The importance of heat radiation in radiator design

The role of thermal radiation in radiator design is often overlooked. There are many references to the percentage of heat lost by a radiator. As with most phenomena in physics and engineering, the effects of radiation cannot be summarized by a constant.

The effect of thermal radiation on radiator performance is determined by several factors. Before examining these factors, it is necessary to give a brief introduction to thermal radiation.

Thermal radiation is the electromagnetic wave emitted by all matter with a temperature above 0K (absolute zero). The maximum heat (W) that radiation can release from a surface is given by the following formula:

A:the surface area of the radiant surface;

σ=5.67*10^-8W/m²K⁴,Stefan Boltzman constant;

T_s:surface temperature(K).

This surface is considered an ideal radiator or blackbody. At the same temperature, the surface of a non-ideal radiator radiates less energy than a black body. The radiation properties of these surfaces are called emissivity. The emissivity, with a value between 0 and 1, is a measure of how well a surface dissipates heat compared to a blackbody. The values of common radiator surface treatments and materials are shown in Table 1:

 Table 1. emissivity of common radiator materials and surface treatments

When two or more surfaces are involved, each surface absorbs and releases radiant energy. One of the simplest forms of radiation exchange is on a single surface in a much larger shell. The surface temperature is higher than the shell, the surface area is A, and the emissivity is ε. In this case, the net energy exchange rate due to radiation is derived from formula 1. See Figure 1:

Figure 1. radiant heat transfer between a small heated surface and the inside of a large housing

Because the radiator consists of multiple surfaces that absorb and emit radiation with each other and with the shell, the equation representing these interactions is not as straightforward as equation 1. But the general principle represented by equation 1 still applies. See [1] for a detailed explanation of the radiation calculations and corresponding equations for plate-fin radiators.

The calculations in [1] require the use of multiple equations and can be tedious to calculate. To reasonably estimate the radiant heat loss of a plate-fin radiator, equation 2 can still be used to calculate the apparent radiant surface area. The apparent radiated surface area is calculated assuming that the radiator is a solid block with the same external dimensions. The block surface area shown in Figure 2 is then calculated using formula 3 and used for formula 2. This calculation does not take into account the temperature variation between the bottom of the radiator and the tip of the fins, which can be very noticeable in forced convection, long fins, radiators made of low-conductivity materials, or a combination of the above. In addition, using the apparent radiant surface area does not accurately calculate the surface area of the heat sink. Therefore, this method should not be used if very precise results are required.

L：length of heat sink fin.

 Figure 2. radiator dimensions

There are two ways for a radiator to dissipate heat (power) to the surrounding environment, namely radiation and convection. The formula for convection heat dissipation is 4:

h:convection coefficient;

T_amb:ambient air temperature.

Convection coefficient h values in air range from 2 to 10 W/m2K for natural convection and 20 to 100 W/m2K for fan forced convection. Because forced convection has a much higher h value, the proportion of heat lost by a radiator is usually much greater by convection than by forced convection. This statement is usually true when the temperature of the radiator is below 150°C. From equations 1 and 2, it can be seen that the amount of heat lost by radiation is closely related to the temperature of the heat sink, because the radiated heat is raised to the fourth power.

In order to compare the effects of radiation on the performance of plate-fin radiators, we analyzed two examples using HeatSinkCalculator. The first is a radiator cooled by forced convection. As shown in Figure 2, the heat source covers the entire bottom of the radiator. The airflow passes through the heat sink parallel to the heat sink and the bottom of the heat sink. All air flows through the fins of the radiator and there is no air bypass. Table 2 shows the analysis results for different power inputs. The dimensions of the radiator, the radiator material, and the flow rate through the radiator are listed below.

 Table 2. results of forced convection heat sink analysis

As expected, as the temperature of the radiator increases, the proportion of heat lost by radiation also increases. At higher temperatures, the heat lost through radiation exceeds 5% of the total heat. In some critical cases, this can mean the difference between reaching or not reaching the rated temperature of the element being cooled.

The second example is a radiator cooled by natural convection, with the radiator base and fins placed vertically. As shown in Figure 2, the heat source covers the entire bottom of the radiator. Dimensions and radiator materials are shown in the following table. Table 3 shows the analysis results under different power input and surface emissivity conditions.

 Table 3. analysis results of natural convection radiators

In natural convection, the proportion of heat lost by radiation is much higher. In this example, the percentage of radiative heat dissipation approaches or exceeds 30%. The heat lost through natural convection is also closely related to the surface temperature of the radiator. This explains why the radiation dissipation rate increases as the source temperature decreases. When the surface emissivity is reduced to 0.09, the effect on the heat sink temperature is close to 30°C.

The above examples highlight the importance of radiation in the cooling process of radiators. Although the effect of radiation on forced convection radiator cooling is less, its effect is still significant if a few extra degrees are needed to ensure that the product meets the specifications. Obviously, the effect of radiation on radiators cooled by natural convection is extremely important. The temperature can be significantly reduced by anodizing or painting the surface of the radiator and increasing the surface emissivity value.