Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points

• Published in: Symmetry (Basel) Vol. 11; no. 3; p. 412
• Main Authors: Ali Lund, Liaquat, Omar, Zurni, Khan, Ilyas, Raza, Jawad, Bakouri, Mohsen, Tlili, I.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 20.03.2019
• Subjects: Boundary conditions; Boundary value problems; Computational fluid dynamics; Critical point; Darcy Forchheimer model; dual solution; exponential sheet; Flow stability; Fluid flow; Heat; Incompressible flow; Investigations; Laminar flow; Magnetic fields; Magnetohydrodynamic flow; Magnetohydrodynamics; nanofluid; Nanofluids; Nonlinear differential equations; Permeability; Polymer melts; Porous media; Reynolds number; Runge-Kutta method; Stability analysis; Suction; Two dimensional flow; Velocity; Viscosity
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym11030412

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).