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Convection and Air Properties, Temperature Impact |
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| Home page: | Frigus Primore |
| Calculator: | Thermal Properties for Air |
Introduction
Air convection is complicated matter. Not the least because there are quite a few parameters involved. Velocity is the most important one but air properties, such as density and thermal conductivity, can sometimes also have a significant impact. Some air properties are almost constants while others vary significantly with pressure and temperature. It is often important to have an idea of their impact. This article covers the temperature aspect. Pressure will be discussed at a later occasion.
Figure 1
Air property tendencies normalised for 20 C.
Convection basics
Figure 1 shows air property tendencies normalised for 20 degC. All properties in this diagram have an impact on convection. The ones that are important for an overview discussion of the temperature impact are however only the thermal conductivity, the density and the viscosity.
The impacts of thermal conductivity and density are easy to understand intuitively. They both improve convection when their values increase. The impact of viscosity may be less obvious. A somewhat simplified view is that a high viscosity tends to decrease the mixing movements in a fluid and thereby decrease convection.
Figure 2
Dimensionless representation of the heat transfer coefficient for flow between two parallel plates.
The issue can be made clearer by applying heat transfer theory. One fundamental technique in this theory is to incorporate all parameters of interest in dimensionless numbers. The Nu-number is for example a combination of the heat transfer coefficient, the hydraulic diameter and the thermal conductivity. The basic idea is that one particular dimensionless number only can be a function of other dimensionless numbers.
Figure 2 shows a typical formulation for forced convection between parallel plates. Nu stands for the Nusslet number and Re for Reynolds number. The constant and the exponents vary with the conditions. A particular set of these parameters is therefore only valid for a specific case and within a limited flow range.
The equation makes it easy to study the impact of air temperature changes. Increasing the air temperature decreases both the Re and the Nu-numbers. These two impacts tend to cancel each other. The exponent on the Re-number determines the degree and at ~0.5 the cancelling is almost perfect.
Figure 3
A log-log diagram for the heat transfer coefficient as function of the velocity for a typical PCB case. The slope of the curve reflects the exponent on the Re-number.
If the heat transfer coefficient is drawn as a function of the velocity in a log-log diagram the slope of the curve represents the exponent on the Re-number, figure 3. The heat transfer coefficient is in this case the one defined for the inlet temperature difference. The exponent is near 1.0 for very low velocities. It then decreases to about 0.5 and for strong turbulent flow it increases to 0.8. It can be concluded that the impact of temperature must be velocity dependent, or more correctly expressed Re-number dependent.
There is however also another phenomenon involved, air temperature rise. For PCBs it appears when several sub racks are stacked or if the air is heated by another object before it reaches the PCB. The important air properties are in this case the specific heat and the density. The former does not vary much but density does and in this case there is no other air property that cancels its impact. Air temperature rise is therefore more sensitive to changes of the temperature than convection.
Figure 4
Some examples of how the temperature difference changes with the air temperature.
Some examples
Figure 4 shows some examples of how the temperature difference changes with temperature. They have been calculated for 200x200 mm parallel plates, placed on 20 mm distance. As expected it is the serial heating case that has the highest dependence. The difference between the 20 degC and 60 degC cases is ~6 %. For a temperature difference of 35 K this corresponds to a change on the 2 K level. It is not much but it may sometimes be important.
Pure convection cases have lower dependencies. The largest one is for natural convection. This can be explained by the fact that the velocity is low and slope of the curve in figure 3 is near 1.0. The opposite extreme is low level forced convection cooling that improves when the temperature is increased. A glance at figure 3 explains why.
The flow in heat sinks is almost exclusively laminar. The simple reason is that the pressure drop increases sharply for turbulent flow. Their typical flow region is therefore characterised by a low Re-number exponent. The temperature impact is consequently minor.
A problem when doing these types of comparisons is to find the temperature at which the air properties should be determined. The air temperature is not uniform. It varies both in the flow direction and perpendicular to it. If these temperature variations are large care should be taken to use the particular air temperature definition for which the equation used is calibrated.
Figure 5
It is problematic to determine the average temperature on the convection surfaces of a PCB.
PCBs
It is important to have a rough idea on how convection varies with the temperature on almost isothermal plates. It is however not evident how that information should be interpreted for PCBs. The heat flow paths are in this case much more complicated, figure 5. One part of the heat is dissipated from the component tops and another part from the PCB. The problem is that these convection surfaces operate on different temperature levels. A change of the heat transfer coefficient can therefore result in quite a different absolute component temperature change depending on which of these two flow paths that are dominant.
The component-to-air heat can be estimated with the thermal territory method, (image = component). For modern copper rich PCBs it is typically modest, ~20%. For large components or high air velocities it can nevertheless be considerably higher and if there are heat sinks this is definitely the case. This complexity makes it difficult to achieve high accuracy results with simple methods of the multiplier type. Calculations of the finite element kind is about the only reliable method.
A recommended first level approach is nevertheless to base an estimate on the average PCB temperature. The reason is that a PCB usually only has a limited number of hot spot components. Quite a few other components may have near zero heat dissipation. Their top surface temperatures may therefore even be lower than the PCB temperature, (they function as small heat sinks), which counterbalance the hot spot impact. The total convection surface for the hot spot components is usually also considerably smaller than the total convection surface of the PCB, (primary + secondary side).