FEM Simulation of Triple Diffusive Magnetohydrodynamics Effect of Nanofluid Flow over a Nonlinear Stretching Sheet

Authors: Rangoli Goyal, Rama Bhargava

Abstract:

The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, Thermophoresis, Diffusiophoresis, Brownian motion.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1126273

References:

[1] Bachok N, Ishak A, Pop I (2012) Unsteady boundary layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet. Int. J. Heat Mass Transf. 55, 2102-2109.
[2] Buongiorno J. (2006) Convective transport in nanofluids. Jounal of Heat Transfer 128(3):240-250.
[3] Cortell R (2011) Heat and fluid flow due to non-linearly stretching surfaces, Appl Math Comput 217(19):7564-7572.
[4] Goyal M., Bhargava R., (2014) Numerical study of thermodiffusion effects on boundary layer flow of nanofluids over a power law stretching sheet, Microfluid Nanofluid, 17:591-604.
[5] Hamad MAA, Ferdows M (2012) Similarity solutions to viscous flow and heat transfer of nanofluid over non linearly stretching sheet, Appl. Math. Mech. 33, 923-930.
[6] Kechil S.A., Hashim I. (2008) Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field, Phys. Lett. A, 372, pp. 2258-2263.
[7] Khan WA, Aziz A (2011) Double diffusive natural convective boundary layer flow in a porous medium saturated with a nanofluid over a vertical plate: prescribed surface heat, solute and nanoparticle fluxes. Int. J. Therm. Sci. 50, 2154-2160.
[8] Kumaran, V., Ramanaiah, G. (1996) A note on the flow over a stretching sheet. ActaMechanica 116 (1-4), 229-233.
[9] Kuznetsov A, Nield D (2011) Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Therm. Sci. 50(5):712-717.
[10] Makinde OD, Aziz A (2011) Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Therm. Sci. 50, 1326-1332.
[11] Matin MH, Dehsara M, Abbassi A (2012) Mixed convection MHD flow of nanofluid over a non-linear stretching sheet with effects of viscous dissipation and variable magnetic field, Mechanika Vol. 18(4), 415-423.
[12] Narayana M, Sibanda P (2012) Laminar flow of a nanoliquid film over an unsteady stretching sheet, Int. J. Heat Mass Transf. 55, 7552-7560.
[13] Nkurikiyimfura I, Wang Y, Pan Z (2013) Heat transfer enhancement by magnetic nanofluids - A review, Renewable and Sustainable Energy Reviews 21, 548-561.
[14] Odenbach S. (2004) Recent progress in magnetic fluid research. Journal of Physics: Condensed Matter 16: R1135-50.
[15] Reddy JN (1985) An introduction to the finite element method. McGraw-Hill Book Co, New York.
[16] Sakiadis BC. (1961) Boundary layer behaviour on continuous moving solid surfaces, I. Boundary layer equations for two-dimensional and axis-symmetric flow, II. Boundary layer on a continuous flat surface, III. Boundary layer on a continuous cylindrical surface. Am InstChemEng J; 7:26-8. 221-225, 467-472.
[17] Vajravelu K. (2001) Viscous flow over a nonlinearly stretching sheet, Applied Mathematics and Computation, vol. 124, no. 3, pp. 281-288.
[18] Vajravelu K., Prasad KV, Ng C (2013) Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties, Nonlinear analysis: Real world applications 14, 455-464.
[19] Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultrafine particles. NetsuBussei 7(4):227-233.
[20] Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA (2001) Anomalous thermal conductivity enhancement in nanotube suspensions. ApplPhysLett 79(14):2252-2254.
[21] Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-newtonian flows, ASME FED-vol. 231/MD-vol. 66:99-105.
[22] Crane, L.J., (1970) Flow past a stretching plate, Volume 21, Issue 4, pp 645-647.
[23] Ziabakhsh Z., G. Domairry, H. Bararnia and H. Babazadeh (2010), Analytical solution of flow and diffusion of chemically reactive species over a non-linearly stretching sheet immersed in a porous medium. Journal of the Taiwan Institute of Chemical Engineers, vol. 14, 22-28.
[24] Lin YY, Lo SP (2003) Finite element modelling for chemical mechanical polishing process under different back pressures. J Mater Process Technol 140(1-3):646-652
[25] Dettmer W, Peric D (2006) A computational framework for fluid-rigidbody interaction: finite element formulation and applications. Comput Methods ApplMechEng 195(13-16):1633-1666.
[26] Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods ApplMechEng 193(33-35):3523-3540.