i just want to make cookie null in browser close, but it not entering in null condition [on hold]

here is my code,

i need to logout during browser or tab close but not during browser reload so for that i just put a cookie, i believe cookie will get null in window.unload event, but it not happening , actually am unable to findout where is the issue happening and why cookie is not getting null in window unload, really get stucked if anyone knows the soultion,then please please help me

please have a look at my code is this idea works

/**
 * This javascript file checks for the brower/browser tab action.
 * It is based on the file menstioned by Daniel Melo.
 * Reference: http://stackoverflow.com/questions/1921941/close-kill-the-session-when-the-browser-or-tab-is-closed
 */
var validNavigation = false;
 $.cookie("test",1,'');
 var cookiename= $.cookie("test");
function endSession() {
  // Browser or broswer tab is closed
  // Do sth here ...
  $.ajax({
        url: 'ajax/User/user_logout',
        type: "POST",
        async: false,
        data: {},
        success: function (response) {
           // global_date_format = response.js_format;
        }
    });
}
function wireUpEvents() {
  /*
  * For a list of events that triggers onbeforeunload on IE
  * check http://msdn.microsoft.com/en-us/library/ms536907(VS.85).aspx
  */
  window.onunload = function() {
      if (!validNavigation) {
          if(cookiename==null){
         endSession();
     }
     else
     {
         alert("shanyy");
     }
      }
  }
  // Attach the event keypress to exclude the F5 refresh
  $(document).bind('keypress', function(e) {
    if (e.keyCode == 116){
      validNavigation = true;
    }
  });
  // Attach the event click for all links in the page
  $("a").bind("click", function() {
    validNavigation = true;
  });
  // Attach the event submit for all forms in the page
  $("form").bind("submit", function() {
    validNavigation = true;
  });
  // Attach the event click for all inputs in the page
  $("input[type=submit]").bind("click", function() {
    validNavigation = true;
  });
}
// Wire up the events as soon as the DOM tree is ready
$(document).ready(function() {
  wireUpEvents();  
});