Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

Document Type : Research Article

Authors

1 Department of Chemical Engineering, Yasooj Branch, Islamic Azad University, Yasooj, Iran

2 Young Researchers Club, Yasooj Branch, Islamic Azad University, Yasooj, Iran

Abstract

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number and local Sherwood number as well as the velocity, temperature and concentration profiles for some values of the governing parameters were presented graphically and discussed in detail for both the cases of assisting and opposing flows. It was observed that, the magnitude of the reduced Nusselt number decreases with the increases in the Brownian motion and thermophoresis effects for both cases of buoyant assisting and opposing flows. In addition to, the local Sherwood number increases by increasing the Brownian motion in both cases of buoyant assisting and opposing flows. A similar effect on the local Sherwood number was observed when thermophoresis effects decreases.

Keywords


[1] K. Hiemenz, Die Grenzschicht an einem in den gleichformingen Flussigkeitsstrom einge-tauchten
graden Kreiszylinder, Dinglers Polytech. J. 326 (1911) 321.
[2] F. Homann, Der Einfluss grosser Zahigkeit bei der Stromung um den Zylinder und um die Kugel, Z. Angew. Math. Mech. 16 (1936) 153.
[3] S. Dinarvand, on explicit, purely analytic solutions of off-centered stagnation flow towards a rotating disc by means of HAM, Nonlinear Anal. Real World Appl. 11 (2010) 3389.
[4] D. A. Nield, A. Bejan, Convection in Porous Media, third ed., Springer, New York, (2006). 
[5] D. B. Ingham, I. Pop (Eds.), Transport Phenomena in Porous Media, Vol. II 2002, Pergamon, Oxford, (1998).
[6] D. B. Ingham, I. Pop (Eds.), Transport Phenomena in Porous Media, Vol. III, Elsevier, Oxford, (2005).

