Active and passive controls of nanoparticles in Maxwell stagnation point flow over a slipped stretched surface
Tóm tắt
A steady stagnation-point flow of an incompressible Maxwell fluid towards a linearly stretching sheet with active and passive controls of nanoparticles is studied numerically. The momentum equation of the Maxwell nanofluid is inserted with an external velocity term as a result of the flow approaches the stagnation point. Conventional energy equation is modified by incorporation of nanofluid Brownian and thermophoresis effects. The condition of zero normal flux of nanoparticles at the stretching surface is defined to impulse the particles away from the surface in combination with nonzero normal flux condition. A hydrodynamic slip velocity is also added to the initial condition as a component of the entrenched stretching velocity. The governing partial differential equations are then reduced into a system of ordinary differential equations by using similarity transformation. A classical shooting method is applied to solve the nonlinear coupled differential equations. The velocity, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, Nusselt number and Sherwood number are graphically presented to visualize the effects of particular parameters. Temperature distributions in passive control model are consistently lower than in the active control model. The magnitude of the reduced skin friction coefficient, Nusselt number and Sherwood number decrease as the hydrodynamic slip parameter increases while the Brownian parameter has negligible effect on the reduced heat transfer rate when nanoparticles are passively controlled at the surface. It is also found that the stagnation parameter contributes better heat transfer performance of the nanofluid under both active and passive controls of normal mass flux.
Tài liệu tham khảo
Pearson JRA, Tardy PMJ (2002) Models for flow on non-Newtonian and complex fluids through porous media. J Non-Newton Fluid Mech 102:447–473
Xu H, Liao SJ, Pop I (2006) Series solution of unsteady boundary layer flows of non-Newtonian fluids neat a forward stagnation point. J Non-Newton Fluid Mech 139:31–43
Schowalter WR (1960) The application of boundary-layer theory to power-law pseudoplastic fluids: similar solutions. AICHE J 6:24–28
Acrivos A, Shah MJ, Petersen EE (1960) Momentum and heat transfer in laminar boundary layer flows of non-Newtonian fluids past external surfaces. AICHE J 6:312–318
Shehzad SA, Alsaedi A, Hayat T (2013) Hydromagnetic steady flow of Maxwell fluid over a bidirectional stretching surface with prescribed surface temperature and prescribed surface heat flux. PLoS One 8(7):e68139. doi:10.1371/journal.pone.0068139
Awais M, Hayat T, Alsaedi A, Asghar S (2014) Time-dependent three-dimensional boundary layer flow of a Maxwell fluid. Comput Fluids 91:21–27
Abbasbandy S, Naz R, Hayat T, Alsaedi A (2014) Numerical and analytical solutions for Falkner–Skan flow of MHD Maxwell fluid. Appl Math Comput 242:569–575
Nadeem S, Haq RU, Khan ZH (2014) Numerical study of MHD boundary layer flow of a Maxwell fluid past a stretching sheet in the presence of nanoparticles. J Taiwan Inst Chem Eng 45:121–126
Ramesh GK, Gireesha BJ (2014) Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. Ain Shams Eng J 5(3):991–998
Hussain T, Hussain S, Hayat T (2016) Impact of double stratification and magnetic field in mixed convective radiative flow of Maxwell nanofluid. J Mol Liq 220:870–878
Khan N, Mahmood T, Sajid M, Hashmi MS (2016) Heat and mass transfer on MHD mixed convection axisymmetric chemically reactive flow of Maxwell fluid driven by exothermal and isothermal stretching disks. Int J Heat Mass Transf 92:1090–1105
Hayat T, Awais M, Qasim M, Hendi AA (2011) Effects of mass transfer on the stagnation point flow of an upper-convected Maxwell (UCM) fluid. Int J Heat Mass Transf 54:3777–3782
Ramesh GK, Gireesha BJ, Bagewadi CS (2012) MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with non-uniform source/sink. Int J Heat Mass Transf 55:4900–4907
Ramesh GK, Gireesha BJ, Bagewadi CS (2014) Stagnation point flow of a MHD dusty fluid towards a stretching sheet with radiation. Afrika Matematika 25(1):237–249
Mustafa I, Javed T, Ghaffari A (2016) Heat transfer in MHD stagnation point flow of a ferrofluid over a stretchable rotating disk. J Mol Liq 219:526–532
Hayat T, Khan MI, Farooq M, Yasmeen T (2016) Stagnation point flow with Cattaneo–Christov heat flux and homogeneous-heterogeneous reactions. J Mol Liq 220:49–55
Mustafa M, Hayat T, Pop I, Asghar S, Obaidat S (2011) Stagnation-point flow of a nanofluid towards a stretching sheet. Int J Heat Mass Transf 54:5588–5594
Bachok N, Ishak A, Pop I (2012) The boundary layers of an unsteady stagnation-point flow in a nanofluid. Int J Heat Mass Transf 55:6499–6505
Alsaedi A, Awais M, Hayat T (2012) Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions. Commun Nonlinear Sci Numer Simul 17:4210–4223
Noor NFM, Haq RU, Nadeem S, Hashim I (2015) Mixed convection stagnation flow of a micropolar nanofluid along a vertically stretching surface with slip effects. Meccanica. doi:10.1007/s11012-015-0145-9
Ramesh GK, Gireesha BJ, Hayat T, Alsaedi A (2016) Stagnation point flow of Maxwell fluid towards a permeable surface in the presence of nanoparticles. Alex Eng J. doi:10.1016/j.aej.2016.02.007
Nield DA, Kuznetsov AV (2009) The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 52:5792–5795
Kuznetsov AV, Nield DA (2013) The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid: a revised model. Int J Heat Mass Transf 65:682–685
Nield DA, Kuznetsov AV (2014) The onset of convection in a horizontal nanofluid layer of finite depth: a revised model. Int J Heat Mass Transf 77:915–918
Kuznetsov AV, Nield DA (2014) Natural convective boundary-layer flow of a nanofluid past a vertical plate: a revised model. Int J Therm Sci 77:126–129
Nield DA, Kuznetsov AV (2014) Thermal instability in a porous medium layer saturated by a nanofluid: a revised model. Int J Heat Mass Transf 68:211–214
Rahman MM, Rosca AV, Pop I (2014) Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno’s model. Int J Therm Sci 77:1133–1143
Mustafa M, Khan JA, Hayat T, Alsaedi A (2015) Boundary layer flow of nanofluid over a nonlinearly stretching sheet with convective boundary condition. IEEE Trans Nanotechnol 14(1):159–168
Ul Haq R, Nadeem S, Khan ZH, Akbar NS (2015) Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet. Phys E 65:17–23
Zaimi K, Ishak A, Pop I (2011) Flow past a permeable stretching/shrinking sheet in a nanofluid using two-phase model. PLoS One 9(11):e111743. doi:10.1371/journal.pone.0111743
Dhanai R, Rana P, Kumar L (2015) Multiple solutions of MHD boundary layer flow and heat transfer behavior of nanofluids induced by a power-law stretching/shrinking permeable sheet with viscous dissipation. Powder Technol 273:62–70
Sadeghy K, Hajibeygim H, Taghavi S-M (2006) Stagnation-point flow of upper-convected Maxwell fluids. Int J Non-linear Mech 41:1242–1247
Buongiorno J (2006) Convective transport in nanofluids. Trans ASME 128:240–250
Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483