How to perform Auto Sign out on close of Browser in asp.net

In my main layout (master page) of my ASP.NET MVC site I am ussing the next java script:

<script>
function onWindowClosing() { 
            if (window.event.clientX < 0 || window.event.clientY < 0)
            {
                $.ajax({
                    type: "POST",
                    url: "/Account/OnWindowClosing"
                });
            }
       };

       function onKeydown(evt){ 
            if (evt != undefined && evt.altKey && evt.keyCode==115) //Alt + F4 
            { 
                $.ajax({
                    type: "POST",
                    url: "/Account/OnWindowClosing"
                });
            } 
       };

       window.onbeforeunload = onWindowClosing; 
       window.document.onkeydown = onKeydown; 
 
    </script>

You should do something similar in your master page.
Then in your source code ("OnWindowClosing" action from "Account" controller in my example) you could do what you want.