I want to show my post for limited time, how is it possible?

You should use cron job. Yes WordPress has a function wp_schedule_event (). This function will perform certain operations based on the time difference you add it.

Say for example, if you schedule it daily this will works everyday and perform the operarions on daily basis.
you can hook a function with wp_schedule_event. Just get the published posts list and from the posts check the date of publish and current time. If it marches today leave it. Otherwise you can edit the post and change the status as draft or you can even delete it.
Here I didn’t give you code samples. If you require there are many question available about cron job and post status change. Just Go through it.