**ABSTRACT**

This study investigates the effect of induced magnetic field, melting heat transfer and Stefan blowing effects of mass transfer as well as mass convective boundary condition on the stagnation point flow of a bionanofluid over a vertical plate. The nonlinear boundary layer equations are transformed, by using suitable similarity transformations, into ordinary differential equations (ODEs) which are then solved numerically using the BVP4C technique. The solutions of the problem depends on parameters of magnetic M, blowing s, Brownian motion Nb, thermophoresis Nt, reciprocal of magnetic Prandtl number A, Lewis number Le, Bioconvection Schmidt number Sb and Péclet number Pe. The effects of these controlling parameters on the flow, heat, mass and microorganism transfer are studied. It is found that magnetic parameter leads to a decrease in the thickness of the momentum boundary layer. The temperature profile decreases with the increase of melting parameter. The blowing parameter enhances the concentration. The results of the present study are useful in many industrial applications such as heat exchangers, coolants, micro-channel heat sinks, lubricants and microbial fuel cell.

**KEYWORDS**

PAPER SUBMITTED: 2017-01-15

PAPER REVISED: 2017-05-23

PAPER ACCEPTED: 2017-05-24

PUBLISHED ONLINE: 2017-06-04

- Michael, D.H., A two dimensional magnetic boundary layer problem, Mathematika, 1(1954), 02, pp.131-142.
- Davies, T.V., The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate. I. Uniform conditions at infinity, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 273(1963), 1355, pp. 496-508.
- Ishak, A.M., Nazar, R.M. and Pop, I., MHD boundary-layer flow past a moving wedge, Magnetohydrodynamics, (2009), 1, pp.103-110.
- Jafar, K., Nazar, R., Ishak, A. and Pop, I., MHD boundary layer flow due to a moving wedge in a parallel stream with the induced magnetic field, Boundary Value Problems, 2013(2013), 1, pp.1-14.
- Khan, W.A., Makinde, O.D. and Khan, Z.H., MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip, International Journal of Heat and Mass Transfer, 74(2014), pp.285-291.
- Khan, W.A. and Makinde, O.D., MHD nanofluids bioconvection due to gyrotactic microorganisms over a convectively heat stretching sheet, International Journal of Thermal Sciences, 81(2014), pp.118-124.
- Shateyi, S., and Mabood, F., MHD mixed convection slip flow near a stagnation-point on a nonlinearly vertical stretching sheet in the presence of viscous dissipation, Thermal Science, (2015), 00, pp.219-219.
- Prasannakumara, B.C., Gireesha, B.J. and Manjunatha, P.T., Melting phenomenon in MHD stagnation point flow of dusty fluid over a stretching sheet in the presence of thermal radiation and non-uniform heat source/sink, International Journal for Computational Methods in Engineering Science and Mechanics, 16(2015), 5, pp.265-274. 11
- Ali, F.M., Nazar, R., Arifin, N.M. and Pop, I., MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field, Applied Mathematics and Mechanics, 32(2011), 4, pp.409-418.
- Ibrahim, W., Shankar, B. and Nandeppanavar, M.M., MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet, International Journal of Heat and Mass Transfer, 56(2013), 1, pp.1-9.
- Hiemenz, K., Die Grenzschicht an einem in den gleichförmigenFlüssigkeitsstromeingetauchtengeraden Kreiszylinder, Dingler's Polytech Journal, 326(1911), 321-324.
- Wang, C.Y., Stagnation flow on a plate with anisotropic slip, European Journal of Mechanics-B/Fluids, 38(2013), 73-77.
- Nandy, S.K. and Mahapatra, T.R., Effects of slip and heat generation/absorption on MHD stagnation flow of nanofluid past a stretching/shrinking surface with convective boundary conditions, International Journal of Heat and Mass Transfer, 64(2013), pp.1091-1100.
- Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, ASME-Publications-Fed, 231(1995), pp.99-106.
- Hayat, T., Imtiaz, M., and Alsaedi, A., MHD flow of nanofluid over permeable stretching sheet with convective boundary conditions, Thermal Science, (2014),00, pp.139-139.
- Ravi, K.J.and Vinod, K.G.P. Nanofluids: A promisingfuture, Journal of Chemical and Pharmaceutical Sciences, (2014), pp.57-61.
- Shokoohi, Y. and Shekarian, E., Application of Nanofluids in Machining Processes-A Review, Journal of Nanoscience and Technology, (2015), pp.59-63.
