ACCESS
The purpose of this study is to investigate behavioural features of nanoparticles and microorganisms of Powell-Eyring nanofluid flow past a stretching surface with a magnetic influence. Consequences regarding stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were analysed to focus associated parameters. Intention of introducing gyrotactic microorganisms was initially to keep nanoparticle suspension in steady state. The governing flow equations are remodel invariantly to the system of nonlinear ordinary differential equations using appropriate similarity variables. To described nanofluid flow characteristics, associated parameters were computed and analysed using numerical shooting technique. Pertinent results were revealed through graphs. Our investigation shows significant effect of Newtonian heating over a stretching sheet for associated physical parameters. Comparison was carried out between Newtonian and Powell-Eyring nanofluid on velocity and temperature field.
micro-organismes gyrotactiques, nanofluide de Powell-Eyring
B0 b M T u v $T_∞$ $T_w$ |
magnetic field strength chemotaxis constant dimensionless magnetic number temperature of the fluid velocity component along x-axis velocity component along y-axis temperature of the fluid in the free stream temperature of the fluid at surface |
C $C_w$ $C_∞$ Pr DT DB Dn N j |
nanoparticle volume fraction nanoparticle volume fraction at the surface nanoparticle volume fraction in the free stream Prandtl number Thermophoresis diffusion coefficient Brownian diffusion coefficient diffusivity of microorganisms motile microorganism concentration flux of microorganism |
Nb Nt Nw Pe Sc uw(x) Wc |
Brownian motion parameter Thermophoresis parameter wall concentration of microorganism bioconvection Peclet number Schmidt number stretching velocity maximum cell swimming speed |
Greek symbols |
|
η |
dimensionless similarity variable |
σ |
Dimensionless number |
θ |
dimensionless temperature |
ϕ |
dimensionless nanoparticle volume fraction |
μ γ v ψ α ΔC ΔN τ |
Viscosity Mixed convection parameter kinematic viscosity stream function thermal diffusivity of the nanofluid characteristic nanoparticle volume fraction characteristic motile microorganisms density difference ratio of the effective heat capacity of the nanoparticle to that of the fluid |
Subscripts |
|
∞ |
condition at free steam |
w
Superscripts
' |
condition at the surface
differentiation with respect to η |
Akbar N. S., Ebaid A., Khan Z. H. (2015). Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet. Journal of Magnetism and Magnetic Materials, Vol. 382, pp. 355-358. http://doi.org/10.1016/j.jmmm.2015.01.088
Aziz A., Khan W. A., Pop I. (2012). Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. International Journal of Thermal Sciences, Vol. 56, pp. 48-57. http://doi.org/10.1016/j.ijthermalsci.2012.01.011
Babu M. J., Sandeep N. (2016). 3D MHD slip flow of a nanofluid over a slendering stretching sheet with thermophoresis and Brownian motion effects. Journal of Molecular Liquids, Vol. 222, pp. 1003-1009. http://doi.org/10.1016/j.ijthermalsci.2012.01.011
Bakier A. Y. (2009). Thermophoresis effects on heat and mass transfer in MHD flow over a vertical stretching surface with radiation. International Journal of Fluid Mechanics Research, Vol. 36, No. 6. http://doi.org/10.1615/InterJFluidMechRes.V36.i6.10
Buongiorno J. (2006). Convective transport in nanofluids. Journal of Heat Transfer, Vol. 128, No. 3, pp. 240-250. http://doi.org/10.1115/1.2150834
Crane L. J. (1970). Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 21, No. 4, pp. 645-647. http://doi.org/10.1007/BF01587695
Geng P., Kuznetsov A. V. (2005). Settling of bidispersed small solid particles in a dilute suspension containing gyrotactic micro-organisms. International Journal of Engineering Science, Vol. 43, No. 11-12, pp. 992-1010. http://doi.org/10.1016/j.ijengsci.2005.03.002
Gireesha B. J., Gorla R. S. R., Mahanthesh B. (2015). Effect of suspended nanoparticles on three-dimensional MHD flow, heat and mass transfer of radiating Eyring-Powell fluid over a stretching sheet. Journal of Nanofluids, Vol. 4, No. 4, pp. 474-484. http://doi.org/10.1166/jom.2015.1177
Hamad M. A. A. (2011). Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International Communications in Heat and Mass Transfer, Vol. 38, No. 4, pp. 487-492. http://doi.org/10.1016/j.cheatmasstransfer.2010.12.042
Hayat T., Waqas M., Shehzad S. A., Alsaedi A. (2016). Mixed convection stagnation-point flow of Powell-Eyring fluid with Newtonian heating, thermal radiation, and heat generation/absorption. Journal of Aerospace Engineering, Vol. 30, No. 1. http://doi.org/10.1061/(ASCE)AS.1943-5525.0000674
Jalil M., Asghar S., Imran S. M. (2013). Self similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream. International Journal of Heat and Mass Transfer, Vol. 65, pp. 73-79. http://doi.org/10.1016/j.ijheatmasstransfer.2013.05.049
Jhankal A. K., Kumar M. (2013). MHD boundary layer flow past a stretching plate with heat transfer. International J. of Engineering and Science, Vol. 2, No. 3, pp. 9-13.
