Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.126.
Aus ibn Aus reports that the Prophet said: “The most virtuous of your days is Jumu’ah. On that day, Adam was created and on that day he died, (on that day) the horn will be blown and the people will be dumbfounded! Increase your prayers upon me as your prayers upon me will be presented to me.” The people said: “O Messenger of Allah, how will our prayers be presented to you when you have passed away?” He said: “Allah has prohibited the earth from eating the bodies of the Prophets.” This is related by the five, except for at-Tirmizhi.
Ibn al-Qayyim says: “It is preferred to pray for (Allah’s blessings on the Prophet during the day and night of Jumu’ah as the Prophet said: ‘Make many prayers upon me during the day of Friday and the night of Friday.’ The Messenger of Allah is the leader of mankind, and Jumu’ah is the best of the days of the week. Prayers upon him during that day are a privilege [he deserves] which belongs to no other. This act also has another wisdom to it and that is that all of the good that has passed onto this [Muslim] ummah, in this life and the hereafter, has passed through him. Allah has gathered the good of this life and the next life for this ummah, and the greatest honour and success will be granted to them on Friday. On that day, they will be granted their houses and palaces in paradise and that is the day they will be given more when they enter paradise. It is a day of celebration for them in this life. It is also a day in which Allah fulfils their needs and answers their prayers and requests in this world. They are aware of all of that and are able to attain it because of the Prophet and it is through him [that they received these teachings]; therefore, in gratitude and appreciation for the great blessings we received through him, we should make many prayers upon him during the day and night of Jumu ‘ah.”