# Fins for Cooling Success

## Increasing Surface Area in Limited Volumes

As high-power electronics continue to push power density limits, component design engineers are facing greater challenges and trade-offs in their choice for cooling solutions. One way to meet these challenges and trade-offs is through the engineering of fin geometry and fin density of heat transfer devices such as heat exchangers and cold plates.

Below will explain how fin geometry and fin density affect the performance of heat exchangers and cold plates. It will briefly review some basic heat transfer theory, compare different types of fin geometries and their role in improving performance, and focus on minimizing thermal resistance as a way to maximize performance.

## Heat Transfer

The basic equation that describes the total heat transfer in a process is given by:

Q = U × A x LMTD (1)

Where:
• Q = Amount of heat transferred, BTU/hr (W)
• U = Overall heat transfer coefficient, BTU/hr-ft2-ºF (W/m2-ºC)
• A = Heat transfer area, ft2 (m2)
• LMTD = Log Mean Temperature Difference between the two incoming fluids in a heat exchanger or between the local surface and the fluid flowing underneath in the case of cold plates, assuming an evenly distributed heat load, ºF (ºC)

Increasing U, A, or LMTD will result in more heat transfer.

For most heat exchanger and cold plate applications, the overall heat transfer coefficient consists mainly of a combination of conduction and convection terms, where the conduction term tends to be much smaller than the convection term(s). This is important because component designers usually have little control over the materials of construction, which affects conduction, and the coolant to be used. They do, however, wield considerable control over fin geometry and fin density, which affects convection.

## Fin Geometry and Density

Fin geometries and densities that create turbulent flow and improve performance also increase pressure drop, which is a critical requirement in most high performance applications. The optimum fin geometry and fin density combination is then a compromise of performance, pressure drop, weight, and size. A figure-of-merit comparison based on performance, pressure drop, weight, and size among common fin types is described in “Air Cooled Compact Heat Exchanger Design for Electronics Cooling.”

Aside from fin geometry, parameters such as thickness, height, pitch, and spacing can also be altered to improve performance. Typically, fin thicknesses vary from 0.004 in. (0.1 mm) to 0.012 in. (0.3 mm), heights vary from 0.035 in. (0.89 mm) to 0.6 in. (15.24 mm), and densities vary from 8 to 30 FPI (Fins Per Inch).

In most high performance applications, fins are made of copper or aluminum. Aluminum fins are preferred in aircraft electronic liquid cooling applications due to their lighter weight. Copper fins are mostly used in applications where weight is not an important factor but compatibility with other cooling loop materials is.

There are many different fin geometries used in heat transfer applications. Some of the most commonly used are louvered, lanced offset, straight, and wavy fins. (See Figure 1.)

## Maximizing Performance by Minimizing Thermal Resistance

The task of optimizing performance and minimizing thermal resistance can be best demonstrated by a theoretical example. Consider a heat transfer process where 50/50 ethylene glycol and water (EGW) is cooled by ambient air in a plate-fin heat exchanger. Figure 2 illustrates the heat flow path through the heat exchanger using an electrical analogy.

In this example, heat flows by convection between temperatures TH and T1, then by conduction between temperatures T1 and T2, and finally by convection between T2 and TC. The total thermal resistance is then equal to the sum of the three thermal resistances in series.

By comparison, a cold plate typically has only one coolant flowing through it. As a result, heat flows by conduction from the heat-dissipating electronic device mounted on the cold plate through the thermal interface material and cold plate materials. Heat then flows by convection from the internal surface of the fluid path material to the coolant.

As shown in the example above, if we want to maximize heat transfer we must minimize thermal resistance. To accomplish this, we must increase the corresponding heat transfer areas, the film coefficients, or both. Increasing the heat transfer area is relatively easy in concept, though sometimes constrained by application requirements such as weight, size, and pressure drop. An effective way to increase the heat transfer area is to increase the fin density (fins per unit length). Increasing the film coefficient is more complicated, however, because the film coefficient is dependent upon the properties of the fluid being considered, the fluid velocity, and the fin geometry.

## Meeting the Challenge

When faced with demanding and sometimes conflicting application requirements, including performance, pressure drop, weight, and size, working with an experienced supplier that understands how to optimize the fin geometry and fin density of heat exchangers and cold plates is essential in order to maximize performance and meet the application requirements.

Check out our Extended Surface Liquid Cold Plates which use folded fins to enhance performance.

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