Just like a car’s radiator keeps its engine from overheating, the heat associated with the processing of electricity must be reduced significantly in order for consumer electronic devices like computers, televisions and smartphones to function properly. Whether a device is a smartphone or a vehicle, work creates heat, and that heat must be transported away from the device so it does not malfunction.

Traditional modeling software and the manufacturing processes used to produce advanced geometries have determined the boundaries of heat exchanger efficiency for consumer electronics. With advanced computational modeling software and additive manufacturing (AM) technology, heat exchanger designs can be created with optimized surface areas and reduced weight. Designs that are a step-change in functionality and appearance from traditionally designed counterparts are possible with 3D printing (figure 1).

Regardless of design or manufacturing method, there are many examples of heat exchangers that can be used to transport heat away from the device that is creating it. The designs are defined by both system requirements and the physical method in which they move heat away from critical areas. Three methods are possible (figure 2):

• Conduction is the transfer of heat energy by direct contact.
• Convection is the movement of heat by the actual motion of air or fluids.
• Radiation is the transfer of energy with the help of electromagnetic waves.

FIGURE 2. There are three methods of heat transfer: conduction, convection and radiation.

A heat sink is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant. From the fluid medium, the heat is dissipated away from the device, thereby allowing regulation of the device’s temperature at optimal levels.

FIGURE 3. Computational modeling can be used to enable design studies to identify the optimal geometry for a product to be 3D printed. In this example, several TPMS structures — gyroid, Schwarz-p and lidinoid with varying periodicity and thickness — are demonstrated.

### Electronic Heat Dissipation: Conduction/Convection Heat Sink

The amount of surface area of a heat sink that comes into contact with the cooling medium surrounding it determines the heat sink’s effectiveness. With the ever-rising computational requirements of our data-intensive world, designers must optimize heat sink performance by maximizing the surface area of a heat sink in a given volume. This quickly becomes a geometry game.

Computational modeling technology offers an advantage to designers. The advanced geometry kernel can be used strategically to provide complex surfaces with large amounts of surface area and very thin walls.

In the example in figure 3, the software was used to define a volume that could be applied to generatively design a heat sink to maximize surface area while minimizing mass. This was implemented using an advanced geometry representation to mathematically control surfaces. In this case, triply periodic minimal surfaces (TPMS) were used. They have been shown to have high strength-to-weight ratios for structural applications. When coupled with advanced manufacturing methods like additive manufacturing, the structures allow designers to create multifunctional structures with both high strength and heat-dissipative properties.

FIGURE 4. The schematic demonstrates a workflow for passive heat sink design and evaluation.

For the purposes of this study, three classes of TPMS structures — commonly referred to as gyroids, Schwarz primitives and lidinoids — were evaluated. The key factors that make each these structures unique is that each is a linear combination of sines and cosines that form a periodic waveform geometry in 3D space. Just like a 2D waveform, the amplitude and period of these equations can be varied to generatively create multitudes of design possibilities. By coupling these design inputs with a design of experiments (DOE) approach, the performance of these components can be evaluated (figure 4).

A passive electronic heat sink is dominated by all three modes of heat transfer methods. Heat must first be conducted from the heat source (i.e., computer chip) to the base of the heat sink and then dissipated from the heat sink via convection (70 percent) and radiation (30 percent). To maximize the heat dissipation of a heat sink, it is necessary to maximize the amount of ambient air that is in contact with the heat sink.

As heat is dissipated, convection naturally will induce the flow of air over the fins of the heat sink. The gyrating fins of a TPMS heat sink allow for enhanced boundary-layer mixing that has the potential to provide a higher effective surface area than traditional heat sink designs.

As part of this work, a simple numerical study was performed to identify the highest performing TPMS heat sink whose design inputs maximize surface area and minimize the mass of the resultant heat sink. This experiment was enabled through the use of a computational geometry kernel coupled with advanced analytical methods. The modeling software allowed the designer to make geometry changes and evaluate the performance outputs of the design inputs. The results are plotted in figure 5.

FIGURE 5. Heat sink performance is compared to identify the optimal heat sink designs that maximize surface area while minimizing mass. The design with the highest surface-area-to-mass ratio effected the greatest amount of heat transfer.

Designing heat exchangers with optimally maximized surface area and minimal mass can be a challenge for the design engineer. This can be more easily accomplished by employing computational modeling software that uses advanced geometry representation capabilities to mathematically and precisely control surfaces.

The real challenge lies in developing a manufacturing process that can produce such designs reliably and affordably. As shown by the work with the TPMS structures, 3D printing is an effective solution for producing such heat sinks. PC