Minhag to Place Hoshaanos on top of the Aron Hakodesh

 Nitey Gavriel (Sukkos pg. 379 footnote 15) brings the custom in the name of the Malbushei Yom Tov to Levush 664:4 and Nitzutzei Zohar Parshas Tzav, who explain that it is in order to leave the sparks of judgment behind at the conclusion of the yemei hadin and not take them back home. The custom is also brought in the Bikurey Yaakov (S"K 16). The Nitey Gavriel himself writes that he heard the reason to commemorate the arovos in the Beis Hamikdosh that they would place on the mizbeach. Mishna Berurah writes that it is a good practice to burn one’s Chometz together with the Hoshanos from Sukkos--since one Mitzvah was done with it, a second Mitzvah of Tashbisu should be performed with it as well. The Rema brings a different Minhag--to bake Matzos with the Hoshanos (Shulchan Aruch Orach Chaim 445, Mishna Berurah seif katan 7, Dirshu Note 10).

Mishnah Berurah 445:7

אם יש לו הושענות טוב לשרוף החמץ בהושענות הואיל ואיתעביד בו מצוה חדא ליתעביד בו גם מצות תשביתו:

The Rema writes (664:9):

ונהגו להצניע ההושענות לאפיית מצות, כדי לעשות בה מצוה