## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Mixed convection flow and heat transfer in ferromagnetic fluid over a stretching sheet with partial slip effects

**ABSTRACT**

Two-dimensional steady boundary layer mixed convection flow and heat transfer in ferromagnetic fluid over a stretching sheet is investigated. Velocity slip is taken into account. The governing partial differential equations are first transformed into the non-linear ordinary coupled differential equation using a similarity transformation and then solved numerically by Runge-Kutta-Fehlberg method. The role of local skin friction, heat transfer rate, ferromagnetic-interaction parameter, slip parameter and the buoyancy parameter on velocity and temperature profiles inside the boundary layers are examined through tables and graphically. Finally a comparison is also made with the existing literature and found in good agreement.

**KEYWORDS**

PAPER SUBMITTED: 2016-06-10

PAPER REVISED: 2016-10-08

PAPER ACCEPTED: 2016-10-12

PUBLISHED ONLINE: 2016-11-06

- Crane, L. J., Flow past a stretching plate, J. Appl. Math. Phys., 21 (1970), 4, pp. 645-647
- Gupta, P. S., Gupta, A. S., Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering, 55 (1977), pp. 744-746
- Grubka, L. J., Bobba, K. M., Heat transfer characteristics of a continuous, stretching surface with variable temperature, Journal of Heat Transfer., 107 (1985), 1, pp. 248-250
- Vafai et al., The study of Hall current on peristaltic motion of a non-Newtonian fluid with heat transfer and wall properties, Journal of Zeitschrift Fur Naturforschung A, 70 (2015), 4, pp. 281-293
- Ellahi et al., Non-Newtonian fluid flow through a porous medium between two coaxial cylinders with heat transfer and variable viscosity, Journal of Porous Media, 16 (2013), 3, pp. 205-216
- Ellahi, R., The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions, Applied Mathematical Modeling, 37 (2013), 3, pp. 1451-1457
- Faiza A. Salama, Effects of radiation on convection heat transfer of Cu-water nanofluid past a moving wedge, Thermal Science, 20 (2016), pp. 437-447
- Moradi et al., Investigation of heat transfer and viscous dissipation effects on the Jeffery Hamel flow of nanofluids, Thermal Science, 19 (2015), 2, pp. 563-578
- Kandelousi, M. S., Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition, The European Physical Journal Plus, (2014) 129- 248
- Kandelousi, M. S., KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel, Physics Letters A, 378 (2014), 45, pp. 3331-3339
- Sheikholeslami et al., convection of Al2O3-water nanofluid considering thermal radiation: A numerical study, International Journal of Heat and Mass Transfer, 96 (2016), 513-52
- Mohyud-Din et al., Magnetohydrodynamic flow and heat transfer of nanofluids in stretchable convergent/divergent channels, Applied Sciences, 5 (2015), 1639-1664
- Mohyud-Din et al., On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates, Aerospace Science and Technology, 46 (2015), 514-522
- Rashidi, et al., Entropy generation analysis of the revised Cheng-Minkowycz problem for natural convective boundary layer flow of nanofluid in a porous medium, Thermal Science, 19 (2015), pp. 169 -178
- Ellahi, et al., A study of heat transfer in power law nanofluid, Thermal Science, doi: 10.2298/TSCI150524129E (2016)
- Hathway, D. B., Use of ferrofluid in moving coil loudspeakers dB-Sound Engg. Mag., 13 (1979), pp. 42-44
- Raj, K., Moskowitz, R., Commercial applications of ferrofluids, J. Magn. Mater., 85 (1990), pp. 233-245
- Feynman, R. P., et al., Lecturers on Physics, Addison-Wesley. Reading Shliomis, MI 2004 (1963)
- Shliomis, M. I., Ferrofluids as Thermal Ratchets, Physical Review Letters, 92 (2004), 18, pp. 188901
- Maruno, S., et al., Plain paper recording process using magnetic fluids, J. Mgn. Magn. Mater., 39 (1983), pp. 187-189
- Rosensweig, R. E., Ferrohydrodynamics, Cambridge University Press Cambridge London, (1985)
- Neuringer, J. L., Some viscous flows of a saturated ferrofluid under the combined influence of thermal and magnetic field gradients, Int. J. Nonlinear. Mech., 1 (1966), pp. 123-127
