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

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).

[1]  U. Yilmazer,et al.  Slip velocity and slip layer thickness in flow of concentrated suspensions , 1998 .

[2]  Rahmat Ellahi,et al.  Simultaneous effects of MHD and partial slip on peristaltic flow of Jeffery fluid in a rectangular duct , 2015 .

[3]  C. Wang,et al.  Viscous flow due to a shrinking sheet , 2006 .

[4]  C. L. Roux,et al.  Existence and Uniqueness of the Flow of Second‐Grade Fluids with Slip Boundary Conditions , 1999 .

[5]  Ahmed Alsaedi,et al.  A revised model for Darcy-Forchheimer flow of Maxwell nanofluid subject to convective boundary condition , 2017 .

[6]  Paul A. Janmey,et al.  Control of cell morphology and differentiation by substrates with independently tunable elasticity and viscous dissipation , 2018, Nature Communications.

[7]  Arshad Riaz,et al.  Analytical solutions for MHD flow in a third-grade fluid with variable viscosity , 2010, Math. Comput. Model..

[8]  John H. Merkin,et al.  On dual solutions occurring in mixed convection in a porous medium , 1986 .

[9]  Machireddy Gnaneswara Reddy,et al.  MICROPOLAR FLUID FLOW OVER A NONLINEAR STRETCHING CONVECTIVELY HEATED VERTICAL SURFACE IN THE PRESENCE OF CATTANEO-CHRISTOV HEAT FLUX AND VISCOUS DISSIPATION , 2017 .

[10]  Muhammad Sajid,et al.  Dual Solutions in Hydromagnetic Viscous Fluid Flow Past a Shrinking Curved Surface , 2018 .

[11]  Rahmat Ellahi,et al.  On boundary layer nano-ferroliquid flow under the influence of low oscillating stretchable rotating disk , 2017 .

[12]  Ioan Pop,et al.  Stability analysis of impinging oblique stagnation-point flow over a permeable shrinking surface in a viscoelastic fluid , 2017 .

[13]  Mohammad Tauviqirrahman,et al.  CFD analysis of partial slip effect on the performance of hydrodynamic lubricated journal bearings , 2018 .

[14]  Ahmed Alsaedi,et al.  Simultaneous effects of melting heat and internal heat generation in stagnation point flow of Jeffrey fluid towards a nonlinear stretching surface with variable thickness , 2018, International Journal of Thermal Sciences.

[15]  Ilyas Khan,et al.  Effects of slip condition and Newtonian heating on MHD flow of Casson fluid over a nonlinearly stretching sheet saturated in a porous medium , 2017 .

[16]  A. Zeeshan,et al.  Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: An application of Stefan blowing , 2019, Journal of Molecular Liquids.

[17]  M. Nakamura,et al.  Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis. , 1988, Journal of biomechanical engineering.

[18]  Mohsen Sheikholeslami,et al.  Rotating frame analysis of radiating and reacting ferro-nanofluid considering Joule heating and viscous dissipation , 2018 .

[19]  Ali Saleh Alshomrani,et al.  Effects of Homogeneous–Heterogeneous Reactions and Convective Condition in Darcy–Forchheimer Flow of Carbon Nanotubes , 2018, Journal of Heat Transfer.

[20]  Hashim,et al.  A review on slip-flow and heat transfer performance of nanofluids from a permeable shrinking surface with thermal radiation: Dual solutions , 2017 .

[21]  Ioan Pop,et al.  Mixed convection boundary-layer stagnation point flow past a vertical stretching/shrinking surface in a nanofluid , 2017 .

[22]  Ioan Pop,et al.  Boundary layer flow and heat transfer past a permeable shrinking surface embedded in a porous medium with a second-order slip: A stability analysis , 2017 .

[23]  Derek B. Ingham,et al.  Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip , 2009 .

[24]  Jawad Raza,et al.  Rheology of the Cu-H2O nanofluid in porous channel with heat transfer: Multiple solutions , 2017 .

[25]  Iskander Tlili,et al.  MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect , 2019, Symmetry.

[26]  Shirley Abelman,et al.  Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation , 2014 .

[27]  Tasawar Hayat,et al.  Entropy generation minimization (EGM) in nonlinear mixed convective flow of nanomaterial with Joule heating and slip condition , 2018 .

[28]  Ahmed Alsaedi,et al.  A modified homogeneous-heterogeneous reactions for MHD stagnation flow with viscous dissipation and Joule heating , 2017 .

[29]  Jawad Raza,et al.  Rheology of micropolar fluid in a channel with changing walls: Investigation of multiple solutions , 2016 .

[30]  Kai-Long Hsiao,et al.  Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects , 2017 .

[31]  Ilyas Khan,et al.  Heat and mass transfer phenomena in the flow of Casson fluid over an infinite oscillating plate in the presence of first-order chemical reaction and slip effect , 2016, Neural Computing and Applications.

[32]  Jawad Raza,et al.  A Note on Some Solutions of Copper-Water (Cu-Water) Nanofluids in a Channel with Slowly Expanding or Contracting Walls with Heat Transfer , 2016 .

[33]  L. Crane.  Flow past a stretching plate , 1970 .

[34]  M. J. Uddin,et al.  Melting and second order slip effect on convective flow of nanofluid past a radiating stretching/shrinking sheet , 2018 .

[35]  I. Pop,et al.  Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno’s model , 2014 .

[36]  Ioan Pop,et al.  Boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective boundary condition using Buongiorno’s model , 2015 .

[37]  Mohammad Mehdi Rashidi,et al.  Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface , 2016, Entropy.

[38]  Ioan Pop,et al.  FORCED CONVECTION BOUNDARY LAYER STAGNATION-POINT FLOW IN DARCY-FORCHHEIMER POROUS MEDIUM PAST A SHRINKING SHEET , 2016 .

[39]  Brian Straughan,et al.  Convection in Porous Media , 2008 .

[40]  Ioan Pop,et al.  Three-dimensional flow of a nanofluid over a permeable stretching/shrinking surface with velocity slip: A revised model , 2018 .

[41]  Prashanta Kumar Mandal,et al.  Hydromagnetic rotating flow of Casson fluid in Darcy-Forchheimer porous medium , 2018 .

[42]  Tasawar Hayat,et al.  Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux , 2016 .

[43]  Tasawar Hayat,et al.  Numerical study for Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions , 2017 .

[44]  W. C. Krumbein,et al.  The Flow of Homogeneous Fluids through Porous Media , 1938 .