[7] A. Bejan, I. Dincer, S. Lorente, A.F. Miguel, A.H. Reis, Porous and Complex Flow Structures in Modern Technologies, Springer, New York, (2004).
[8] M.C. Ece, Free convection flow about a cone under mixed thermal boundary conditions and a magnetic
field, Appl. Math. Model. 29 (2005) 1121.
[9] S. Dinarvand, A. Doosthoseini, E. Doosthoseini, M.M. Rashidi , Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces, Nonlinear Anal. Real World Appl. 11 (2010) 1159‌.
[10] S. Dinarvand, The laminar free-convection boundarylayer flows about a heated and rotating down-pointing
vertical cone in the presence of a transverse magnetic field, Int. J. Numer. Meth. Fluids 67 (2011) 2141.
[11] T. Z. Hayat, I. Pop, S. Asghar, Effects of radiation and magnetic field on the mixed convection stagnationpoint
flow over a vertical stretching sheet in a porous medium, International Journal of Heat and Mass
Transfer, 53 (2010) 466.
[12] K. Das, Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties. Heat and Mass Transf. 48 (2011) 1.
[13] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticle, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non- Newtonian Flows, ASME FED, 231/66 (1995) 99.
[14] S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood, E. A. Grulke, Anomalously thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett. 79 (2001) 2252.
[15] H. Kang, S.H. Kim, J. M. Oh, Estimation of Thermal Conductivity of Nanofluid using Experimental Effective Particle Volume, Exp. Heat Transf. 19 (2006) 181.
[16] V. Velagapudi, R. K. Konijeti, C. S. K. Aduru, Empirical Correlation to Predict Thermophysical and Heat Transfer Characteristics of Nanofluids, Thermal Sci. 12 (2008) 27.
[17] A. Turgut, Tavman, I., Chirtoc, M., Sauter, C., Tavman, S., Thermal Conductivity and Viscosity Measurements of Water-Based TiO2 Nanofluids, Int. J. Thermophys 30 (2009) 1213.
[18] V.Y. Rudyak, Belkin, A. A., E. A.Tomilina, On the Thermal Conductivity of Nanofluids, Technical Physics Letters 36 (2010) 660.
[19] C. Murugesan, S. Sivan, Limits for Thermal Conductivity of Nanofluids, Thermal Sci. 14 (2010) 65.
[20] R.J. Tiwari, M.K. Das, Heat transfer augmentation in two-sided lid-driven differentially heated square
cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50 (2007) 2002.
[21] A. K. Nayak, K. Singh, P. P. Kulkarni, Measurement of Volumetric Thermal Expansion Coefficient of Various Nanofluids, Technical Physics Letters, 36 (2010) 696.
[22] S. Ahmad, I. Pop, Mixed convection boundary layer flow from a vertical flat plate embedded in a porous
medium filled with nanofluids, Int. Comm. Heat Mass Transfer, 37 (2010) 987.
[23] S. Dinarvand, A. Abbassi, R. Hosseini, I. Pop,homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder, Thermal Science, 19 (2015) 549.
[24] J. A. Gbadeyan, M.A. Olanrewaju, P.O. Olanrewaju, Boundary Layer Flow of a Nanofluid Past a Stretching
Sheet with a Convective Boundary Condition in the Presence of Magnetic Field and Thermal Radiation, Australian Journal of Basic and Applied Sciences, 5(2011) 1323.
[25] S. Dinarvand, R. Hosseini, E. Damangir, I. Pop, Series solutions for steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder with sinusoidal radius variation, Meccanica, 48 (2013) 643.
[26] A. Chamkha, A. Al-Mudhaf, I. Pop, Effect of heat generation or absorption on thermophoretic free convection boundary layer from a vertical flat plate embedded in a porous medium, Int. Commun. Heat Mass Transfer, 33 (2006) 1096.
[27] S. L. Goren, The role of thermophoresis in laminar flow of a viscous and incompressible fluid, J. Colloid. Interface Sci. 61(1977) 77.
[28] A.J. Chamkha, I. Pop, Effects of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium, Int. Commun. Heat Mass Transfer, 31(2004) 421.
[29] M.S. Aslam, M.M. Rahman, M.A. Sattar, Effects of variable suction and thermophoresis on steady MHD combined free-forced connective heat and mass transfer flow over a semi-infinite permeable inclined plate in the presence of thermal radiation, Int. J.Thermal. Sci. 47 (2008) 758.
[30] R. Kandasamya, Muhaimina, I. Hashim, Ruhailaa, Thermophoresis and chemical reaction effects on non-Darcy mixed convective heat and mass transfer past a porous wedge with variable viscosity in the presence of suction or injection, Nuclear Eng. Design, 238 (2008) 2699.
[31] T. Gsosan, R. Pop, I. Pop, Thermophoretic deposition of particles in fully developed mixed convection flow
240 A. G. J. Ghadam et al. / Journal of Particle Science and Technology (2015) 225-240 in a parallel-plate vertical channel, Heat Mass Transfer 45 (2009) 503.
[32] K. Das, Effects of thermophoresis and thermal radiation on MHD mixed convective heat and mass
transfer flow, Africa Mathematica 24 (2012) 511.
[33] A. V. Kuznetsov, D. A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical
plate, Int. J. Thermal Sci. 49 (2010) 243.
[34] D.A. Nield, A.V. Kuznetsov, The Cheng-Minkowycz problem for natural convective boundary layer flow in
a porous medium saturated by a nanofluid, Int. J. Heat Mass Transfer 52 (2009) 5792.
[35] P. Cheng, W.J. Minkowycz, Free convection about a vertical flat plate embedded in a porous medium with
application to heat transfer from a dike, J. Geophys. Res. 82 (1977) 2040. Heat Transfer, 128 (2006) 240.
[36] J. Buongiorno, Convective transport in nanofluids, J. (2009) 145.
[37] W. A. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat Mass
Transfer 53 (2010) 2477.
[38] T. R. Mahapatra, A.S. Gupta, Heat transfer in stagnation-point towards a stretching sheet, Heat Mass
Transfer, 38 (2002) 517.
[39] R. Nazar, N. Amin, D. Flip, I. Pop, Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet, Int. J. Eng. Sci. 42 (2004) 1241.
[40] A. Ishak, R. Nazar, I. Pop, Mixed convection boundary layers in the stagnation-point flow toward
a stretching vertical sheet, Mechanica 41 (2006) 509.
[41] D. Pal, Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of
buoyancy force and thermal radiation, Mechanica 44 (2009) 145.