How To Design A Flat Panel Heat Sink

A heat sink is a component that conducts heat from a hot component to a larger surface area in order to dissipate heat into the surrounding environment, thereby reducing the temperature of the component. According to this definition, everything from rectangular metal sheets to complex copper or aluminum extrusion fins can be used as heat sinks. Aluminum or copper plates can be used as effective heat sinks when space is sufficient and/or the component heat output is low. As shown in Figure 1, the radiator can be a simple flat plate or a metal wall of the element housing.

Figure 1. Flat plate radiator dimensions

To estimate the size of a flat radiator, it is necessary to determine the path of heat flow to the surrounding environment and the amount of resistance that path to the heat flow. The thermal resistance circuit shown in Figure 2 will be used to represent the heat flow path. Let's examine each thermal resistance element:

Figure 2. Thermal resistance circuit of flat plate heat sink

Thermal resistance from junction to housing:

Node-to-housing thermal resistance (Rth-jc) refers to the thermal resistance from the working part of the semiconductor device to the outer surface of the package (housing), on which the heat sink will be installed. The housing temperature is considered to be a constant temperature throughout the accessory surface. Rth-jc is usually a measurement value provided by the device manufacturer and indicated in the device data sheet.

Thermal contact resistance and thermal interface resistance:

Contact thermal resistance (Rcont) refers to the thermal resistance between the housing and the heat sink. As shown in Figure 3, the actual contact area is smaller than the apparent contact area due to defects in the surface of the housing and radiator. A mathematical model based on contact pressure, material surface roughness and material hardness has been proposed to calculate Rcont. These models can be quite complex, and material surface and hardness information can be difficult to obtain. Typically, Rcont is determined based on experimental data and previous experience.

Figure 3. Thermal resistance from contacts, interfaces, and junctions to case

To reduce the impact of the Rcont interface material, we used a material that fills the gap between the housing and the radiator. Types of these materials include special thermal grease, filling compounds, phase change thermal pads, and thermal tape. The thermal conductivity of these materials is usually between 0.5 W/m-K and 4 W/m-K. Since the gap between the two mating surfaces is filled by the thermal interface material, the thermal resistance between the shell and the heat sink is a function of the thickness, thermal conductivity and surface area of the thermal interface material, as shown in formula 1:

t:thermal interface material thickness

k:thermal conductivity of thermal interface materials

A:apparent contact area

Please note that the thermal conductivity of many thermal interface materials varies with the clamping pressure. Manufacturers usually provide this data in the product specification sheet.

Thermal resistance of diffusion:

Thermal diffusion resistance (Rsp) is the result of heat flow through conduction between the shell contact area on the surface of the plate and the larger cooling surface area of the plate. Lee et al. [1] established a closed equation for Rsp. These equations provide very close approximations to exact solutions, but will not be discussed here due to the complexity of the calculations required.

The first step in using the Lee equation is to convert the dimensions of the two interacting rectangular surfaces to equivalent radii using equations 2 and 3.

Rsp can then be calculated using the following formula:

Here:

heff: effective convection coefficient of the plate

See Equation 18 for the calculation of heff.

kp: Thermal conductivity of the plate

Convective thermal resistance:

Convective thermal resistance is the degree to which heat is removed from the surface of a plate by air movement. For a heated vertical plate with natural convection, the dimensionless Nusselt number (Nu) [2] is derived from equation 11. Nusselt number is a dimensionless variable used in convection calculations.

Here:

The average convection coefficient is calculated by equation 14. The convective thermal resistance Rconv is a function of the plate surface area Ap and the average convective coefficient, calculated by equation 15. Note that the plate surface area does not include the area generated by the plate thickness, as this is much smaller than the front and back surface area.

Here:

kair : air thermal conductivity evaluated at Tavg

Radiation thermal resistance:

The thermal resistance due to radiation is given by Equation 16.

Here:

The plate is assumed to radiate heat to the surrounding larger surface, so the surrounding environment can be viewed as an ideal radiator or blackbody. In some cases, the temperature of the surrounding surface may be different from the ambient air temperature. In this case, the Tamb in formula 15 should be replaced by the temperature of the surrounding surface.

The effective convection coefficient heff, which is used to calculate the thermal diffusion resistance, is derived from equation 18.

The values of Rrad, Rconv, and Rsp cannot be solved directly because they are a function of the plate surface temperature Ts. Assuming that all the heat generated by the heat source is dissipated by the flat radiator, the energy balance equation is equation 19.

Here:

Q:heat generated by heat source

Ts can be calculated using numerical solvers in most mathematics software or the "Target Search" function in Excel.

When all thermal resistances are known, the thermal circuit shown in Figure 2 can be simplified to a single junction-to-ambient thermal resistance Rj-a using Equation 20.

Finally, the junction or heat source temperature can be found using Equation 21.

For diversified heat sinks, Winshare Thermal Energy has professional customization capabilities and diversified application markets, and can customize cooling products for different systems for customers. In the meantime, we will take many factors into account when designing the radiator and continue to optimize and improve the design of the radiator. If you have any other questions about heat sinks or need a cooling solution suitable for your business, please feel free to leave a comment or contact Winshare via email.