- Tzirtzilakis, E. E., et al., Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field, Zeitschrift fr angewandte Mathematik und Physik, 61 (2010), 5, pp. 929-947
- Sheikholeslami, M., Ellahi, R., Simulation of ferrofluid flow for magnetic drug targeting using Lattice Boltzmann method, Journal of Zeitschrift Fur Naturforschung A, 70 (2015), 2, pp. 115-124
- Sheikholeslami, M., Gorji-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
- Li, Q., Xuan, Y., Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field, Exp. Therm. Fluid. Sci., 33 (2009), 4, pp. 91-596
- Motozawa, M., et al., Effect of magnetic field on heat transfer in rectangular duct flow of a magnetic fluid, Phys. Procedia., 9 (2010), pp. 190-193
- Feng, W. u., et al., Acoustically controlled heat transfer of ferromagnetic fluid, International journal of heat and mass transfer, 44 (2001), 23 pp. 4427-4432
- Tangthieng, C., et al., Heat transfer enhancement in ferrofluids subjected to steady magnetic fields, J. Magn. Magn. Mater., 201 (1999), 13 pp. 252-255
- Stiles, P. J., et al., Heat transfer through ferrofluids as a function of the magnetic field strength, J. Colloid Interface. Sci., 155 (1993), 1, pp. 256-258
- Abdallah, I. A., Analytical solution of heat and mass transfer over a permeable stretching plate affected by a chemical reaction, internal heating, Dufour-Souret effect and hall effect, Thermal Science, 13 (2009), pp. 183-197
- Zeeshan, et al., Effect of magnetic dipole on viscous ferrofluid past a stretching surface with thermal radiation, Journal of Molecular Liquids, 215 (2016), pp. 549-554
- Nawaz et al., Joules heating effects on stagnation point flow over a stretching cylinder by means of genetic algorithm and Nelder-Mead method, International Journal for Numerical Methods for Heat and Fluid Flow, 25 (2015), 3, pp. 665-684
- Kazem, S., et al., Improved analytical solutions to a stagnation-point flow past a porous stretching sheet with heat generation, Journal of the Franklin Institute, 348 (2011), 8, pp. 2044-2058
- Hayat, T., et al., Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space, International Journal of Heat and Mass Transfer, 51 (2008), 17, pp. 4528-4534
- Martin, M. J., Boyd, I. D., Momentum and heat transfer in a laminar boundary layer with slip flow, J. Thermophys. Heat Transf., 20 (2006), pp. 710-719
- Andersson, H. I., Slip flow past a stretching surface, Acta. Mechanica., 158 (2002), 1, pp. 121-125
- Ali, M. E., The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface, International Journal of Thermal Sciences, 45 (2006), 1, pp. 60-69
- Hayat, T., et al., Heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid, Communications in Nonlinear Science and Numerical Simulation ,15 (2010), 5, pp. 1183-1196.
- Akbar, et al. Influence of mixed convection on blood flow of Jeffery fluid through a tapered stenosed artery, Thermal Science, 17 (2013), 2, pp. 533-546.
- Ellahi, et al., A study on the mixed convection boundary layer flow and heat transfer over a vertical slender cylinder, Thermal Science, 18 (2014) 1247-1258.
- Nezhad, A. H. and Ardalan, M. V., A new approach for the analysis of the nanoparticles effects on Cu-water nanofluid mixed convection heat transfer and required power in a lid-driven cavity, Thermal Science, 20 (2016), 20, pp. 133-139
- Pourmahmoud, N,. et al., Mahmoodi, M., Mixed convection inside nanofluid filled rectangular enclosures with moving bottom wall, Thermal Science, 15 (2011), 3, pp. 889-903
- Ellahi et al., Shape effects of mixed convection MHD nanofluid over a vertical stretching permeable sheet, DOI: 10.1631/jzus.A1500119, Journal of Zhejiang University-SCIENCE A, (2016)
- Andersson, H. I., Valnes, O. A., Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole, Acta Mechanica, 12 (1998), 8, pp. 39-47
- Chen, C. H., Laminar mixed convection adjacent to vertical continuously stretching sheets, Heat and Mass Transfer, 33 (1998), 5-6, pp. 471-476.
- Abel, M. S., et al., Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and ohmic dissipations, Communications in Nonlinear Science and Numerical Simulation, 13 (2008) , 9, pp. 1808-1821
- Ali, M. E., Heat transfer characteristics of a continuous stretching surface, Wärme-und Stoffübertragung, 29 (1994), 4, pp. 227-234.