Journal Pre-proof Modeling of hybrid nanoﬂuid behavior within a permeable media involving buoyancy effect Qingang Xiong, I. Tlili, Jagar A. Ali, Samir Mustafa Hamad, Ahmad Shafee, Trung Nguyen-Thoi, Hassen Hamouda PII: S0378-4371(19)32186-7 DOI: https://doi.org/10.1016/j.physa.2019.123940 Reference: PHYSA 123940 To appear in: Physica A Received date : 21 March 2019 Revised date : 19 June 2019 Please cite this article as: Q. Xiong, I. Tlili, J.A. Ali et al., Modeling of hybrid nanoﬂuid behavior within a permeable media involving buoyancy effect, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123940. This is a PDF ﬁle of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the deﬁnitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its ﬁnal form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.