In this article, the authors provided the stability analysis for Darcy porous medium saturated by a Ti-alloy nanofluid in the presence of tilted magnetic field, Joule heating, heat generation, and velocity slip effects. The Tiwari-Das model is implemented and the relevant similarity transformations are identified for mathematical modeling of the proposed fluid flow problem. The set of resultant ODEs has been solved using the shooting method in conjunction with the RK-4th order scheme. The existence of dual solutions is observed along with their critical values for the present setup at and after the bifurcation point but for a limited range of certain fixed parameters. Through the eigenvalue approach, it is shown that the first solutions are stable, but not the second solutions. The streamlines are depicted to understand the flow patterns in addition to the identification of flow separation point and flow reversal. The important findings are as follows: (a) the delay of boundary layer separation is pointed out with the enhancing values of volume fraction of Ti-alloy nanoparticles and the inclined magnetic parameter in the presence of suction, (b) the Ti-alloy nanofluids velocity rises but the temperature decays with rising values of the Ti-alloy nanoparticle volume fraction, and (c) the value of smallest eigenvalues is growing with the growing values of magnetic parameter. Finally, this type of research may be extremely beneficial in the fields of aerodynamics (i.e. production of engine components, aircraft turbines, and high-performance automatic parts) and medicine.
ChoiSUEastmanJA. Enhancing thermal conductivity of fluids with nanoparticles. Argonne National Lab., IL (United States), 1995.
2.
BuongiornoJ. Convective transport in nanofluids. J Heat Transfer2006; 128: 240–250.
3.
PetersMKumpfertJWardCH, et al. Titanium alloys for aerospace applications. Adv Eng Mater2003; 5: 419–427.
4.
SinghPPungotraHKalsiNS. On the characteristics of titanium alloys for the aircraft applications. Mater Today: Proc2017; 4: 8971–8982.
5.
DarcyH. Les fontaines publiques de la ville de Dijon. Paris: Victor Dalmont, 1856.
6.
PopIInghamDB. Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media. Kidlington: Elsevier, 2001.
7.
DasSKChoiSUYuWet al. Nanofluids: science and technology. Hoboken, NJ: John Wiley and Sons, 2007.
8.
MinkowyczWJSparrowEMAbrahamJPet al. Nanoparticle heat transfer and fluid flow. Boca Raton, FL: CRC press, 2012.
9.
NieldDBejanA. Convection in porous media. New York, NY: Springer International Publishing, 2017.
10.
KasaeianADaneshazarianRMahianO, et al. Nanofluid flow and heat transfer in porous media: a review of the latest developments. Int J Heat Mass Transf2017; 107: 778–791.
11.
NayakMKShawSMakindeOD. Chemically reacting and radiating nanofluid flow past an exponentially stretching sheet in a porous medium. Indian J Pure Appl Phys2018; 56: 773–786.
12.
ChettetiRRSrivastavA. Aqueous titanium alloy-MWCNTs hybrid nanofluid flow in a non-darcy porous medium. Comput Therm Sci2021; 13: 31–43.
13.
ChettetiRRSrivastavA. Numerical study and error estimation in power-law nanofluid flow over vertical frustum of a cone. Indian J Phys2021; 13: 1–13.
14.
CraneLJ. Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP1970; 21: 645–647.
15.
MerkinJH. On dual solutions occurring in mixed convection in a porous medium. J Eng Math1986; 20: 171–179.
16.
MerrillKBeauchesneMPreviteJ, et al. Final steady flow near a stagnation point on a vertical surface in a porous medium. Int J Heat Mass Transf2006; 49: 4681–4686.
17.
BhattacharyyaK. Steady boundary layer flow and reactive mass transfer past an exponentially stretching surface in an exponentially moving free stream. J Egypt Math Soc2012; 20: 223–228.
18.
BhattacharyyaK. Heat transfer analysis in unsteady boundary layer stagnation-point flow towards a shrinking/stretching sheet. Ain Shams Eng J2013; 4: 259–264.
19.
IshakA. Flow and heat transfer over a shrinking sheet: a stability analysis. Int J Comput Sci Math2014; 8: 902–906.
20.
NajibNBachokNArifinN. Stability of dual solutions in boundary layer flow and heat transfer over an exponentially shrinking cylinder. Indian J Sci Technol2016; 9: 1–6.
21.
BakarNABachokNArifinN, et al. Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect. Results Phys2018; 9: 1335–1344.
22.
FangTYaoSZhangJ, et al. Viscous flow over a shrinking sheet with a second order slip flow model. Commun Nonlinear Sci Numer Simul2010; 15: 1831–1842.
