"Dear professor" is a correct and usable part of a sentence in written English.
You can use it in formal correspondence or when addressing someone in the academic community. For example: "Dear professor, I hope you are doing well."
"Dear Professor Dodd, I thought you were dead, but now that I know that you're alive, I'd like to come study with you," Mr. Buffett said he wrote in his letter.
Dear Professor Stone, This is Richard Spencer of Alt-Right fame.
Dear Professor Investor, I have come up with a never-been-done-yet app idea that is really legitimate.
Dear Professor Jones and Dr. Dyson, I've been feeling lonely working in this graveyard dug by systemic injustice and filled by life-robbers.
Dear Professor Investor, Why is it important for me to have my own money invested in my startup before reaching out to investors?
Dear Professor Afshari, During my past 16 years of practice as a refractive surgeon, I have seen more than 3000 cases of keratoconus and ectatic corneal disorders at my center and in the refractive clinic in the Damascus University hospital, and many of those cases were referred to me for a second opinion.
"My dear old professor, Alan Westin, would be shaking his head if he read this article," the mayor said with a laugh, and he was right.
"Oh dear," the Professor said, "another bloody dead turtle boy in the garden.
SAMETZ--Arnold W. The members of the NYU Leonard N. Stern School of Business community mourn the passing of our dear friend and professor emeritus, Arnie Sametz.
"I want to completely better myself, I want to be worthy of you, you must help me to transform, you will be my little professor, dear, and I will blindly listen to you like a master that I adore," she wrote in January 1952.
