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I use nearly the exact setup at home. 2013 13" MBA i7/8gb/512 with a 2010 27" ACD with Apple bluetooth keyboard and trackpad and USB 3 hub. ABSOLUTELY LOVE IT!
Wouldn't trade it for a brand new iMac.

Thank you for your response. What is your habit while using the setup? Do you always use plugged charger or sometimes unplug charging? I just care about the MBA's battery?
 
Thank you for your response. What is your habit while using the setup? Do you always use plugged charger or sometimes unplug charging? I just care about the MBA's battery?

Stop worrying about the battery.

It's better for the battery to have the laptop plugged in.

If you unplug the laptop, then it has to use the battery for power, and that wears the battery out.
 
Thank you for your response. What is your habit while using the setup? Do you always use plugged charger or sometimes unplug charging? I just care about the MBA's battery?

When I'm connected to the ACD I usually keep the ACD's charger plugged into the MBA. Once a month I unplug and let it run down to 25%. Never had a problem with the battery cycles.
 
My orders have just arrived. I really liked the TBD. I wish I had this setup for a long time ago. Thank you for your valuable advises.

This is my setup:

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I have got a translation project. I used my MacBook Air for a while with Thunderbolt Display. Then I noticed that I was nout using my MacBook Air, not even Thunderbolt Display. Because I have another computer at my school as well.
Then I sold my MacBook Air and Thunderbolt Display, too. I'm thinking to go with this "They work together beautifully." setup.

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