The unsteady forced bioconvection boundary layer flow of a viscous incompressible micropolar nanofluid containing microorganisms over a stretching/shrinking sheet is studied numerically. A mathematical model, with the aid of appropriate transformations, is presented. The transformed non-linear ordinary differential equations are solved numerically by the Runge–Kutta–Fehlberg fourth- to fifth-order numerical method. The effect of the governing parameters on the dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction and microorganism as well as the local skin friction coefficient, the heat transfer rate and microorganisms transfer rate is thoroughly examined. The findings show that the value of skin friction and Nusselt number are decreased and microorganism number is increased as velocity slip, thermal slip and microorganism slip parameter are increased, respectively. Results from this investigation were compared with previous investigations demonstrating very good correlation. The present results are relevant to improving the performance of microbial fuel cells deploying nanofluids.
DasSKChoiSUSWenhuaY. Nanofluids: science and technology. Hoboken, NJ: Wiley-Interscience, 2007.
2.
NieldDAKuznetsovAV. The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Tran2009; 52: 5792–5795.
3.
NieldDAKuznetsovAV. The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Tran2011; 54: 374–378.
4.
BuongiornoJ. Convective transport in nanofluids. J Heat Trans: T ASME2006; 128: 240–250.
5.
WangXQMujumdarAS. A review on nanofluids—part I: theoretical and numerical investigations. Braz J Chem Eng2008; 25(4): 613–630.
6.
KakaçSPramuanjaroenkijA. Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Tran2009; 52(13–14): 3187–3196.
7.
KoleMDeyT. Nanofluid based on car engine coolant. J Phys D Appl Phys2010; 43: 315501–315510.
8.
YuWXieH. A review on nanofluids: preparation, stability mechanisms, and applications. J Nanomater2012; 2012: 1–17.
9.
MahianOKianifarAKalogirouSA. A review of the applications of nanofluids in solar energy. Int J Heat Mass Tran2013; 57(2): 582–594.
10.
MahdiRMohammedHAMunisamyKM. Review of convection heat transfer and fluid flow in porous media with nanofluid. Renew Sust Energ Rev2015; 41: 715–734.
11.
RohniAMAhmadSIsmailAI. Flow and heat transfer over an unsteady shrinking sheet with suction in a nanofluid using Buongiorno’s model. Int Commun Heat Mass2013; 43: 75–80.
12.
ZaimiKIshakAPopI. Unsteady flow due to a contracting cylinder in a nanofluid using Buongiorno’s model. Int J Heat Mass Tran2014; 68: 509–513.
13.
AhmadiARZahmatkeshAHatamiM. A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate. Powder Technol2014; 258: 125–133.
14.
RoşcaNCPopI. Unsteady boundary layer flow of a nanofluid past a moving surface in an external uniform free stream using Buongiorno’s model. Comput Fluids2014; 95: 49–55.
15.
NadeemSSadafH. Theoretical analysis of Cu-blood nanofluid for metachronal wave of cilia motion in a curved channel. IEEE T Nanobiosci2015; 14(4): 447–454.
16.
NadeemSSaleemS. Analytical study of third grade fluid over a rotating vertical cone in the presence of nanoparticles. Int J Heat Mass Tran2015; 85: 1041–1048.
17.
NadeemSMehmoodRMotsaSS. Numerical investigation on MHD oblique flow of Walter’s B type nano fluid over a convective surface. Int J Therm Sci2015; 92: 162–172.
18.
RanaPBhargavaRBégOA. Finite element simulation of unsteady magneto-hydrodynamic transport phenomena on a stretching sheet in a rotating nanofluid. Proc IMechE, Part N: J Nanoengineering and Nanosystems2013; 227(2): 77–99.
19.
SheikholeslamiMGorji-BandpyMGanjiDD. Magnetohydrodynamic free convection of Al2O3–water nanofluid considering Thermophoresis and Brownian motion effects. Comput Fluids2014; 94: 147–160.
20.
Abdul HakeemAKVishnu GaneshNGangaB. Magnetic field effect on second order slip flow of nanofluid over a stretching/shrinking sheet with thermal radiation effect. J Magn Magn Mater2015; 381: 243–257.