Kandasamy R., Loganathan P., Arasu P. P. (2011). Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection. Nuclear Engineering and Design, Vol. 241, No. 6, pp. 2053-2059. http://doi.org/10.1016/j.nucengdes.2011.0.011
Kandasamy R., Muhaimin I., Mohamad R. (2013). Thermophoresis and Brownian motion effects on MHD boundary-layer flow of a nanofluid in the presence of thermal stratification due to solar radiation. International Journal of Mechanical Sciences, Vol. 70, pp. 146-154. http://doi.org/10.1016/j.ijmechsci.2013.03.007
Khan U., Ahmed N., Khan S. I. U., Mohyud-din S. T. (2014). Thermo-diffusion effects on MHD stagnation point flow towards a stretching sheet in a nanofluid. Propulsion and Power Research, Vol. 3, No. 3, pp. 151-158. http://doi.org/10.1016/j.jppr.2014.07.006
Kuznetsov A. V. (2010). The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. International Communications in Heat and Mass Transfer, Vol. 37, No. 10, pp. 1421-1425. http://doi.org/10.1016/j.icheatmasstransfer.2010.08.015
Kuznetsov A. V., Geng P. (2005). The interaction of bioconvection caused by gyrotactic micro-organisms and settling of small solid particles. International Journal of Numerical Methods for Heat Fluid Flow, Vol. 15, No. 4, pp. 328-347. http://doi.org/10.1108/09615530510590597
Makinde O. D., Aziz A. (2011). Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Therm. Sci, Vol.50, No.7, pp.1326-1332. http://doi.org/10.1016/j.ijthermalsci.2011.02.019
Makinde O. D., Khan W. A., Khan Z. H. (2013). Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet. International Journal of Heat and Mass Transfer, Vol. 62, pp. 526-533. http://doi.org/10.1016/j.ijheatmasstransfer.2013.03.049
Malik M. Y., Khan I., Hussain A., Salahuddin T. (2015). Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet: A numerical study. AIP advances, Vol. 5, No. 11, pp.117118. http://doi.org/10.1063/1.4935639
Mutuku W. N., Makinde O. D. (2014). Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gyrotactic microorganisms. Computers & Fluids, Vol. 95, pp. 88-97. http://doi.org/10.1016/j.compfluid.2014.02.026
Nadeem S., Haq R. U. (2014). Effect of thermal radiation for megnetohydrodynamic boundary layer flow of a nanofluid past a stretching sheet with convective boundary conditions. Journal of Computational and Theoretical Nanoscience, Vol. 11, No. 1, pp. 32-40. http://doi.org/10.11656/jctn.2014.3313
Naramgari S., Sulochana C. (2016). MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection. Alexandria Engineering Journal, Vol. 55, No. 2, pp. 819-827. http://doi.org/10.1016/j.aej.2016.02.001
Nayak M. K., Dash G. C., Singh L. P. (2016). Heat and mass transfer effects on MHD viscoelastic fluid over a stretching sheet through porous medium in presence of chemical reaction. Propulsion and Power Research, Vol. 5, No. 1, pp. 70-80. http://doi.org/10.1016/j.jppr.2016.01.006
Panigrahi S., Reza M., Mishra A. K. (2014). MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface. Applied Mathematics and Mechanics, Vol. 35, No. 12, pp. 1525-1540. http://doi.org/10.1007/s10483-014-1888-6
Pantokratoras A. (2008). Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity: a numerical reinvestigation. International Journal of Heat and Mass Transfer, Vol. 51, No. 1-2, pp. 104-110. http://doi.org/10.1016/j.ijheattransfer.2007.04.007
Rajput G. R., Patil V. S., Krishna Prasad J. S. V. R. (2017). Hydromagnetic bioconvection flow in the region of stagnation-point flow and heat transfer in non-Newtonian nanofluid past a moving surface with suction: similarity analysis. International Journal of Heat and Technology, Vol. 35, No. 1, pp. 25-31. http://doi.org/10.18280/ijht.350104
Raptis A., Perdikis C. (2006). Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field. International Journal of Non-Linear Mechanics, Vol. 41, No. 4, pp. 527-529. http://doi.org/10.1016/j.ijnonlinmec.2005.12.003
Rehman K. U., Malik M. Y., Salahuddin T., Naseer M. (2016). Dual stratified mixed convection flow of Eyring-Powell fluid over an inclined stretching cylinder with heat generation/absorption effect. AIP Advances, Vol. 6, No. 7, pp. 075112. http://doi.org/10.1063/1.4959587
Roşca A. V., Pop I. (2014). Flow and heat transfer of Powell–Eyring fluid over a shrinking surface in a parallel free stream. International Journal of Heat and Mass Transfer, Vol. 71, pp. 321-327. http://doi.org/10.1016/j.ijheatmasstransfer.2013.12.020
Sparrow E. M., Cess R. D. (1961). The effect of a magnetic field on free convection heat transfer. International Journal of Heat and Mass Transfer, Vol. 3, No. 4, pp. 267-274. http://doi.org/10.1016/0017-9310(61)90042-4
Tham L., Nazar R., Pop I. (2013). Mixed convection flow over a solid sphere embedded in a porous medium filled by a nanofluid containing gyrotactic microorganisms. International Journal of Heat and Mass Transfer, Vol. 62, pp. 647-660. http://doi.org/10.1016/j.ijheatmasstransfer.2013.03.012
Xu H., Pop I. (2014). Fully developed mixed convection flow in a horizontal channel filled by a nanofluid containing both nanoparticles and gyrotactic microorganisms. European Journal of Mechanics-B/Fluids, Vol. 46, pp. 37-45. http://doi.org/10.1016/j.euromechflu.2014.02.005