Is it acceptable to e-mail a professor at another university to ask for a meeting to discuss common research interests?
The answer is simple: yes, it is acceptable and common. Don't worry about your rank or about the status of your school. If your email is polite, friendly, is not too long but still includes enough relevant information about you to make it clear to the professors that you and they have shared interests, I estimate that the chances of success (meaning they will agree to meet) are very high — basically the only reasons why this may not work are if the professor is out of town on the day you are proposing to visit, is overwhelmingly busy with other commitments, or is an unpleasant and unfriendly person you probably wouldn't want to meet anyway. Good luck!