Single website permanently on a Chromecast powered TV

Yes, it is possible without a computer - but unfortunately you will still need SOMETHING on the other end to cast. You would need an Android phone/tablet running Android 4.4 (KitKat) or higher, and then use the Google Cast app to mirror your entire device screen to Chromecast. (From what I've gathered, this doesn't seem to be possible on an iOS device, at least not without a computer acting as an intermediary - which is what you're trying to avoid in the first place.)

As far as I know, Chromecast does not have a built-in asynchronous browser that would allow you to simply "control" its actions from your mobile device, but actually run as an internal app directly on the Chromecast, which is what happens with the YouTube app, for example. So the only way to get a website on your Chromecast would be to cast an entire screen from a another device.

As for setting up auto-refresh, there's no way to do it inside an Android browser directly, but you can use Tasker to do this - here's how: Auto refresh a webpage every N minutes

Tom

The matter has been reviewed with more answers on this thread

So basically yes you can instruct your Chromecast to display a webpage autonomously using its own built-in web-browser which mean there are a few limitations.

I personally use Dashcast for this purpose, with the following caveats:

• Have to instruct periodically Chromecast to re-display the page whenever the dongle decides to drop it, this usually happen at least once per week. Which meant that for a professional setup this is not a viable option.
• Dashcast sometimes do not prompt for the Chromecast to send the webpage, I have not yet understood what is going wrong with it or my Chrome browser on the smartphone. Usually a reboot of the phone will do, but it's a bit annoying and again not practical for a professional display setting.