- Devendiran, D.K. and Amirtham, V.A., A review on preparation, characterization, properties and applications of nanofluids, Renewable and Sustainable Energy Reviews, 60(2016), pp.21-40.
- Epstein, M. and Cho, D.H., Melting heat transfer in steady laminar flow over a flat plate, Journal of Heat Transfer, 98(1976), 3, pp.531-533.
- Kazmierczak, M., Poulikakos, D. and Pop, I., Melting from a flat plate embedded in a porous medium in the presence of steady natural convection, Numerical Heat Transfer, 10(1986), 6, pp.571-581.
- Hayat, T., Iqbal, Z., Mustafa, M., and Hendi, A.A., Melting heat transfer in the stagnation-point flow of third grade fluid past a stretching sheet with viscous dissipation. Thermal Science, 17(2013), 3, pp. 865-875.
- Das, K., Nanofluid flow over a shrinking sheet with surface slip, Microfluidics and Nanofluidics, 16(2014), 1-2, pp.391-401.
- Gireesha, B.J., Mahanthesh, B., Shivakumara, I.S. and Eshwarappa, K.M., Melting heat transfer in boundary layer stagnation-point flow of nanofluid toward a stretching sheet with induced magnetic field, Engineering Science and Technology, an International Journal, 19(2016), 1, pp.313-321.
- Mutuku, W.N. and Makinde, O.D., Hydromagneticbioconvection of nanofluid over a permeable vertical plate due to gyrotactic microorganisms, Computersand Fluids, 95(2014), pp.88-97.
- Kuznetsov, A.V., The onset of nanofluids bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms, International Communications in Heat and Mass Transfer, 37(2010), 10, pp.1421-1425.
- Kuznetsov, A.V., Nanofluid bioconvection: interaction of microorganisms oxytacticupswimming, nanoparticle distribution, and heating/cooling from below, Theoretical and Computational Fluid Dynamics, 26(2012), 1-4, pp.291-310.
- Aziz, A., Khan, W.A. and Pop, I., 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, 56(2012), pp.48-57.
- Latiff, N.A.A., Uddin, M.J., Bég, O.A. and Ismail, A.I., Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching/shrinking sheet, Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, (2015) p.1740349915613817.
- Uddin, M.J., Kabir, M.N., and Bég, O.A., Computational investigation of Stefan blowing and multiple-slip effects on buoyancy-driven bioconvectionnanofluid flow with microorganisms, International Journal of Heat and Mass Transfer, 95(2016), pp. 116-130.
- Basir, M.F.M., Uddin, M.J., Ismail, A.M. and Bég, O.A., Nanofluid slip flow over a stretching cylinder with Schmidt and Péclet number effects, AIP Advances, 6(2016), 5, p.055316.
- Nellis G. and Klein, S., Heat Transfer. Cambridge University Press; 9(2008), p. E23-5
- Lienhard IV JH, Lienhard VJH, A Heat Transfer. 3rd ed. Cambridge, MA: Phlogiston Press; 2005
- Acrivos, A., The asymptotic form of the laminar boundary-layer mass-transfer rate for large interfacial velocities, Journal of Fluid Mechanics, 12(1962), 03, pp.337-357.
- Fang, T. and Jing, W., Flow, heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer, Communications in Nonlinear Science and Numerical Simulation, 19(2014), 9, pp. 3086-3097.
- Uddin, M.J., Alginahi, Y., Bég, O.A. and Kabir, M.N., Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects,Computers and Mathematics with Applications, 72(2016), 10, pp. 2562-2581.
- Bég, O.A., Bakier, A.Y., Prasad, V.R., Zueco, J. and Ghosh, S.K., Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects, International Journal of Thermal Sciences, 48(2009), 8, pp.1596-1606.
- Shampine, L.F., Kierzenka, J. and Reichelt, M.W., Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c, Tutorial notes, (2000), pp.437-448.
- Kameswaran, P.K., Shaw, S., Sibanda, P. and Murthy, P.V.S.N., Homogeneous-heterogeneous reactions in a nanofluid flow due to a porous stretching sheet, International Journal of Heat and Mass Transfer, 57(2013), 2, pp.465-472.
- Rahman, M.M., Roşca, A.V. and Pop, I., Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno's model, International Journal of Heat and Mass Transfer, 77(2014), pp.1133-1143.
- Rosca, N.C., Rosca, A.V., Aly, E.H. and Pop, I., Semi-analytical solution for the flow of a nanofluid over a permeable stretching/shrinking sheet with velocity slip using Buongiorno's mathematical model, European Journal of Mechanics B Fluids, 58(2016), pp.39-49.
- Rajagopal, K.R., Gupta, A.S. and Na, T.Y., A note on the Falkner-Skan flows of a non-Newtonian fluid, International Journal of Non-Linear Mechanics, 18(1983), 4, pp.313-320.