Magneto-Hydrodynamics (MHD) Bioconvection Nanofluid Slip Flow over a Stretching Sheet with Microorganism Concentration and Bioconvection Péclet Number Effects
American Journal of Mechanical and Industrial Engineering
Volume 4, Issue 6, November 2019, Pages: 86-95
Received: Jun. 2, 2019;
Accepted: Jul. 12, 2019;
Published: Jan. 4, 2020
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Falana Ayodeji, Department of Mechanical Engineering, University of Ibadan, Ibadan, Nigeria
Alegbeleye Tope, Department of Mechanical Engineering, University of Ibadan, Ibadan, Nigeria
Owoeye Samuel, Department of Mechanical Engineering, Federal University of Agriculture, Abeokuta, Nigeria
This study analyzes the effect of slip parameter, microorganism concentration and bioconvection Péclet number on Magneto-hydrodynamics (MHD) bioconvection nanofluid flow over a stretching sheet. Similarity transformation is employed to convert the governing partial differential equations into coupled non-linear ordinary differential equations with appropriate boundary conditions. These equations are solved numerically using fourth order Runge Kutta-Fehlberg integration method along with a shooting technique. The dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms were obtained together with the local skin friction, reduced Nusselt, Sherwood and motile microorganism density numbers. It was observed that nanoparticle concentration decreases with increase in the nanoparticle concentration slip but increases as magnetic field parameter increases. Also the velocity of the fluid decreases with increase in both velocity slip parameter ξ and magnetic field parameter M. It is also noticed that the temperature of the flow is continuously decreasing as the value of velocity slip parameter ξ, temperature slip parameter β and concentration slip parameter γ increase. Furthermore, as velocity and nanoparticle concentration slip parameters increase, the Nusselt number was observed to increase while the Sherwood number decreases. The skin friction coefficient also decreases as the values of velocity slip parameter increases. Finally we found that local microorganism transfer rate increases with greater values of bioconvection Lewis number Lb, microorganism concentration Ω and bioconvection Péclet number Pe. Comparisons between the previously published works and the present results reveal excellent agreement.
Magneto-Hydrodynamics (MHD) Bioconvection Nanofluid Slip Flow over a Stretching Sheet with Microorganism Concentration and Bioconvection Péclet Number Effects, American Journal of Mechanical and Industrial Engineering.
Vol. 4, No. 6,
2019, pp. 86-95.
Choi, S. U. S., Developments and Applications of Non-Newtonian Flows, ASME Press, NewYork, USA, 1995.
J. Buongiorno, W. Hu, Nanofluid coolants for advanced nuclear power plants. Paper No. 5705, Proceedings ofICAPP ’05, Seoul, May 15-19, 2005.
J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006) 240-250.
W. Duangthongsuk, S. Wongwises, Effect of thermophysical properties models on thepredicting of the convective heat transfer coefficient for low concentration nanofluid, Int. Commun. Heat Mass Transf. 35 (10) (December 2008) 1320-1326.
A. V. Kuznetsov, D. A. Nield, Natural convective boundary-layer flow of a nanofluidpast a vertical plate, Int. J. Therm. Sci. 49 (2) (February 2010) 243-247.
Rana, P. and Bhargava, R. Flow and heat transfer over a nonlinearly stretching sheet: Anumerical study. Comm. Nonl. Sci. and Numer. Simulat. 17, 212-226 (2012).
Makinde OD, Aziz A. Boundary layer flow of a nanofluid past a stretching sheetwithconvective boundary condition. Int J ThermSci 2011; 50: 1326–32.
J. A. V. Kuznetsov, Thermo-bioconvection in a suspension of oxytactic bacteria, Int. Commun. Heat Mass Transfer32 (2005) 991–999.
O. D. Makinde, W. A. Khan, Z. H. Khan, Buoyancy effects on MHD stagnation point flowandheat transfer of a nanofluid past a convectively heated stretching/shrinking sheet, Int. J. Heat Mass Transf. 62 (July 2013) 526-533.
H. Xu and I. Pop, “Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in; he presence of both nanoparticles and gyrotacticmicroorganisms,” Int. J. Heat and Mass Transf75, 610-623 (2014).
W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” Int. J. Heat Mass transf. 53 (11–12), 2477-2483 (2010).
Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006) 240-250.
A. V. Kuznetsov, The onset of nanofluidbioconvection in a suspension containing bothnanoparticles and gyrotactic microorganisms, Int. Commun. Heat Mass Transf. 37 (10) (December 2010) 1421-1425.
W. Ibrahim, B. Shanker, MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slipboundaryconditions. Int J Heat Mass Transfer 2013; 75: 1–10.
Andersson H. Slip flow past a stretching surface. ActaMech 2002; 158: 121–5.
Hayat T, Qasim M, Mesloub S. MHD flow and heat transfer over permeable stretching sheetwith slip conditions. Int J Numer Meth Fluid 2011; 66: 963–75.
Sakiadis BC. Boundary layer behavior on continuous solid surface: II. The boundary layer on a continuous flat surface. J Am Ins ChemEng 1961; 7 (2): 221–5.
R. Nazar, N. Amin, I. Pop, Unsteady boundary layer flow due to a stretching surfacein a rotatingfluid, Mech. Res. Commun. 31 (1) (2004) 121–128.
Abel M. S,. Kumar K. A, Ravikumara R, MHD flow, and heat transfer with effects of buoyancy, viscous and Joules dissipation over a nonlinear vertical stretching porous sheetwith partial slip, Engineering 3 (3) (March 2011) 285-291.
A. Y. Bakier, Thermophoresis effects on heat and mass transfer in MHD flow over averticalstretching surface with radiation, Int. J. Fluid Mech. 36 (2010) 489-501.
Wang CY. Stagnation slip flow and heat transfer on a moving plate. ChemEngSci 2006; 61: 7668–72.
Fang T, Zhang J, Yao S. Slip MHD viscous flow over a stretching sheet – an exactsolution. Commun Non-linear SciNumerSimul 2009; 14: 3731–7.
Aziz A. Hydrodynamic and thermal slip flow boundary layer over a flat platewith constant heat flux boundary condition. Commun Non-linear SciNumerSimul 2010; 15: 573–80.