In this article, the steady two-dimensional stagnation point flow of a viscous incompressible electrically conducting bio-nanofluid over a stretching/shrinking wedge in the presence of passively control boundary condition, Stefan blowing and multiple slips is numerically investigated. Magnetic induction is also taken into account. The governing conservation equations are rendered into a system of ordinary differential equations via appropriate similarity transformations. The reduced system is solved using a fast, convergent Chebyshev collocation method. The influence of selected parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction and density of motile microorganisms as well as on the local skin friction, local Nusselt number, local Sherwood number and density of motile microorganism numbers is discussed and presented graphically. Validation with previously published results is performed and an excellent agreement is found. The study is relevant to electromagnetic manufacturing processes involving bio-nanofluids.
RosenheadL.Laminar boundary layers: an account of the development, structure, and stability of laminar boundary layers in incompressible fluids, together with a description of the associated experimental techniques. New York: Dover Publications, 1988.
2.
AtalıkKSönmezlerÜ.Symmetry groups and similarity analysis for boundary layer control over a wedge using electric forces. Int J Nonlin Mech2009; 44(8): 883–890.
3.
Abdul GaffarSPrasadVRVijayaBet al. Mixed convection flow of magnetic viscoelastic polymer from a nonisothermal wedge with biot number effects. Int J Eng Math2015; 2015: 287623.
4.
RashadAM.Impact of thermal radiation on MHD slip flow of a ferrofluid over a non-isothermal wedge. J Magn Magn Mater2017; 422: 25–31.
5.
OlagunjuDO.The Falkner–Skan flow of a viscoelastic fluid. Int J Nonlin Mech2006; 41(6): 825–829.
6.
RashidiMMRastegariMTAsadiMet al. A study of non-Newtonian flow and heat transfer over a non-isothermal wedge using the homotopy analysis method. Chem Eng Commun2012; 199(2): 231–256.
7.
MansuttiDPontrelliGRajagopalKR.Non-similar flow of a non-Newtonian fluid past a wedge. Int J Eng Sci1993; 31(4): 637–647.
8.
YihKA.MHD forced convection flow adjacent to a non-isothermal wedge. Int Commun Heat Mass1999; 26(6): 819–827.
9.
YacobNAIshakAPopI.Falkner–Skan problem for a static or moving wedge in nanofluids. Int J Therm Sci2011; 50(2): 133–139.
10.
AhmadKHanoufZIshakA.MHD Casson nanofluid flow past a wedge with Newtonian heating. Eur Phys J Plus2017; 132(2): 87.
11.
RamzanMBilalMChungJDet al. Impact of generalized Fourier’s and Fick’s laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions. Phys Fluids2017; 29(9): 093102.
12.
RamzanMBilalMChungJD.Effects of thermal and solutal stratification on Jeffrey magneto-nanofluid along an inclined stretching cylinder with thermal radiation and heat generation/absorption. Int J Mech Sci2017; 131: 317–324.
13.
LuDCRamzanMBilalMet al. Upshot of chemical species and nonlinear thermal radiation on Oldroyd-B nanofluid flow past a bi-directional stretched surface with heat generation/absorption in a porous media. Commun Theor Phys2018; 70(1): 071.
14.
LuDCRamzanMBilalMet al. A numerical investigation of 3D MHD rotating flow with binary chemical reaction, activation energy and non-Fourier heat flux. Commun Theor Phys2018; 70(1): 089.
15.
SajidTSagheerMHussainSet al. Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy. AIP Adv2018; 8(3): 035102.
16.
BilalMSagheerMHussainS.On MHD 3D upper convected Maxwell fluid flow with thermophoretic effect using nonlinear radiative heat flux. Can J Phys2017; 96(1): 1–10.
17.
SagheerMBilalMHussainSet al. Thermally radiative rotating magneto-nanofluid flow over an exponential sheet with heat generation and viscous dissipation: a comparative study. Commun Theor Phys2018; 69(3): 317.
18.
RanaPUddinMJGuptaYet al. Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions. J Braz Soc Mech Sci2017; 39(9): 3363–3374.
19.
UddinMJKabirMNAlginahiYM.Lie group analysis and numerical solution of magnetohydrodynamic free convective slip flow of micropolar fluid over a moving plate with heat transfer. Comput Math Appl2015; 70(5): 846–856.
20.
UddinMJKabirMNAlginahiY.Computational investigation of hydromagnetic thermo-solutal nanofluid slip flow in a Darcian porous medium with zero mass flux boundary condition using stretching group transformations. J Porous Media2015; 18(12): 1187–1200.
21.
FarooqUZhaoYLHayatTet al. Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner–Skan flow of nano-fluid. Comput Fluids2015; 111: 69–75.
22.
RashidiMMAbelmanSMehrNF.Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int J Heat Mass Tran2013; 62: 515–525.
