Radiation Effect on MHD Stagnation-Point Flow of a Nanofluid over an Exponentially Stretching Sheet
Keywords:
MHD, radiation effect, stagnation-point flow, numerical solutionAbstract
This paper theoretically investigates the radiation effect on magnetohydrodynamics (MHD) stagnation-point flow of a nanofluid over an exponentially stretching sheet under the assumptions of a small magnetic Reynolds number. The sheet is stretched with an exponential velocity in the presence of a non-uniform magnetic field B applied in a transverse direction normal to the flow. By using the modified Bernoulli's equation, a highly nonlinear nanofluid problem is modeled for an electrically conducting nanofluid. The momentum, thermal and concentration boundary layer thicknesses are intensified for the incorporated flow parameters such as Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr, Lewis number Le, Hartmann number Mexp and velocity ratio parameter ε. Also by an appropriate similarity transformation, the system of nonlinear partial differential equations is reduced to ordinary differential equations. These equations subjected to the boundary conditions are solved numerically using the Keller-box method. Numerical results are plotted and discussed for pertinent flow parameters. A comparison with existing results in the literature is also provided.doi:10.14456/WJST.2014.11
Downloads
Metrics
References
K Hiemenz. Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Dingler's Polytech. J. 1911; 326, 321-4.
TR Mahapatra and AS Gupta. Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Tran. 2002; 38, 517-21.
TR Mahapatra and AS Gupta. Stagnation-point flow towards a stretching surface. Can. J. Chem. Eng. 2003; 81, 258-63.
R Nazar, N Amin, D Filip and I Pop. Stagnation point flow of a micropolar fluid towards a stretching sheet. Int. J. Nonlinear Mech. 2004; 39, 1227-35.
YY Lok, N Amin and I Pop. Non-orthogonal stagnation point flow towards a stretching sheet. Int. J. Nonlinear Mech. 2006; 41, 622-7.
S Nadeem, A Hussain, MY Malik and T Hayat. Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet. Appl. Math. Mech. Eng. Ed. 2009; 30, 1255-62.
S Nadeem, A Hussain and M Khan. HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Comm. Nonlinear Sci. Numer. Simulat. 2010; 15, 475-81.
F Labropulu, D Li and I Pop. Non-orthogonal stagnation-point flow towards a stretching surface in a non-Newtonian fluid with heat transfer. Int. J. Therm. Sci. 2010; 49, 1042-50.
A Ishak, YY Lok and I Pop. Stagnation-point flow over a shrinking sheet in a micropolar fluid. Chem. Eng. Comm. 2010; 197, 1417-27.
N Bachok, A Ishak and I Pop. Boundary-layer flow of nanofluid over a moving surface in a flowing fluid. Int. J. Therm. Sci. 2010; 49, 1663-8.
M Patel and MG Timol. Orthogonal stagnation point flow of a power law fluid towards a stretching surface. Int. J. Appl. Math. Mech. 2011; 7, 31-7.
N Bachok, A Ishak and I Pop. On the stagnation point flow towards a stretching sheet with homogeneous-heterogeneous reactions effects. Comm. Nonlinear Sci. Numer. Simulat. 2011; 16, 4296-302.
AV Kuznetsov and DA Nield. Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Therm. Sci. 2010; 49, 243-7.
N Bachok, A Ishak and I Pop. Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet. Phys. Lett. A 2010; 374, 4075-9.
N Bachok, A Ishak and I Pop. Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid. Int. J. Heat Mass Tran. 2012; 55, 8122-8.
M Ashraf and M Rashid. MHD boundary layer stagnation point flow and heat transfer of a micropolar fluid towards a heated shrinking sheet with radiation and heat generation. World Appl. Sci. J. 2012; 16, 1338-51.
AA Afify and NS Elgazery. Lie group analysis for the effects of chemical reaction on MHD stagnation-point flow of heat and mass transfer towards a heated porous stretching sheet with suction or injection. Nonlinear Anal. Model. Contr. 2012; 17, 1-15.
M Ferdows, MS Khan, MM Alam and S Sun. MHD mixed convective boundary layer flow of a nanofluid through a porous medium due to an exponentially stretching sheet. Math. Prob. Eng. 2012; 2012, Article ID 408528.
B Bidin and R Nazar. Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Eur. J. Sci. Res. 2009; 33, 710-7.
A Ishak. MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malays. 2011; 40, 391-5.
Y Ding, H Chen, L Wang, CY Yang, Y He, W Yang, WP Lee, L Zhang and R Huo. Heat transfer intensification using nanofluids. Kona 2007; 25, 23-38.
CH Chen. Effects of magnetic field and suction or injection on convection heat transfer of non-Newtonian power law fluids past a power law stretched sheet with surface seat slux. Int. J. Therm. Sci. 2008; 47, 954-61.
RD Cess. The interaction of thermal radiation with free convection heat transfer. Int. J. Heat Mass Tran. 1966; 9, 1269-77.
FM Hady, FS Ibrahim, SM Abdel-Gaied and MR Eid. Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet. Nanoscale Res. Lett. 2012; 7, Article ID 229.
T Cebeci and P Bradshaw. Physical and Computational Aspects of Convective Heat Transfer. Springer-Verlag, New York, 1988.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Walailak University
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.