{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:25:39Z","timestamp":1774355139041,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,20]],"date-time":"2019-03-20T00:00:00Z","timestamp":1553040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, steady two-dimensional laminar incompressible magnetohydrodynamic flow over an exponentially shrinking sheet with the effects of slip conditions and viscous dissipation is examined. An extended Darcy Forchheimer model was considered to observe the porous medium embedded in a non-Newtonian-Casson-type nanofluid. The governing equations were converted into nonlinear ordinary differential equations using an exponential similarity transformation. The resultant equations for the boundary values problem (BVPs) were reduced to initial values problems (IVPs) and then shooting and Fourth Order Runge-Kutta method (RK-4th method) were applied to obtain numerical solutions. The results reveal that multiple solutions occur only for the high suction case. The results of the stability analysis showed that the first (second) solution is physically reliable (unreliable) and stable (unstable).<\/jats:p>","DOI":"10.3390\/sym11030412","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T04:11:56Z","timestamp":1553141516000},"page":"412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":66,"title":["Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5203-5588","authenticated-orcid":false,"given":"Liaquat","family":"Ali Lund","sequence":"first","affiliation":[{"name":"School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Malaysia"},{"name":"KCAET Khairpur Mir\u2019s Sindh Agriculture University, Tandojam Sindh 70060, Pakistan"}]},{"given":"Zurni","family":"Omar","sequence":"additional","affiliation":[{"name":"School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Ilyas","family":"Khan","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam"}]},{"given":"Jawad","family":"Raza","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Institute of Southern Punjab (ISP), Multan 32100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7244-2949","authenticated-orcid":false,"given":"Mohsen","family":"Bakouri","sequence":"additional","affiliation":[{"name":"Department of Medical Equipment Technology, College of Applied Medical Science, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}]},{"given":"I.","family":"Tlili","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia."}]}],"member":"1968","published-online":{"date-parts":[[2019,3,20]]},"reference":[{"key":"ref_1","unstructured":"Nield, D.A., and Bejan, A. 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