So let's say I have some heat generating machine be it a combustion engine or a fridge cooled by a fluid. I don't have a single radiator that is big enough for the amount of heat being generated but I do have a couple of smaller ones so I guess I could connect them together. Should I put the radiators in series (one connected to the next one and so on) or in parallel (having the coolant intake pipe split into all of the radiators) and why? What would be the most efficient set up?
The efficiency of any radiator (heat exchanger) is a function of the temperature difference between the two fluids in question. All else being equal, a heat exchanger with a greater temperature differential will transfer more heat.
Each radiator will have a temperature gradient across it. (Here I'm talking about how much the temperature of each fluid changes as it passes through the heat exchanger.) If you hook them in parallel, each one will be getting 1/N of the flow, but they will all have the same temperature gradient from input to output.
If you hook them in series, all of the flow will be going through all of them, but each one will have only roughly 1/N of the overall temperature difference across it — with the hottest one also having the highest differential, because it's transferring more heat to the other fluid.
Note that you can make this "series or parallel" decision independently for each of the two fluids. There is a total of four different ways you can configure them.
Overall, I don't think it really makes any practical difference in terms of the thermodynamics. Personally, I would be inclined to hook them in parallel+parallel (i.e., parallel paths for both fluids) — partly because I like that kind of symmetry, and partly because of secondary considerations such as maintenance. When you have a parallel connection with individual shutoff valves, you can repair or replace one radiator without shutting down the system altogether. You can either run at reduced capacity, or design the radiator system to have N+1 redundancy in the first place.
- "Radiator" means a forced-air air-to-fluid heat exchanger.
- Radiators in either setup will pull from their own fresh air source (not from the exhaust of another radiator).
- Ignoring radiator design, natural convection, and internal fluid turbulence effects.
- Flow through parallel radiators is perfectly equal.
The efficiency would be the same either way. I invented some fluid temp numbers to help visualize. Flow follows the arrows. Air temp would be 20C for example.
40C -> Radiator1 -> 34C -> Radiator2 -> 30C
- Radiator1 is exhausting more heat than Radiator2.
Parallel (new names for radiators for comparison)
40C -> RadiatorA -> 30C
40C -> RadiatorB -> 30C
- Both A and B are exhausting the same heat. Both will exhaust less heat than Radiator1 but more than Radiator 2. The net of both systems will be the same.
- RadiatorA gives the same temperature drop as Radiator1&2 combined because it has half the flow and half the cooling surface area.
- The temperature gradient efficiency difference that is made obvious by the less efficient Radiator2 and more efficient Radiator1 is present in both A&B radiators. If we were able to sample the center of A or B we would get the same temperature as between 1 and 2.
Other Design Considerations
- The primary benefit of series radiators is that you can guarantee that the flow through each radiator is equal. This is necessary for optimum efficiency. In a parallel system, you can make all hose lengths identical and have all the same fittings (minor losses) for each path, but it is not a guarantee.
- The second benefit of series, is that increased flow velocity increases turbulence inside the radiator. It may cause a measurable increase in total heat transfer if the fluid is not as good of thermal conductor like oil.
- It takes less fittings to plumb radiators in series. This means less install labor and less potential leak locations.
- Increased flow velocity in the series configuration also increases pressure drop, pumping energy requirements, and heat added to the fluid from this pumping energy input (it all has to go somewhere).
- Parallel has the ability to isolate a radiator for service during operation as Dave Tweed mentioned. But this is a minor benefit, because with a few more plumbing additions, series can be isolated and serviced during operation as well.
- It is easier to compare radiator efficiencies when running in parallel. When one radiator has fouled from internal or external contamination it is easy to see that it has less of a differential than the other without doing any math.
The answers above look a little over-complex. The problem is pretty simple: how much overall heat you can transfer from your source to the radiators. Since no detailed information is available, I can generally say that:
- The best setup is the setup that offers the most radiating surface in contact with the heat-generating surface (in your case, if the coolant intake pipe can touch all of the radiators, it's the best case).
- If you can only have one of the radiators in actual contact with the heat generating surface, then the same rule applies between the 1st and 2nd radiator: set the second one up so it has maximum shared surface with the 1st one. That most likely happens when they are in parallel.
If we consider two equal size radiators connecting them parallel is more effective. ∆Q/∆t = -K×A×∆T/x, where ∆Q/∆t is the rate of heat flow; -K is the thermal conductivity factor; A is the surface area; ∆T is the change in temperature and x is the thickness of the material (∆T/x is called the temperature gradient and is always negative because of the heat of flow always goes from more thermal energy to less). Wikipedia.
This way we maintain a higher slope of heat exchange rate due to maintaining original delta T across the two radiators.