Translation:Do you have time this afternoon?
"Are you free this afternoon?" was accepted and seems a bit more natural to me.
You're absolutely correct that the meaning of 你有时间吗 can best be expressed in English as "are you free", but the literal meaning is "do you have time". Also, depending on the context, the latter may be more appropriate.
I can tell you it will not take: "Will you have time this afternoon". I really can't see much difference.
That would be implied if I said "the afternoon," unless there is a specific context to suggest something else.