2002 Jeep Wrangler, had a slight tranmission leak, drained and filled-up with new fluid. Now transmission whines at least twice as loud as before. But at least the leak appears to have stopped. Any ideas?

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Unless you have a flushing machine you will not be able to empty the torque converter.If you have a 3 speed auto you are looking at 9 quarts total.If you have a 4 speed transmission you are looking at 10 half total.Be sure you check the fluid in neutral and not park.

Here is a diagram with the fill plug location.
Fill Plug Location

Transmission generally takes a bit less than two quarts, Use 75/90 gear lube in that (in very cold climates you can add a small amount of automatic trans fluid to keep it flowing on cold starts) Transfer case takes a bit over one quart and takes dextron mercon 3. When filling either, fluid is full when on a level surface it begins to come out of the fill hole while filling. When changing either, always make sure you can open the fill plug before draining so you know you can replace what you removed.

Most have a drain plug on the pan. to do a simple change, just remove the plug and drain it, then re-fill. to do a filter change, you need to remove the pan and the filter inside, remove all the gasket material (or it will leak) and put everything back together. There is no provision for draining the converter so if you want to do a better more complete change, drain from plug, refill, drive a few miles to circulate new fluid, then do a complete change with filter. You won't get it all out but a considerably larger portion of the old fluid will be removed.

check passenger side of transmission - it is a 3/8 ext that will fit the bolt - does not really look like a regular fill hole -

Let it sit for awhile because it takes cold oil a while to leak down to fill everything. Did you get 3.5 quarts of oil out when you drained? Just add as much as you can, wait awhile, check your dipstick, and add more until you can get it all in the fill hole. With a cold engine and cold oil, it takes a little while.

the plug of the transmission of 1992 jeep is under the transmission case .

You should check the transfer case fluid level. There are two plugs that require a 3/8" drive ratchet to remove. If you look closely, you may have to do some cleaning, one should be marked fill and the other should be marked drain. Remove the fill plug and use a small scrap piece of paper if no fluid comes out to dip in the hole. The fluid should be right at the top. If you can't get any fluid on a piece of paper that is about 2" long then you may have damaged the transfer case. If the fluid level is okay and the leak isn't severe(no puddles or drips in the driveway) then you may want to change the fluid, make sure there isn't excessive amounts of metal flakes in the fluid, and your whine may be a bearing, gear, or pump in the transmission.

First check fluid. Make sure it's full and clean and does not smell burned (compare to another good car)
Converter failure is usually most obvious when trans shifts to OD. if shift is late or makes bang noise going in, you likely have a problem. to check lockup, after od engages, lightly touch brake, trans should momentarily shift out of od. Whining is usually due to low fluid. Also check transfer case and both differentials for proper level and leaks.