Peace be upon you.

Is there evidence in Shari`ah that would make it recommended (mustahabb) to recite Surat al-Kahf and Surat ad-Dukhan on Friday?

In the Name of Allah, all praise is due to Allah, and may peace and blessing be upon the Messenger of Allah. To proceed:

Authentic ahadith from the Prophet (saws) have been related concerning the excellence of reciting Surat al-Kahf (#18) on Friday, or the night before. Among them are:

A. On the authority of Abi Sa`id al-Khudri, "Whoever recites Surat al-Kahf on the night before Friday, it will shine for him with light over that which is between him and the Ancient House (the Ka`bah)." Related by ad-Darimi (3407). Shaikh al-Albani declared it authentic in Sahih al-Jami` (6471).

B. "Whoever recites Surat al-Kahf on Friday, it will shine for him with light over that which is between both Fridays [this one and the previous one]."

Related by al-Hâkim (2/399) and al-Baihaqi (3/249). Ibn al-Hajr said in Takhrij al-Adhkar, "[It is] a good (hasan) hadith." He also said, "It is one of the strongest of that which is related concerning the recitation of Surat al-Kahf."

See: Fayd al-Qadir (6/198).

Shaikh al-Albani declared it authentic in Sahih al-Jami` (6470).

C. On the authority of Ibn`Umar (raa), "The Messenger of Allah (saws) said, 'Whoever recites Surat al-Kahf on Friday, light radiates for him from beneath his feet to the firmament of heaven, lighting his way on the Day of Judgment; and he will be forgiven what is between both Fridays.'"

Al-Mundhiri commented, "Abu Bakr ibn Mardawaih related this in his exegesis of the Qur'an with an acceptable chain of narrators.

(At-Targhib wa at-Tarhib, 1/298)

As for the ahadith related concerning the excellence of Surat ad-Dukhan, they are either very weak or fabricated. For example, what was related by at-Tirmidhi on the authority of Abi Hurairah (may Allah be pleased with him), "Whoever recites Ha-Mim ad-Dukhan [an alternate name for the same chapter] at night, seventy thousand angels ask forgiveness for him in the morning." Al-Albani said that this is fabricated, "This type of hadith should not be acted upon even in supererogatory matters [those which exceed obligation], due to the intensity of its weakness or because it is fabricated."