23.
SinghGChamkhaAJ. Dual solutions for second-order slip flow and heat transfer on a vertical permeable shrinking sheet. Ain Shams Eng J2013; 4: 911–917.
24.
UddinMJKhanWAIsmailAM. Melting and second order slip effect on convective flow of nanofluid past a radiating stretching/shrinking sheet. Propuls Power Res2018; 7: 60–71.
25.
MahianOKolsiLAmaniM, et al. Recent advances in modeling and simulation of nanofluid flows-part I: fundamentals and theory. Phys Rep2019; 790: 1–48.
26.
RossowVJ. On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field. (No. NACA-TN-3971), 1957.
27.
VajraveluKRollinsD. Heat transfer in an electrically conducting fluid over a stretching surface. Int J Non Linear Mech1992; 27: 265–277.
28.
SharmaRIshakAPopI. Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. Comput fluids2014; 102: 94–98.
29.
MortujaSGSahooB. Dual solutions of a magnetohydrodynamic stagnation point flow of a non-Newtonian fluid over a shrinking sheet and a linear temporal stability analysis. Proc Inst Mech Eng E: J Process Mech Eng2021; 235: 527–535.
30.
AnuarNSBachokNArifinNM, et al. MHD flow past a nonlinear stretching/shrinking sheet in carbon nanotubes: stability analysis. Chin J Phys2020; 65: 436–446.
31.
WainiIIshakAPopI. Hybrid nanofluid flow induced by an exponentially shrinking sheet. Chin J Phys2020; 68: 468–482.
32.
SrinivasacharyaDJagadeeshwarP. Effect of Joule heating on the flow over an exponentially stretching sheet with convective thermal condition. Math Sci.s2019; 13: 201–211.
33.
LundLAOmarZKhanI, et al. Magnetohydrodynamic (MHD) flow of micropolar fluid with effects of viscous dissipation and joule heating over an exponential shrinking sheet: triple solutions and stability analysis. Symmetry2020; 12: 142.
34.
DuttaSBhattacharyyaSPopI. Nonhomogeneous model for conjugate mixed convection of nanofluid and entropy generation in an enclosure in presence of inclined magnetic field with Joule heating. Int J Numer Methods Heat Fluid Flow2020; 31: 418–441.
35.
ReddyJRSugunammaVSandeepN. Simultaneous impacts of joule heating and variable heat source/sink on MHD 3D flow of Carreau-nanoliquids with temperature dependent viscosity. Nonlinear Eng2019; 8: 356–367.
36.
JafarABShafieSUllahI. MHD radiative nanofluid flow induced by a nonlinear stretching sheet in a porous medium. Heliyon2020; 6: e04201.
37.
MemonAAMemonMABhattiK, et al. Analysis of power law fluids and the heat distribution on a facing surface of a circular cylinder embedded in rectangular channel fixed with screen: a finite element’s analysis. IEEE Access2021; 9: 74719–28.
38.
GanieAHMemonAAMemonMA, et al. Numerical analysis of laminar flow and heat transfer through a rectangular channel containing perforated plate at different angles. Energy Reports2022; 8: 539–50.
39.
BachokNIshakAPopI. Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid. Int J Heat Mass Transf2012; 55: 8122–8.
40.
IsmailNSAriffinNMNazarR, et al. Stability analysis of stagnation-point flow and heat transfer over an exponentially shrinking sheet with heat generation. Malaysian J Math Sci2019; 13: 107–122.
41.
YanLDeroSKhanI, et al. Dual solutions and stability analysis of magnetized hybrid nanofluid with joule heating and multiple slip conditions. Processes2020; 8: 332.
42.
BrinkmanHC. The viscosity of concentrated suspensions and solutions. J Chem Phys1952; 20: 571–571.
43.
RajuCSSandeepNSugunammaV. Unsteady magneto-nanofluid flow caused by a rotating cone with temperature dependent viscosity: a surgical implant application. J Mol Liq2016; 222: 1183–1191.
44.
HarrisSDInghamDBPopI. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp Porous Media2019; 77: 267–285.
45.
SubhashiniSVSumathiRMomoniatE. Dual solutions of a mixed convection flow near the stagnation point region over an exponentially stretching/shrinking sheet in nanofluids. Meccanica2014; 49: 2467–2478.
46.
KhanZHQasimMHaqRU, et al. Closed form dual nature solutions of fluid flow and heat transfer over a stretching/shrinking sheet in a porous medium. Chin J Phys2017; 55: 1284–93.
