We can draw parallels between these systems in the following approximate way.
Heat Electricity Fluid Driving agent temperature voltage pressure D difference difference difference Resisting agent thermal electrical pipe/fluid R impedance resistance resistance Flow rate power (Watts) current (amps) flow (litres/sec) F (energy/sec) (charge/sec) (fluid vol/sec) If we consider this flow to be constrained by say a solid cylinder, a wire, or a pipe respectively, then generally we can say that :
Where A is cross sectional area, l is length and C1 is a constant of proportionality
and that
Where C
The obvious example of this is Ohm's Law for electricity which states that Click here to return
Let us say that we need to achieve a detector temperature of less than
100K and that we only have enough room to have a cooling radiator of
0.5 m
If we opt for a single radiator (0.5 m If we split the area 50:50 then we can show that
T thus achieving our objective. If we split the area 10:90 then we achieve something apparently better i.e.
T Clearly this is not the whole story because we have ignored the heat transfer between the shrouds which do the intercepting and which are coupled to the radiators. The magnitude of the transfer will be greater in the second case because there is a temperature difference of 158K driving it compared to that of 67K in the first case. So there is a limit to which we can divide up the area. It can be shown that there is an optimum solution and this confirms the common sense approach that if we have an n-stage radiator the dedicated areas should progressively increase from the outer radiator to the inner. Click here to return |
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