The present paper deals with study of free convection in two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an incompressible, viscous, electrically conducting, and steady nanofluid. The governing equations representing fluid flow are transformed into a set of simultaneous ordinary differential equations by using appropriate similarity transformation. The equations thus obtained have been solved numerically using adaptive Runge-Kutta method with shooting technique. The effects of physical parameters like magnetic parameter, temperature buoyancy parameter on relative velocity and temperature distribution profile, shear stress profile, and temperature gradient profile were depicted graphically and analyzed. Significant changes were observed due to these parameters in velocity and temperature profiles. 1. Introduction Applications of heat transfer through moving material in a moving fluid medium have wide range of applications in real world. Various researchers studied the concepts of moving sheet in a flowing fluid medium. Numerical and analytical solution for momentum and energy in laminar boundary layer flow over continuously moving sheet was discussed by Zheng and Zhang [1]. The authors found that the effect of velocity ratio parameter and other parameters on heat transfer were significant. Al-Sanea [2] studied the flow and thermal characteristic of a moving vertical sheet of extruded material close to and far downstream from the extrusion slot. Regimes of forced, mixed, and natural convection have been delineated, in buoyancy flow, as a function of Reynolds and thermal Grashof numbers for various values of Prandtl number and buoyancy parameter. Seddeek [3] analyzed the effect of magnetic field on the flow of micropolar fluid past a continuously moving plate. Patel et al. [4] suggested a new model for thermal conductivity of nanofluids which is found to agree excellently with a wide range of experimental published data. The momentum and heat transfer flow of an incompressible laminar fluid past a moving sheet based on composite reference velocity was studied by Cortell [5]. The author found that the direction of the wall shear stress changes in such an interval and an increase of the relative velocity parameter yields an increase in temperature. Ishak et al. [6] studied the magnetohydrodynamic boundary layer flow due to a moving extensible surface. It was found that the dual solutions exist for the flow near -axis, where the velocity profiles show a reversed flow. Bachok et al. [7] investigated steady, laminar boundary layer flow of a
References
[1]
L. C. Zheng and X. X. Zhang, “Skin friction and heat transfer in power-law fluid laminar boundary layer along a moving surface,” International Journal of Heat and Mass Transfer, vol. 45, no. 13, pp. 2667–2672, 2002.
[2]
S. A. Al-Sanea, “Convection regimes and heat transfer characteristics along a continuously moving heated vertical plate,” International Journal of Heat and Fluid Flow, vol. 24, no. 6, pp. 888–901, 2003.
[3]
M. A. Seddeek, “Flow of a magneto-micropolar fluid past a continuously moving plate,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 306, no. 4, pp. 255–257, 2003.
[4]
H. E. Patel, T. Sundararajan, T. Pradeep, A. Dasgupta, N. Dasgupta, and S. K. Das, “A micro-convection model for thermal conductivity of nanofluids,” Pramana—Journal of Physics, vol. 65, no. 5, pp. 863–869, 2005.
[5]
R. Cortell, “Flow and heat transfer in a moving fluid over a moving flat surface,” Theoretical and Computational Fluid Dynamics, vol. 21, no. 6, pp. 435–446, 2007.
[6]
A. Ishak, R. Nazar, and I. Pop, “MHD boundary-layer flow due to a moving extensible surface,” Journal of Engineering Mathematics, vol. 62, no. 1, pp. 23–33, 2008.
[7]
N. Bachok, A. Ishak, and I. Pop, “Boundary-layer flow of nanofluids over a moving surface in a flowing fluid,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1663–1668, 2010.
[8]
H. M. Habib and E. R. El-Zahar, “Mathematical modeling of heat-transfer for a moving sheet in a moving fluid,” Journal of Applied Fluid Mechanics, vol. 6, no. 3, pp. 369–373, 2013.
[9]
K.-L. Hsiao, “Energy conversion conjugate conduction-convection and radiation over non-linearly extrusion stretching sheet with physical multimedia effects,” Energy, vol. 59, pp. 494–502, 2013.
[10]
C. M. Raguraman, A. Ragupathy, and L. Sivakumar, “Experimental determination of heat transfer coefficient in stirred vessel for coal-water slurry based on the taguchi method,” Journal of Engineering, vol. 2013, Article ID 719296, 8 pages, 2013.
[11]
K.-L. Hsiao, “Conjugate heat transfer for mixed convection and Maxwell fluid on a stagnation point,” Arabian Journal for Science and Engineering, vol. 39, no. 6, pp. 4325–4332, 2014.
[12]
K.-L. Hsiao, “Nanofluid flow with multimedia physical features for conjugate mixed convection and radiation,” Computers & Fluids, vol. 104, pp. 1–8, 2014.
[13]
N. Idusuyi, I. Babajide, O. K. Ajayi, and T. T. Olugasa, “A computational study on the use of an aluminium metal matrix composite and aramid as alternative brake disc and brake pad material,” Journal of Engineering, vol. 2014, Article ID 494697, 6 pages, 2014.
[14]
A. Einstein, Investigation on the Theory of the Brownian Movement, Dover, New York, NY, USA, 1956.
[15]
D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, Springer, New York, NY, USA, 1999.
[16]
Y. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” International Journal of Heat and Mass Transfer, vol. 43, no. 19, pp. 3701–3707, 2000.
[17]
E. Mamut, “Characterization of heat and mass transfer properties of nanofluids,” Romanian Journal of Physics, vol. 51, pp. 5–12, 2006.
