I am working on a corner light fixture in a bathroom. I've mounted two ~2' long T5 fluorescent strip light fixtures on a board 4" from the corner. I plan to enclose the fixtures with a diffuser set 9" from the corner. I've calculated the free volume (that not occupied by the fixtures and bulb) at 0.87 cu ft. T5 bulbs have their optimum light output at 35 °C and generate significant heat while operating. I temporarily enclosed the space and inserted a thermometer. The temperature stabilized at 55° C. I've purchased a 40 mm computer fan that is rated at 5 cfm at 12V DC. It starts and runs fine at DC voltages down to 6 V and is rated at 8 - 14 V. I'm thinking of running it at 9 V to lower wear-and-tear and improve quietness. It will run slower, I believe at 9/12 the rated 3500 rpm or ~2625 rpm, moving less air. Should I estimate 9/12 of 5 cfm or 3.75 cfm? Schedule 5, 1-1/2" PVC pipe has an ID of 45 mm (~10% greater than the 40 mm fan). Schedule 40 (more available) is 40.9 mm in diameter. Since the next step will be to place a medicine cabinet below the lights, any pvc pipe air duct will be ~ 48" long.
I know that ducting produces resistance to flow, but don't know how to calculate it. Am I correct in concluding that the placement of the fan is of no relevance? By that I mean that the same fan drawing air through 48" of pipe with a cross-sectional area of 2 sq inches delivers the same volume of air as one blowing it through the same pipe.
How much bigger does the duct need to be than the fan for the improvement in flow to become negligible? Schedule 5 pipe at 1.5" is 20% bigger in cross sectional area. Schedule 40 pipe at 2" is 65% bigger.
Am I being over optimistic in thinking that a change of air once a minute will overcome any overheating problem?
I also have some thermostats that close at 90 °F. I could put one of those at the top of the fixture on a small heat sink and cycle the fan on and off as needed.
I think you should determine what the OEM's installation recommendations are for the light fixture. There will a minimum clearance or free-area guidelines provided as well as ambient temperature specifications.
With out operating specifications, trying to calculate heat transfer parameters seems ambitious.