## THERMAL SCIENCE

International Scientific Journal

### MAGNETOHYDRODYNAMICS FLOW OF NANOFLUID WITH HOMOGENEOUS-HETEROGENEOUS REACTIONS AND VELOCITY SLIP

**ABSTRACT**

This article focuses on the steady magnetohydrodynamic flow of viscous nanofluid. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. An incompressible fluid fills the porous space. Copper-water and silver-water nanofluids are investigated in this study. Transformation method reduces the non-linear partial differential equations governing the flow into the ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. Effects of different parameters on the velocity, concentration and skin friction coefficient are shown and analyzed through graphs.

**KEYWORDS**

PAPER SUBMITTED: 2014-09-22

PAPER REVISED: 2015-04-25

PAPER ACCEPTED: 2015-04-25

PUBLISHED ONLINE: 2015-06-07

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**Issue 2**, PAGES [901 - 913]

- Choi, S. U. S., Enhancing thermal conductivity of fluids with nanoparticle, In proceedings of the ASME International Mechanical Engineering Congress and Exposition, 66 (1995), pp. 99-105.
- Eastman, J.A., Choi, S. U. S., Li, S., Yu, W., Thompson, L. J., Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles, Applied Physics Letters, 78 (2001), pp. 718-720.
- Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwoow, F. E., Grulke, E. A., Anomalous thermal conductivities enhancement on nanotube suspension, Applied Physics Letters, 79 (2001), pp. 2252-2254.
- Turkyilmazoglu, M., Nanofluid flow and heat transfer due to a rotating disk, Computers & Fluids, 94 (2014), pp. 139-146.
- Turkyilmazoglu, M., Unsteady convection flow of some nanofluids past a moving vertical flat plate with heat transfer, Journal of Heat Transfer, 136 (2013), doi:10.1115/1.4025730.
- Sheikholeslami, M., Goriji-Bandpy, M., Free convection of ferrofluid in a cavity heated from below in the presence of an external magnetic field, Powder Technology, 256 (2014), pp. 490-498.
- Sheikholeslami, M., Hatami, M., Ganji, D. D., Analytical investigation of MHD nanofluid flow in a semi-porous channel. Powder Technology, 246 (2013), pp. 327-336.
- Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D. D., Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid, Powder Technology, 254 (2014), pp. 82-93.
- Xu, H., Pop, I., You, X. C., Flow and heat transfer in a nano-liquid film over an unsteady stretching surface, International Journal of Heat and Mass Transfer, 60 (2013), pp. 646-652.
- Rashidi, M. M., Abelman, S., Mehr, N. F., Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid, International Journal of Heat and Mass Transfer, 62 (2013), pp. 515-525.
- Niu, J., Fu, C., Tan, W. C., Slip flow and heat transfer of a non-Newtonian nanofluid in a microtube, Plos One, 7 (2012), (5) e37274.
- Khan, J. A., Mustafa, M., Hayat, T., Farooq, M. A., Alsaedi, A., Liao, S. J., On model for threedimensional flow of nanofluid: An application to solar energy, Journal of Molecular Liquids, 194 (2014), pp. 41-47.
- Farooq, U., Hayat, T., Alsaedi, A., Liao, S., Heat and mass transfer of two-layer flows of thirdgrade nanofluids in a vertical channel, Applied Mathematics and Computation, 242 (2014), pp. 528-540.
- Sheikholeslami, M., Gorji-Bandpay, M., Ganji, D. D., Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid, International Communications in Heat and Mass Transfer, 39 (2012), pp. 978-986.
- Nadeem, S., Haq, R. U., Khan, Z. H., Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet, Alexandria Engineering Journal, 53 (1) (2014), pp. 219-224.
- Haq, R. U., Khan, Z. H., Khan, W. A., Thermophysical effects of carbon nanotubes on MHD flow over a stretching surface, Physica E: Low-dimensional Systems and Nanostructures, 63 (2014), pp. 215-222.
- Haq, R. U., Nadeem, S., Khan, Z. H., Noor, N. F. M., Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes, Physica B: Condensed Matter, 457(15) (2015), pp. 40-47.
- Zhang, W. M., Meng, G., Wei, X., A review on slip models for gas microflows, Journal of Microfluid Nanofluid, 13 (2012), pp. 845-882.
- Merkin, J. H., A model for isothermal homogeneous-heterogeneous reactions in boundary layer flow, Mathematical and Computer Modelling, 24 (1996), pp. 125-136.
- Chaudhary, M. A., Merkin, J. H., A simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow: I. Equal diffusivities, Fluid Dynamics Research, 16 (1995), pp. 311-333.
- Bachok, N., Ishak, A., Pop, I., On the stagnation-point flow towards a stretching sheet with homogeneous--heterogeneous reactions effects, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), pp. 4296-4302.
- Khan, W. A., Pop, I., Effects of homogeneous-heterogeneous reactions on the viscoelastic fluid towards a stretching sheet, Journal of Heat Transfer, 134 (2012), pp. 1-5.
- Kameswaran, P. K, Shaw, S., Sibanda, P., Murthy, P. V. S. N., Homogeneous-heterogeneous reactions in a nanofluid flow due to porous stretching sheet, International Journal of Heat and Mass Transfer, 57 (2013), pp. 465-472.
- Rashidi, M. M., Kavyani, N., Abelman, S., Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties, International Journal of Heat and Mass Transfer, 70 (2014), pp. 892-917.
- Mahmoud, M. A. A., Waheed, S. E., MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity, Journal of the Egyptian Mathematical Society, 20 (2012), pp. 20-27.
- Ibrahim, W., Shankar, B., MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions, Computers & Fluids, 75 (2013), pp. 1-10.
- Rooholghdos, S. A., Roohi, E., Extension of a second order velocity slip/temperature jump boundary condition to simulate high speed micro/nanoflows, Computers & Mathematics with Applications, 67 (2014), pp. 2029-2040.
- Malvandi, A., Ganji, D. D., Brownian motion and thermophoresis effects on slip flow of alumina/water nanofluid inside a circular microchannel in the presence of a magnetic field, International Journal of Thermal Sciences, 84 (2014), pp. 196-206.
- Liao, S. J., On the relationship between the homotopy analysis method and Euler transform, Comunications in Nonlinear Science and Numerical Simulation, 15 (2010), pp. 1421-1431.
- Arqub, O. A., El-Ajou, A., Solution of the fractional epidemic model by homotopy analysis method, Journal of King Saud University, 25 (2013), pp. 73-81.
- Turkyilmazoglu, M., A note on homotopy analysis method, Applied Mathematics Letters, 23 (2010), pp. 1226-1230.
- Abbasbandy, S., Shivanian, E., Predictor homotopy analysis method and its application to some nonlinear problems, Comunications in Nonlinear Science and Numerical Simulation, 16 (2011),pp. 2456-2468.
- Shehzad S. A., Alsaedi A., Hayat, T., Alhuthali, M. S., Thermophoresis particle deposition in mixed convection three-dimensional radiative flow of an Oldroyd-B fluid, Journal of Taiwan Institute of Chemical Engineers, 45 (2014), pp. 787-794.