What about add a "unanswered questions" tab to the user page? So I can see my questions that are not answered easily.
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By your question, I assume you are looking for your own questions that need answering.
You can use the search page to find your questions without answers:
To get your questions where you have not accepted an answer:
Who goes to someones profile specifically to answer one of their questions? Usually the "Newest" tab takes me to my unanswered questions. I don't think adding a new sorting category will add much value, if anything we need to get rid of "Most viewed".