How to split a string after every 10 words?

I am looking for a way to split my chunk of string every 10 words

A regex with a non-capturing group is a more concise way of achieving that:

str = str.replaceAll("((?:[^\\s]*\\s){9}[^\\s]*)\\s", "$1\n");

The 9 in the above example is just words-1, so if you want that to split every 20 words for instance, change it to 19.

That means your code could become:

jTextArea14.setText(jTextArea13.getText().replaceAll("((?:[^\\s]*\\s){9}[^\\s]*)\\s", "$1\n"));

To me, that's much more readable. Whether it's more readable in your case of course depends on whether users of your codebase are reasonably proficient in regex.