Category Archives: Thermal Design

Nanoparticles to Enhance the Thermal Management of Electronics

The addition of nanoparticles to a coolant are an alternative approach that can be considered to improve the performance of a liquid cooled system or perhaps to further reduce the size of such a system. But nanoparticles are not necessarily well known by engineers engaged in thermal management. This list of material may help.

The addition of nanoparticles to a coolant are an alternative approach that can be considered to improve the performance of a liquid cooled system or perhaps to further reduce the size of such a system.  But nanoparticles are not necessarily well known by engineers engaged in thermal management. This list of material may help.

First, a new paper by Moita, Moreira and Pereira, does an excellent job of reviewing nanofluids for the next generation of thermal management. This paper contributes to the body of knowledge in this space by looking at typical nanoparticle/base fluid mixtures used and combined in technical and functional solutions. It covers the science of nanofluids and their practical application. You can download this open-access paper from the Multidisciplinary Digital Publishing Institute, at this link (download is a PDF): Nanofluids for the Next Generation Thermal Management of Electronics: A Review

Second, ATS was fortunate enough to have had on our research staff, Dr. Reza Azizian. He and others authored a white paper titled “Nanofluids in Electronics Cooling Applications”. This piece discusses the theory and use of nanofluids for thermal management. We’ve posted that paper on the ATS blog here: Nanofluids in Electronics Cooling Applications.

We hope you find these resources helpful. Like always, if you have trouble accessing them, drop us a comment and we’ll get you a copy.

Nanoparticles Shapes & Forms Image used by permission from the artist normaals

Integrate More Electronics in Less Space with ATS Integration, Chassis Design and Cooling Solutions

ATS has designed custom housing and chassis for a variety of products including

  • ATCA chassis with 4.5KW cooling capability,
  • Small enclosures such set-top boxes, network interface units, industrial and autonomous vehicle systems
  • High capacity 1U and 2U chassis with integrated air jet impingement to push the air-cooling capacity of the 1U chassis to over 1.8KW.
ATS develops chassis and does systems integration for a wide variety of electronics in datacomm, telecomm, autonomous vehicles, industrial IoT and more

Integration of the cooling system, whether liquid or air, has enabled ATS clients to get their product out to the market right-the-first-time with superb thermal performance and right-cost.

Where Can Thermal Solutions for Electronics Equipment be Tested and Characterized? at ATS!

One of ATS’ core principles is basing our solutions on data: from analytical modeling, to CFD to manufacturing the thermal solution then actually testing it in our labs. Our vertical integration allows for excellent quality control and reliable solutions. With our investment in 6 characterization labs, we take this seriously for ourselves and for our customers.

ATS runs six Thermal Characterization Labs. Featuring a unique selection of air velocity, air temperature and air pressure measurement instruments and wind tunnels for thermal management research, testing and analysis. Virtually any electronic system can be characterized.

==> Learn more on our web site here:
==> Got questions on our labs and how we might help your next project? email us at

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