Change your fstab. The usage of the variable device nodes like /dev/sda is discouraged now.
Look at your /dev/disk/by-id/ directory. Mine looks like this:
> ls /dev/disk/by-id/
[...]
scsi-SATA_WDC_WD15EADS-00_WD-XXXX08150815
scsi-SATA_WDC_WD15EADS-00_WD-XXXX08150815-part1
scsi-SATA_WDC_WD15EADS-00_WD-XXXX08150815-part2
scsi-SATA_WDC_WD15EADS-00_WD-XXXX08150815-part5
usb-Generic_STORAGE_DEVICE_123456789289-0:0
usb-Generic_STORAGE_DEVICE_123456789289-0:1
usb-Generic_STORAGE_DEVICE_123456789289-0:2
There you have your disks including serial numbers. I have a SATA hdd and an USB card reader here.
You can use these links in your boot loader and in /etc/fstab unless your distribution is ancient.
There are also /dev/disk/by-uuid/and/dev/disk/by-label`.
Ah, and don't forget the boot loader. If sda is also the first disk 0x80 that the BIOS sees, you might not have one installed on sdb.