Well, I have a pressure plenum, so all the high pressure is in there. When it exits into the cowl, you really want a pressure drop so the air gets sucked out.
Nope, no sucking.
There is a pressure drop across the fins, that drop being related to mass flow. You can read the mass in lbs per second directly from a Lycoming cooling chart.
The initial goal is maximum conversion of dynamic pressure to increased static pressure in the chamber above the fins. Pressure coefficients (a measure of that conversion) typically range from 0.6 to 0.85 (see NASA CR3405 or similar). Let's assume 0.75 for your James cowl (which may be a generous assumption). Standard day max dynamic pressure at 8500 altitude and 160 TAS will ballpark around 12.9 inches H2O. From the O-320 cooling chart, at 8500 an approximate 7" drop across the fins would result in 2 lbs per second mass flow, more than enough to keep CHT happy given winter OAT at altitude (say, 40~50F in SoCal?).
12.9 inches x .75 = 9.675"
9.675" - 7" = 2.675"
That 2.675" is positive pressure, the sort that would blow open a wimpy oil door. The atmosphere immediately outside your cowl exit is (usually) at freestream static pressure, so the 2.675" difference provides the force necessary to generate velocity through the exit opening.
Here's a key point. A cowl with a better pressure coefficient would have a higher static pressure in the upper cowl volume. For example, 0.85 would mean 10.965" in the upper cowl under the same flight conditions. The exit could be throttled so as to have the same 7" drop across the fins, thus the same 2 lbs per second mass flow and the same CHT. However, the lower cowl pressure would 3.965", resulting in higher exit velocity. Cooling drag = mass x loss of velocity, so the same mass and less velocity loss equals the same cooling with less drag.
... and what I need to do, is to seal the oil door and make sure the latch works properly.
Yes. From the beginning, my cowl was set up with an eye toward increasing pressure, so the oil door has 10 additional plies of 9 oz glass on the inner surface. Too bad I didn't have any honeycomb handy at the time, as it still bulges a little when cruising at 185 knots with the cowl exit pulled down to about 30 sq inches. That air leak is another drag source.