Calculating the effectiveness of a Radiator and Fan Combination

[GiraffePencils]

Hello,

I am trying to compare different combinations of Radiators and fans on their ability to cool water(or any liquid for that matter)
Now I've been showen some Bernoulli's equation things and been pointed at Reynolds number but To be honest I haven't looked at any physics outside rigid body interaction since university and I'm getting lost.

Now what I'm looking at is I have A radiators made of copper or brass, with different 'fins per inch' and different depth but a constant width and height.
I also have fans whose performance is measured in Airflow (Cubic feet per minute) and Air Pressure (mmH2O)
I Assume the process would be to:

Calculate the area of the radiator (m2)

Calculate actual airflow over it.( the CFM passing over the metal, something involving the fins per inch impeding the air and the pressure of the fan?)

The amount of heat the metal can transfer to air which is traveling at that rate.

But Alas I am at a loss in how best to go about this, Any and all advice would be appreciated.
Thanks

 

[voko]

Analysing this from first principles is a very difficult task, especially if you had no prior acquaintance with fluid dynamics and thermodynamics. However, I am pretty sure this is a common problem in the HVAC industry and chemical engineering. I would search for established rules and conventions in building heating/cooling systems or heat exchangers.

 

[sanka]

There are a couple of different approaches this. I'll explain one possible method.
Firstly, I would say that it is essential to establish the flow rate of air through the radiator. You said that you have the pressure-flow characteristics of your fan. However, you don't know the operating point on the fan curve. You need to determine the resistance curve (pressure-drop curve) of the radiator. You could do this experimentally but I'm not sure what kind of equipment you have to do this? It would probably be better to find some friction factor correlation in literature and calculate the pressure drop from this. This friction factor is a strong function of the geometry so be carefull when selecting an appropriate correlation. This will enable you to calculate the pressure drop for a range of arbitrary flow rates. This curve can then be plotted against the fan curve and the intersection between them is your operating point!

At this stage you can calculate your heat transfer. One possible way is by using the equation
$\dot{Q}$=$\dot{m}$Cp(Tfluid - Tair)
where mdot is the mass flow of air established from your operating point.

An alternative approach would be to calulate the Nusselt number, which will give you the heat transfer coefficient and you could then use the equation Q=hAdeltaT. But this is probably more complicated.