Rizwan, Just so I am clear on this, Under Workflow history, you are seeing that the workflow work item is getting assigned to the designated user, but the notification is not getting sent to them?
The first thing you should check is under the Workflow history, check if the Work item is getting assigned to the designated User. If it is not, it is most likely that either your workflow windows batch service is not in running state, or the "Workflow message processing" batch job is not in Waiting or Executing state.
If you see the work item getting assigned and the item must appear under the "Work items assigned to me" page. If the approval user requires the notifications to be sent via email , then that requires additional configuration of the email templates and also the User options must be setup to enable email notifications.
Please review and mention clearly where your issue is.