23.
SheikholeslamiMGanjiDDRashidiMM.Magnetic field effect on unsteady nanofluid flow and heat transfer using Buongiorno model. J Magn Magn Mater2016; 416: 164–173.
24.
SheikholeslamiMRashidiMMHayatTet al. Free convection of magnetic nanofluid considering MFD viscosity effect. J Mol Liq2016; 218: 393–399.
25.
SheikholeslamiMVajraveluKRashidiMM.Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field. Int J Heat Mass Tran2016; 92: 339–348.
26.
AliFMNazarRArifinNMet al. MHD mixed convection boundary layer flow toward a stagnation point on a vertical surface with induced magnetic field. J Heat Trans2011; 133(2): 022502.
27.
Morton-JonesGJ.Polymer processing. New York: Springer, 1989.
28.
SuXZhengLZhangXet al. MHD mixed convective heat transfer over a permeable stretching wedge with thermal radiation and ohmic heating. Chem Eng Sci2012; 78: 1–8.
29.
RashidiMMBégOAMehrNFet al. Second law analysis of hydromagnetic flow from a stretching rotating disk: DTM-Pade simulation of novel nuclear MHD propulsion systems. Front Aerospace Eng2013; 2(1): 29–39.
30.
UllahIShafieSMakindeODet al. Unsteady MHD Falkner-Skan flow of Casson nanofluid with generative/destructive chemical reaction. Chem Eng Sci2017; 172: 694–706.
31.
DogonchiASGanjiDD.Investigation of MHD nanofluid flow and heat transfer in a stretching/shrinking convergent/divergent channel considering thermal radiation. J Mol Liq2016; 220: 592–603.
32.
MahapatraTRGuptaAS.Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Tran2002; 38(6): 517–521.
33.
GuptaDKumarLBegOAet al. Finite element simulation of nonlinear magneto-micropolar stagnation point flow from a porous stretching sheet with prescribed skin friction. Comput Therm Sci2015; 7(1): 1–14.
34.
KhanMIKiyaniMZMalikMYet al. Numerical investigation of magnetohydrodynamic stagnation point flow with variable properties. Alex Eng J2016; 55(3): 2367–2373.
35.
KhanZHKhanWAQasimMet al. MHD stagnation point ferrofluid flow and heat transfer toward a stretching sheet. IEEE T Nanotech2014; 13(1): 35–40.
36.
BégOAPrasadVRVasuB.Numerical study of mixed bioconvection in porous media saturated with nanofluid containing oxytactic microorganisms. J Mech Med Biol2013; 13(4): 1350067.
37.
GireeshaBJMahantheshBShivakumaraISet al. Melting heat transfer in boundary layer stagnation-point flow of nanofluid toward a stretching sheet with induced magnetic field. Eng Sci Tech2016; 19(1): 313–321.
DasKDuariPRKunduPK.Nanofluid bioconvection in presence of gyrotactic microorganisms and chemical reaction in a porous medium. J Mech Sci Technol2015; 29(11): 4841–4849.
40.
ShawSKameswaranPKNarayanaMet al. Bioconvection in a non-Darcy porous medium saturated with a nanofluid and oxytactic micro-organisms. Int J Biomath2014; 7(1): 1450005.
41.
UddinMJKabirMNBégOA.Computational investigation of Stefan blowing and multiple-slip effects on buoyancy-driven bioconvection nanofluid flow with microorganisms. Int J Heat Mass Tran2016; 95: 116–130.
42.
BasirMFMUddinMJIsmailAIMet al. Nanofluid slip flow over a stretching cylinder with Schmidt and Péclet number effects. AIP Adv2016; 6(5): 055316.
43.
KuznetsovAV.Nanofluid bioconvection: interaction of microorganisms oxytactic upswimming, nanoparticle distribution, and heating/cooling from below. Theor Comp Fluid Dyn2012; 26(1): 291–310.
44.
KuznetsovAVNieldDA.Natural convective boundary-layer flow of a nanofluid past a vertical plate: a revised model. Int J Therm Sci2014; 77: 126–129.
45.
SuttonGWShermanA.Engineering magnetohydrodynamics. New York: McGraw-Hill, 1965.
46.
DehghanMMahmoudiYValipourMSet al. Combined conduction–convection–radiation heat transfer of slip flow inside a micro-channel filled with a porous material. Transport Porous Med2015; 108(2): 413–436.
UddinMJAlginahiYBégOAet al. Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects. Comput Math Appl2016; 72(10): 2562–2581.
49.
JafarKNazarRIshakAet al. MHD boundary layer flow due to a moving wedge in a parallel stream with the induced magnetic field. Bound Value Probl2013; 2013(1): 20.
50.
KuoBL.Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method. Int J Heat Mass Tran2005; 48(23): 5036–5046.
