Numerical Simulation of MHD Boundary ‎Layer Stagnation Flow of Nanofluid over a ‎Stretching Sheet with Slip and Convective ‎Boundary Conditions

Document Type : Research Paper

Authors

1 ‎Department of Mathematics, University College of Science, Osmania University, Hyderabad, ‎‎500007, Telangana, India.‎

2 ‎Department of Mathematics, Government Degree College, Adilabad, 504001, Telangana, ‎India.‎

Abstract

   An investigation is carried out on MHD stagnation point flow of water-based nanofluids in which the heat and mass transfer includes the effects of slip and convective boundary conditions. Employing the similarity variables, the governing partial differential equations including continuity, momentum, energy, and concentration have been reduced to ordinary ones and solved by using Keller-Box method. The behavior of emerging parameters is presented graphically and discussed for velocity, temperature, and nanoparticles fraction. The numerical results indicate that for the stretching sheet, the velocity at a point decreases with the increase in the values of  and M; whereas both temperature and nanoparticle concentration increase with the increase in velocity slip parameter ( , magnetic parameter (M) and convective parameter ( . And also, observed that the velocity profile increases with the increase in velocity ratio parameter.

Keywords


 1.       Sakiadis B. C., (1961). "Boundary-layer behavior on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow", American Inst. Chemical Eng. J., 7: 26-28.
 2.       Crane L. J., (1970). "Flow past a stretching plate", Zeitschrift für angewandte Mathematik und Physik, 21(4): 645-647.
 3.       Gupta P. S., Gupta A. S., (1977). "Heat and mass transfer on a stretching sheet with suction or blowing", The Canadian J. Chem. Eng., 55: 744-746.
 4.       Cortell R., (2007). "Viscous flow and heat transfer over a nonlinearly stretching sheet", Appl. Math. Comput., 184: 864-873.
 5.       Subhas A., Veena P., (1998). "Visco-elastic fluid flow and heat transfer in a porous medium over a stretching sheet", Int. J. Non-Linear Mech., 33(3): 531-540.
 6.       Choi S. U. S., (1995). "Enhancing thermal conductivity of fluids with nanoparticles", ASME Int. Mech. Eng. Congress. San Francisco, USA, ASME, FED, 231/MD.,           66: 99-105.
 7.       Sheikholeslami M., Gorji-Bandpy M., Ganji D. D., (2013)."Numerical investigation of MHD effects on Al2O3-water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM", Energy, 60: 501-510.
 8.       Hamad M. A. A., Ferdows M., (2012). "Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet",Appl. Math. Mech., 33: 923-930.
 9.       Rana P., Bhargava R., (2012). "Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study", Commun. Nonlinear Sci. Numer. Simul., 17: 212-226.
Makinde O. D., Aziz A., (2011). "Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition", Int. J. Thermal Sci., 50: 1326-1332.
Rashidi M. M., Vishnu Ganesh M., Abdul Hakeem A. K, Ganga B., (2014). "Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the  presence of thermal radiation", J. Molecular Liq., 198: 234-238.
Sheikholeslami M., Houman B. R., (2018). "CVFEM for effect of Lorentz forces on nanofluid flow in a porous complex shaped enclosure by means of non-equilibrium model", J. Molecular Liq., 254: 446-462.
Hiemenz V. K., (1911). "Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder", Polytech. J., 326: 321-324.
Akbar N. S., Nadeem S., Rizwan Ul Haq,  Khan, Z. H., (2013). "Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition", Chinese J. Aeronautics, 26(6): 1389-1397.
Bhatti M. M.,Ali Abbas M., Rashidi M. M., (2018), "A robust numerical method for solving stagnation point flow over a permeable shrinking sheet under the influence of MHD", Appl. Math. Comput., 316: 381-389.
Bhattacharyya K., Layek G. C., (2011). "Effects of suction/blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation", Int. J. Heat Mass Transf., 54: 302-307.
Ibrahim W., Shankar B., Mahantesh N., (2013). "MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet", Int. J. Heat Mass Transf., 56: 1-9.
Bachok N., Ishak A., Pop I., (2011). "Stagnation-point flow over a stretching/shrinking sheet in a nanofluid", Nanoscale Res. Letters, 6: 623.
Sheikholeslami M., Houman B. R., (2018). "Magnetic nanofluid flow and convective heat transfer in a porous cavity considering Brownian motion effects", Phys. Fluids, 30: 012003.
