment in a project.
• No lag time in talking with a thermal design engineering partner about how to approach the thermal measurement of project
• Reducing the need to travel to a thermal design engineering partner’s lab.
• Faster response on lab testing, shortening the design cycle.

A Thermal Load Board (TLB) is another strategy for reducing the cost of a design, while getting a product to market faster. TLBs are created by a thermal engineering partner using a simple one- or two- layer non-populated PCB, heat sinks, thermally equivalent mock semiconductors and other mock components created with a 3-D printer.

TLB 3-D printing

Using these components a populated board is created that allows the testing of the heat sinks chosen for the project work and measurement of the airflow over the components and through the board. (Advanced Thermal Solutions, Inc.)

The thermal engineering partner is effectively creating a mock version of the functional board. The design of the TLB is based on the size and placement of the semiconductors and other components on the actual board, which is provided by the project engineers, and provides a cheaper and quicker means of producing a prototype for testing. The data from that testing will in turn expedite the design process and time to market.

This can be a very cost-effective method for doing heat sink characterization for the following reasons:

It reduces electronic system development cost.
o A system developer can focus on thermal issues very quickly instead of waiting for an expensive prototype to come out of the factory.
o Rather than using a potentially expensive project, testing on prototypes can determine design flaws without requiring a significant
o Because prototypes are less expensive, each iteration of a design can quickly go through an initial series of tests.
It reduces time to market.
o Valuable resources can be applied to engineering the best solution because a load board can generally be created in 1-2 weeks and at a
fraction of the cost of a full PCB.
It allows a physical testing very early in the design.
o Many times components on a PCB will obstruct air flow, requiring either costly design changes during NPI (new product introduction) or
requiring engineers to over-design a board and the thermal management solution, putting the product outside its cost objective.

After a thermal load board is created, the board is ready to be used:

Completed Load Board

A completed load board ready for testing. (Advanced Thermal Solutions, Inc.)

The heaters on the board can be powered up to dissipate the same level of power as the semiconductors they are meant to represent. Heat sinks can then be applied based on initial analysis done via integral modeling, mathematical modeling or through CFD (computational fluid dynamics). To test just air flow, heat sinks can even be created by 3-D printing.

Once populated with heat sinks, the board can be tested in a wind tunnel to see if the air flow will be sufficient. Wind tunnel testing methods include smoke flow visualization or water tunnel testing in order to examine air flow and ensure the most functional and cost-effective design is applied.

Getting to market faster and with the best possible design is very important in today’s product development process. Working with a thermal engineering partner, such as Advanced Thermal Solutions, Inc. (ATS), that offers Virtual Engineering Demos (VED) and Thermal Load Boards (TLB) will benefit a project’s bottom line and ensure a project’s successful completion. Project engineers will know that their design has proper thermal management early in the process, meaning that they will not have to over-design the project, which will save time and money in the long run.

Learn more about ATS and its capabilities as a thermal engineering partner for your next project by visiting or by calling 781-769-2800.


Thermal Load Board Design Considerations