How to calculate thermal resistance to assess heat sink performance

Joris Coddé

Knowing how to effectively assess a heat sink’s performance is a necessity today, making thermal resistance calculation an essential tool to have in a thermal engineer´s toolkit.

Due to the trend to downsize electronics, heat flux densities continue to rise. This is a direct implication of Moore's law for micro electronics. Due to this trend, heat sink performance is arguably more important than ever before.

What is a heat sink?

Typically, the term ‘heat sink’ defines a device used for cooling a target (e.g. electronics, batteries, e-motors, etc) by an air flow. The term ‘cold plate’ is more commonly used when the cooling medium is liquid (e.g. water, oil, glycol) instead of air. In this article, the term heat sink is used in a broad sense; encompassing the cooling of any solid with any fluid.

By calculating the thermal resistance of two different heat sinks, the thermal efficiency gain between them can be measured. Note that the heat sinks in question must be designed to cool the same heat source. Contrary to heat exchangers – it is impossible to calculate the efficiency of a heat sink without comparing it to another design. In this article, we will compare a Diabatix generative heat sink to a conventional s-shaped heat sink.

What is a heat exchanger?

When one fluid is cooled by another fluid, this is called a heat exchanger. Heat exchangers have different goals (e.g. heat recuperation of ventilation flows), and different performance metrics. They are therefore not covered in this article.

The engineering trade-off in active cooling

Before we can measure performance, it’s important to understand the engineering trade-off.

In active cooling, there is a pump for liquids or a fan for air, which drives the flow. Active cooling has high cooling potential, but introduces a clear engineering trade-off. The higher the flow that the pump or fan creates, the higher the cooling potential; but the higher the component’s cost as well as its power requirements. This remains true until a certain point, as the performance gain will eventually plateau due to the physics of convective heat transfer. This can be seen in figures 1 and 2 below. Note that the lower the thermal resistance, the lower the temperature.

Fig. 1: Thermal resistance in relation to mass flow rate in active cooling

Fig. 2: Pressure drop in relation to mass flow rate in active cooling

In passive cooling, the flow is driven by buoyancy, so the engineering trade-off doesn’t exist, as there is no active component. This means that reliability is far better in passive cooling. However, this also implies that the design of the heat sink is all the more crucial.

Bringing a design into virtual space

To evaluate the performance of a heat sink, we must first bring the design into virtual space. That means that the design must be drawn up in a Computer Aided Design (CAD) program and simulated with Computational Fluid Dynamics (CFD).

How do we do it?

We use AutoDesk Inventor for the CAD and OpenFOAM for the CFD. The main bulk of the work is actually done within OpenFOAM; here, the geometry is meshed, with the Navier-Stokes and energy equations solved numerically. In doing so, we arrive at a prediction of fluid velocities and temperatures throughout the heat sink.

Since we specialize in heat transfer, we have tailored our software for heat sink simulation. That allows us to commence a simulation in just a few clicks. From there, cases are automatically meshed, even refined where necessary, and effectively simulated. At the end of a simulation, we check performance characteristics as well as the quality of the simulations. Therefore, residuals on all governing equations must be smaller than 1e-6, as well as the balances on all equations smaller than 1e-4. On top of that, we execute a mesh refinement study. This is very relevant in heat transfer, as an under refined mesh generally predicts inaccurate temperatures. Proper mesh refinement is necessary to accurately capture thermal boundary layers.

Furthermore, apart from the geometry of the heat sink itself, we obtain the specifications of the heat source (a power Q), the inlet temperature of the fluid and the specified flow rate.

Assessing performance - thermal resistance formulas

Now that our design geometry and specifications are known, we’re ready to asses a heat sink’s performance. We do that by calculating its thermal resistance. There are four ways to define thermal resistance. All involve a temperature difference divided by a quantification of the heat source. Possible temperature differences are:

Where T_in is the inlet temperature of the fluid, T_hs,av is the average temperature of the heat source, T_hs,max is the maximal temperature of the heat source and ΔT the temperature difference. Both can be used in the following formulas:

Both are called thermal resistance, although the last formula is also referred to as thermal insulance. Both can be used with the average and maximal temperature differences specified above.

Our preferred thermal resistance formula is the first, which takes the difference between the maximal temperatures:

We prefer the maximum because the maximal temperature typically determines the limits of mounted components and the heating power, which brings us closer to the electrical analogue.

Heat sink comparison - calculating thermal resistance

Using the following specifications, we can use our preferred formula to calculate the thermal resistance of both the s-shaped heat sink and our generative heat sink.

  • Heat source (Q) = 1500 W
  • Inlet temperature (T_in) = 293 K
  • Flow rate (measured at design point) = 4.2 l/min
  • Maximal temperature (T_max) (based on simulation results)
  • Diabatix generative heat sink = 325.81 K
  • Conventional s-shaped heat sink = 334.22 K

Thermal resistance results

  • Diabatix generative heat sink = 0,021873 K/W
  • Conventional s-shaped heat sink = 0,02748 K/W

Want to calculate thermal resistance in a flash? Use our heat sink thermal resistance calculator tool.

Below, in figure 3, you can visualize the thermal efficiency gain percentage at various mass flow rates.

Fig. 3: Thermal efficiency gain of the Diabatix generative heat sink over the conventional s-shaped heat sink

To summarize

To summarize, the rise in heat flux densities due to the trend to downsize electronics calls for heat sinks that perform better than ever. This also means that knowing how to effectively assess a heat sink’s performance is a necessity today, making thermal resistance calculation an essential tool to have in your toolkit.

Want to increase your heat sink performance without increasing, or by decreasing, the power requirements? Get in touch with us.

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