Sachin Shaw, Kameswaran P. K., Sibanda P., (2016). "Effects of slip on nonlinear convection in nanofluid flow on stretching surfaces", Boundary Value Prob., 2: 2016.
Samir Kumar Nandy, Tapas Ray Mahapatra, (2013). "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 Transf., 64: 1091-1100.
Kai-LongHsiao, (2016). "Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet", Appl. Thermal Eng.,98: 850-861.
Mustaffa M., Hina S., Hayat. T., Alsaedi, A., (2013). "Slip effects on the peristaltic motion of nanofluid in channel with wall properties", J. Heat Transf., 135.
Malvandi A., Hedayati F., Ganji D. D., (2014). "Slip effects on unsteady stagnation flow of nanofluid over a stretching sheet", Powder Technol., 253: 377-384.
Sheikholeslami M., Milad D., Sadoughi M. K., (2018). "Heat transfer improvement and pressure drop during condensation of refrigerant-based nanofluid; an experimental procedure", Int. J. Heat Mass Transf., 122: 643-650. 
Sheikholeslami M., Ghasemi A., (2018). "Solidification heat transfer of nanofluid in existence of thermal radiation by means of FEM", Int. J. Heat Mass Transf., 123: 418-431.
Sheikholeslami M., (2018). "Numerical investigation for CuO-H2O nanofluid flow in a porous channel with magnetic field using mesoscopic method", J. Molecular Liq., 249: 739-746.
Sheikholeslami M., Mohadeseh S. N., (2018). "Simulation of nanofluid flow and natural convection in a porous media under the influence of electric field using CVFEM", Int.  J. Heat Mass Transf., 120: 772-781.
Sheikholeslami M., Shehzad S. A., (2018). "Simulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model", Int. J. Heat Mass Transf., 120: 1200-1212.
Sheikholeslami M., Shehzad S. A., (2018). "Numerical analysis of Fe3O4-H2O nanofluid flow in permeable media under the effect of external magnetic source", Int. J. Heat Mass Transf., 118: 182-192.
Sheikholeslami M., Sadoughi M. K., (2018), "Simulation of CuO-water nanofluid heat transfer enhancement in presence of melting surface", Int. J. Heat Mass Transf., 116: 909-919.
Sheikholeslami M., Shamlooei M., Moradi R., (2018). "Fe3O4-Ethylene glycol nanofluid forced convection inside a porous enclosure in existence of Coulomb force", J. Molecular Liq., 249: 429-437.
Sheikholeslami M., (2018). "CuO-water nanofluid flow due to magnetic field inside a porous media considering Brownian motion", J. Molecular Liq., 249: 921-929.
Nadeem S., Rizwan Ul Haq, (2014). "Effect of Thermal Radiation for Magnetohydrodynamic Boundary Layer Flow of a Nanofluid Past a Stretching Sheet with Convective Boundary Conditions", J. Comput. Theoret. Nanosci., 11:1-9.
Gangaiah T., Saidulu, N., Venkata Lakshmi, A., (2019). "The Influence of Thermal Radiation on ‎Mixed Convection MHD Flow of a Casson ‎Nanofluid over an Exponentially Stretching ‎Sheet", Int. J. Nanosci. Nanotechnol., 15(2): 83-98.
Ghozatloo A., Shariaty Niassar M., Rashidi A., (2017). "Effect of Functionalization Process on Thermal Conductivity of Graphene Nanofluids", Int. J. Nanosci. Nanotechnol., 13(1): 11-18.
Dodda Ramya, Srinivasa Raju R., Anand Rao J., Rashidi M. M., (2016). "Boundary layer Viscous Flow of Nanofluids and Heat Transfer Over a Nonlinearly Isothermal Stretching Sheet in the Presence of Heat Generation/Absorption and Slip Boundary Conditions", Int. J. Nanosci. Nanotechnol., 12(4): 251-268.
Sheikholeslami M., Mollabasi H., Ganji D. D., (2015). "Analytical Investigation of MHD Jeffery-Hamel Nanofluid Flow in Non-Parallel Walls", Int. J. Nanosci. Nanotechnol., 11(4): 241-248.
Zeinali Heris S., Nassan T. H. N., Noie S. H., "CuO/water Nanofluid Convective Heat Transfer Through Square Duct Under Uniform Heat Flux", Int. J. Nanosci. Nanotechnol., 7(3): 111-120.
Sahooli M., Sabbaghi S., Shariaty Niassar M., (2012). "Preparation of CuO/Water Nanofluids Using Polyvinylpyrolidone and a Survey on Its Stability and Thermal Conductivity", Int. J. Nanosci. Nanotechnol., 8(1): 27-34.
Hooshyar Z., Bardajee G. R., (2010). "Viscosity and Rheological Behaviour of Ethylene Glycol-Maghemite Nanofluids", Int. J. Nanosci. Nanotechnol., 6(3): 191-193.
Ibrahim W., (2017). "Magnetohydrodynamic (MHD) boundary layer stagnation point flow and heat transfer of a nanofluid past a stretching sheet with melting", Propul. Power Res., 6: 214-222.
Cebeci T., Pradshaw P., (1998). "Physical and Computational Aspects of Convective Heat Transfer". Springer, NewYork.