Technical data for AA batteries can be found at this link:
http://data.energizer.com/Inputting the specifications of Battery, AA, and Alkaline then clicking on E91 brings up the Product Datasheet for a common alkaline AA cell. The Constant Current Performance graph on page 2 shows that at 80 mA the service hours are:
0.8 volts, 33 hours
1.0 volts, 28 hours
1.2 volts, 20 hours
If your fan is powered directly off AA cells four cells (nominal voltage 1.5) will provide 6.0 volts to start. With the fan rated to 4.5 volts each cell can discharge to 1.13 volts. So, interpolating between the 20 hours to 1.2 volts and 28 hours to 1.0 volts gives an approximate service life of 25 hours. If the micro-fan current varies as the voltage varies battery life can be more or less than *25 hours*.
Looking at the datasheet for the NH15-2300mAh NiMH cell we find a different graph; the lowest discharge current graph is 230 mA. But comparing the the different discharge curves we see that life vs current is almost inversely linearly proportional for this chemistry. At 230 mA and 1.1 volts the life is 10 hours and at 80 mA hours this works out to be *29 hours*.
Now let's try the EA91 Advanced Lithium cell. The data is again not directly applicable because the Constant Current Performance graph has only one line at that is for 1.0 volts. But looking at the resistive load graphs we see that the life is almost the same for 1.1 volts as for 1.0 volts. So, let's use the first graph and that shows the life at 80 mA is *40 hours*.
How about a D cell? The datasheet for the common E95 shows the life at 80 mA, and interpolated at 1.1 volts, to be *150 hours*, or six times that of the E91 AA cell.
