narrow gap cooling
calculator: heat transfer coefficient for parallel plates
introduction
air cooling performance is sometimes described as a function of three parameters, velocity, temperature difference and surface area. this is somewhat incomplete. there is another important parameter, the hydraulic diameter. since there are few cooling channels with circular cross sections in electronic devises, it will here be referred to as the channel gap, which essentially is the same thing, (the hydraulic diameter between two parallel plates is 2 times the gap width).
in conventional air cooled sub racks the gap width is determined by various mechanical parameters such as the connector width, component heights and pcb curvature. there is not much a heat transfer engineer can do to change that. things are, however, evolving. pcbs are increasingly being housed in metal boxes. one reason is that the electrical shield needs to be moved from the sub rack level to the pcb level because the frequencies are increasing. another is that pcbs, because of downscaling, are becoming increasingly mechanically sensitive. a third is that some pcbs need to endure rough handling. typical examples from the telecom sector are decentralised devices such as radio base stations and adsl modems.
figure 1 heat transfer as function of the channel gap width assuming that the volumetric flow is unchanged.
there are several ways too cool a rectangular metal box. the most obvious one is to integrate a heat sink with one of the sides. another is to use edge cooling. both these methods are used and have been proven to function well. this article is about yet another method, narrow gap cooling, figure 1. to the authors knowledge this method is not practiced widely. this is somewhat surprising, because it is both a simple and a relatively powerful method.
the diagram shows how the heat transfer coefficient, defined on the inlet temperature difference, changes with the channel gap, provided that the volumetric flow remains constant. given these conditions small gaps perform better than large gaps. the reason is partly that the velocity increases but more importantly, that the heat flow paths from the air to the walls become shorter as the gap decreases. the maximum limit is reached at zero gap, for which case the outlet air temperature is the same as the wall temperature.
narrow gap cooling can actually be made quite powerful. assume that the gap is 3 mm. the diagram then indicates that a factor 3 can be gained relative to a 20 mm gap. assume that the air velocity is 5 m/s, the box sides are 200x200mm and the temperature difference is 30 k. the result is 66 w. the pressure loss is naturally a problem. the friction losses accounts to 37 pa. in addition there are inlet and outlet losses of the order ~20 pa, so the total pressure loss would be ~57 pa. it is high but still in the reach of axial fans. another interesting parameter is the air efficiency. it is ~60%, which ensures that the air is effectively used and minimises the size of the air ducts leading to and from the boxes. considering the simplicity of the arrangement this is quite an impressive performance. provided that the problems involved can be handled it should therefore be an attractive solution for many cases.
figure 2 dimensionless representations of the heat transfer coefficient, (inlet temperature difference,) and the air efficiency.
theory
figure 2 shows a dimensionless representation of the heat transfer coefficient and the air efficiency. the scales are logarithmic and span over a huge range of conditions. the practically interesting part is where the air efficiency has reasonable values, 20%  80%. it can be noted that this also is the region where the two asymptotic tendencies meet. it is not an incident. almost all optimum design points, regardless of their nature, follow this rule. the nunumber is almost constant in this region, which, as shown in figure 1, indicates that the heat transfer coefficient roughly increases inversely proportional the gap.
figure 3 correlations for the friction losses.
figure 3 shows a set of correlations that can be used to calculate the friction losses. it is based on the analogy between convection and friction. there are alternatives that work just as well. correlations for the heat transfer coefficient can be found on the web page for the referenced calculator.
figure 4 non uniform gaps always cause a performance loss.
the non uniform gap problem
narrow gap cooling is used for a wide range of heat transfer applications, both for liquids and gases. it is obviously an attractive solution. a problem in this context is that the actual performance mostly is much lower than the predicted performance, in extreme cases as much as 50%. the fundamental reason is that it is difficult to create a uniform flow distribution in parallel channels. the root of this problem is both on the feeding channel level and on the gap level. the last is closely associated with nonuniform gap widths, figure 4. this problem is typically also located in the region where it hurts the most. a 30% displacement roughly results in a 20% loss.
it may appear as if a 30% displacement is a lot but for a 3 mm gap this is just 1 mm. considering that the mechanical tolerances have a tendency to add up, there is reason to be cautious and check the design carefully. neglecting this impact can result in unpleasant surprises.
figure 5 folded fins. a non uniform gap problem?
it can be noted that this problem also appears for heat sinks and in particular for heat sinks with soldered folded fins. the example in figure 5 seems to have been made with great care to avoid this problem. for other designs it is sufficient with a quick glance to conclude that considerable performance is lost because of the non uniform gap problem.
the plug out problem
plugging out a narrow gap cooled box opens up large air gap, which results in a large local air flow increase of no or little use. the air feed to all other units will decrease and their temperatures will increase. there are several solutions to this dilemma. it might be possible to shut down the device before doing the operation. various types of mechanical air blockers can be employed. it might also be that the temperature increases not are critical at normal room temperature. for that condition the temperature margin is often of the order 25 k, so there is some space for manoeuvring. the essential is that this problem is addressed and that a satisfactory solution can be found.
a related problem is air leaks. it always appears in equipments with high pressure losses. this presure loss can be managed a a higher cost and a more complicated design.
conclusions
narrow gap cooling has many attractive qualities. it is simple, relatively powerful, no air filters are needed and it minimises the volume needed for cooling.
the problems are that the gaps need to be almost uniform, that air leaks between the high and low pressure sides are difficult to avoid and that there is a risk for overheating when units are plugged out.
a personal experience is that i have suggested narrow gap cooling at several occasions, none of them successfully. the critical point was in all cases the cooling lost at plug out. since things constantly are changing i have nevertheless not abandoned the idea. the next time a design that could profit from narrow gap cooling is presented, i will suggest it again. let me know if this is something you have tried as well.
