If you try to use TensorFlow in a website's code on PythonAnywhere, it probably won't work. This is because it tries to create new threads (in a slightly odd way), and then crashes. The crash is so serious that you probably won't even see anything in the error log -- just a message in the server log saying that your worker processes died.
Unfortunately we don't have a good solution for this if you're using TensorFlow directly :-(
However, if you're using Keras with a TensorFlow backend, you can work around the issue -- just switch to using the Theano backend instead. That has been confirmed to work.