Destroy PHP Session on closing
if you use:
session_set_cookie_params(0);
session_start();
Your session cookie will destroy when the browser is closed... so your session will be good until they close the browser. IE. You login, and you are logged in, you close the browser, re-open it, go to the site again, and you wont be logged in.
You will only be able to detect if the browser window has been closed using javascript at which point you might be able to trigger an Ajax request to perform a logout action.