21.
BachokNIshakAPopI. Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid. Int J Heat Mass Tran2012; 55(25–26): 8122–8128.
22.
MakindeODKhanWAKhanZH. Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet. Int J Heat Mass Tran2013; 62: 526–533.
23.
NandySKMahapatraTR. Effects of slip and heat generation/absorption on MHD stagnation flow of nanofluid past a stretching/shrinking surface with convective boundary conditions. Int J Heat Mass Tran2013; 64: 1091–1100.
24.
RahmanMMRoşcaAVPopI. Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno’s model. Int J Heat Mass Tran2014; 77: 1133–1143.
25.
BachokNIshakAPopI. Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet. Int J Heat Mass Tran2012; 55(7–8): 2102–2109.
26.
RosaliHIshakAPopI. Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction. Int Commun Heat Mass Tran2012; 39(6): 826–829.
27.
ZhengLNiuJZhangX. Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet. Int J Heat Mass Tran2012; 55(25–26): 7577–7586.
28.
EringenAC. Theory of micropolar fluids. West Lafayette, IN: School of Aeronautics and Astronautics, Purdue University, 1965.
29.
El-azizMA. Mixed convection flow of a micropolar fluid from an unsteady stretching surface with viscous dissipation. J Egypt Math Soc2013; 21(3): 385–394.
30.
LukaszewiczG. Micropolar fluids: theory and applications. Basel: Birkhäuser, 1999.
31.
HossainMAChowdhuryMK. Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity. Acta Mech1998; 131: 139–151.
32.
KhedrMMChamkhaAJBayomiM. MHD flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption. Nonlinear Anal: Model Control2009; 14(1): 27–40.
33.
NoorNFMHaqRUNadeemS. Mixed convection stagnation flow of a micropolar nanofluid along a vertically stretching surface with slip effects. Meccanica2015; 50: 2007–2022.
34.
RehmanANadeemS. Mixed convection heat transfer in micropolar nanofluid over a vertical slender cylinder. Chinese Phys Lett2012; 29(12): 124701.
35.
NadeemSRehmanAVajraveluK. Axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder. Math Probl Eng2012; 2012: 378259 (1–18 pp.).
36.
BourantasGCLoukopoulosVC. Modeling the natural convective flow of micropolar nanofluids. Int J Heat Mass Tran2014; 68: 35–41.
37.
RoşcaNCPopI. Boundary layer flow past a permeable shrinking sheet in a micropolar fluid with a second order slip flow model. Eur J Mech B: Fluid2014; 48: 115–122.
38.
RizwanUNadeemSAkhbarNS. Buoyancy and radiation effect on stagnation point flow of micropolar nanofluid along a vertically. IEEE T Nanotechnol2015; 14(1): 42–50.
39.
KuznetsovAV. The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms. Eur J Mech B: Fluid2006; 25: 223–233.
40.
EringenA. Microcontinuum field theories. II: fluent media. New York: Springer, 2001.
41.
AzizAKhanWAPopI. Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. Int J Therm Sci2012; 56: 48–57.
42.
KarniadakisGBeskokAAluruN. Microflows and nanoflows: fundamentals and simulation, vol. 29. New York: Springer Science & Business Media, 2006.
43.
KuznetsovAVNieldDA. Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci2010; 49(2): 243–247.
44.
KhanWAUddinMJIsmailAM. Effect of multiple slips and dissipation on boundary layer flow of nanofluid flow over a porous flat plate in porous media. J Porous Media2015; 18(1): 1–14.
45.
SoneY. Kinetic theory and fluid dynamics. New York: Springer Science & Business Media, 2002.
46.
MoGRosenbergerF. Molecular-dynamics simulation of flow in a two-dimensional channel with atomically rough walls. Phys Rev A1990; 42(8): 4688.
47.
IshakANazarRArifinNM. Mixed convection of the stagnation-point flow towards a stretching vertical permeable sheet. Romania2007; 1991: 217–226.
48.
XuRManiasESnyderAJ. New biomedical poly-layered silicate nanocomposites. Macromolecules2001; 34: 337–339.
