How to set the core dump file location (and name)?

I am on CentOS 6, trying to enable core dumps for an application I am developing. I have put:

ulimit -H -c unlimited >/dev/null
ulimit -S -c unlimited >/dev/null

in to my bash profile, but a core dump still did not generate (in a new terminal).

I have also changed my /etc/security/limits.conf so that the soft limits is zero for all users.

How do I set the location of the core files to be output? I wanted to specify the location and append the time the dump was generated, as part of the file name?