Each time when I try to browse SharePoint site using external URL it ask for windows credential.
When using default (internal) URL, credentials are not asked.
How to make SharePoint not ask credentials when accessing external URL?
You probably have your default(internal) URL set as Trusted site (or Local Intranet) in IE settings, making IE to automatically login using your Windows credentials. Add external URL to Trusted sites or Local Intranet and you should no longer get login prompt.