newbcake :
nostall :
Your description lead me to visualize the fan attached to the top of the case, then the radiator attached to the fans. Correct?
You can and should use both methods.
With the case open, preferably both sides start with the vacuum.
Using the brush tool, gently vacuum the exposed radiator, being careful/gentle as the cooling fins are real thin and bend easily. You can then use the same to vacuum the top of the case and thus the fans and grill: it would be as effective but will get some dirt and loosen up some dirt. MAKE CERTAIN you keep a hand in touch with the metal of the case while vacuuming to keep static electricity from nuking some part.
Vacuuming shouldn't take very long. When finished, brake out the compressed air. Hold the fan blade so they don't spin (I use a pencil)and blow down into the case. (Remember not to tip the can). After you have eliminated as much dirt as you think possible, then blow up through the rad. to the outside of the case.
It won't be perfect. Some microscopic dust will cling to the surfaces and usually need to be wiped off. But it will be clean and cool better.
I may have misstated. I think I can work with what you say though.
Here is the best way to explain
Top of case
Radiator
Fans blowing air "into" the case and pulling said air through radiator
Rest of computer
In this case ( ah, no pun intended) you have two choices also;
1. carefully use the vacuum around the fan and radiator; then blast air up through the fans and out of the case (hold the blades); second step is to blast air down through the radiator and fans into the case
2. You could disconnect the fans and clean the radiator with the vacuum brush and air blasting; then do the same to the fan(s) and also use a damp rag to wipe off any stubborn dirt .
Me, depending on how long or how dirty the cooling s ystem was, I would probably give it a once over vacuuming and blow it all off after that and call it good.