update-grub for /dev/sdx

I have two Hard-Drives (/dev/sda and /dev/sdb).

When I do update-grub, it would consider either /dev/sda and /dev/sdb.

Is there any way to do update-grub just for /dev/sda ?

UPDATE

I've tried :

sudo update-grub /dev/sda

Output : (Considered sdb)

Generating grub configuration file ...
Found linux image: /boot/vmlinuz-3.13.0-30-generic
Found initrd image: /boot/initrd.img-3.13.0-30-generic
Found linux image: /boot/vmlinuz-3.13.0-29-generic
Found initrd image: /boot/initrd.img-3.13.0-29-generic
Found linux image: /boot/vmlinuz-3.13.0-24-generic
Found initrd image: /boot/initrd.img-3.13.0-24-generic
Found memtest86+ image: /boot/memtest86+.elf
Found memtest86+ image: /boot/memtest86+.bin
Found Windows 7 (loader) on /dev/sda1
Found Arch on /dev/sdb1 # << Founded Arch on sdb !!!!
done