Can I connect my iPad Air to my hard disk...so that I can send or receive files from my hard disk.

No. You can only use an SD card or USB flash drive (using the camera connection kit) to import photos/videos to the iPad. You can't export any type of file to an SD card or USB drive.

There are some wireless external hard drives that can be used with the iPad.

Best iPad External Hard Drive Storage Options

http://www.unlocktips.com/2012/11/best-ipad-mini-external-hard-drive-memory-stor age-options/

iPad Storage Solutions

http://www.ipadstoragesolutions.com/iPadWirelessStorage.php

SanDisk Connect Wireless Media Drive

http://www.sandisk.com/products/wireless/media-drive/

WD My Cloud

http://www.wdc.com/en/products/products.aspx?id=1140

Another option:

Expand your iPad's storage capacity with HyperDrive

http://www.macworld.com/article/1153935/hyperdrive.html

On the road with a camera, an iPad, and a Hyperdrive

http://www.macworld.com/article/1160231/ipadhyperdrive.html

 Cheers, Tom 😉

There's the new Seagate Wireless Plus hard drive for iPad that works well.