Skip to main content
×
Home

Finite Element Solution for MHD Flow of Nanofluids with Heat and Mass Transfer through a Porous Media with Thermal Radiation, Viscous Dissipation and Chemical Reaction Effects

  • Shafqat Hussain (a1)
Abstract
Abstract

In this paper, the problem of magnetohydrodynamics (MHD) boundary layer flow of nanofluid with heat and mass transfer through a porous media in the presence of thermal radiation, viscous dissipation and chemical reaction is studied. Three types of nanofluids, namely Copper (Cu)-water, Alumina (Al 2 O 3)-water and Titanium Oxide (TiO 2)-water are considered. The governing set of partial differential equations of the problem is reduced into the coupled nonlinear system of ordinary differential equations (ODEs) by means of similarity transformations. Finite element solution of the resulting system of nonlinear differential equations is obtained using continuous Galerkin-Petrov discretization together with the well-known shooting technique. The obtained results are validated using MATLAB “bvp4c” function and with the existing results in the literature. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and the impact of various physical parameters such as the magnetic parameter M, solid volume fraction of nanoparticles 𝜙 and type of nanofluid on the flow is discussed. The results obtained in this study confirm the idea that the finite element method (FEM) is a powerful mathematical technique which can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

Copyright
Corresponding author
*Corresponding author. Email: shafqat.hussain@cust.edu.pk (S. Hussain)
References
Hide All
[1] Sakiadis B. C., Boundary-layer behavior on continuous solid surfaces: I. boundary-layer equations for two-dimensional and axisymmetric flow, AIChE J., 7(1) (1961), pp. 2628.
[2] Sakiadis B. C., Boundary-layer behavior on continuous solid surfaces: II. the boundary layer on a continuous flat surface, AIChE J., 7(2) (1961), pp. 221225.
[3] Sakiadis B. C., Boundary-layer behavior on continuous solid surfaces: III. the boundary layer on a continuous cylindrical surface, AIChE J., 7(3) (1961), pp. 467472.
[4] Tsou F., Sparrow E. and Goldstein R., Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. Heat Mass Transfer, 10(2) (1967), pp. 219235.
[5] Crane L., Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, 21(4) (1970) pp. 645647.
[6] Chakrabarti A. and Gupta A. S., Hydromagnetic flow and heat transfer over a stretching sheet, Quarterly Appl. Math., 37 (1979), pp. 7378.
[7] Grubka L. J. and Bobba K. M., Heat transfer characteristics of a continuous, stretching surface with variable temperature, J. Heat Transfer, 107 (1985), pp. 248250.
[8] Andersson H., Bech K. and Dandapat B., Magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Int. J. Nonlinear Mech., 27(6) (1992), pp. 929936.
[9] Chen C. H., Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat Mass Transfer, 33(5-6) (1998), pp. 471476.
[10] Vajravelu K. and Rollins D., Hydromagnetic flow of a second grade fluid over a stretching sheet, Appl. Math. Comput., 148(3) (2004), pp. 783791.
[11] Cortell R., A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Appl. Math. Comput., 168(1) (2005), pp. 557566.
[12] Abel M. S. and Mahesha N., Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation, Appl. Math. Model., 32(10) (2008), pp. 19651983.
[13] Aziz A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simulation, 14(4) (2009), pp. 10641068.
[14] Yohannes K. and Shankar B., Heat and mass transfer in mhd flow of nanofluids through a porous media due to a stretching sheet with viscous dissipation and chemical reaction effects, Caribbean J. Sci. Tech., 1 (2013),, pp. 0117.
[15] Choi S., Enhancing thermal conductivity of fluids with nanoparticles, developments and applications of non-newtonian flows, Argonne National Laboratory, United States, 66 (1993), pp. 99105.
[16] Kang H. U., Kim S. H. and Oh J. M., Estimation of thermal conductivity of nanofluid using experimental effective particle volume, Exp. Heat Transfer, 19(3) (2006), pp. 181191.
[17] Vasu V., Rama K. K. and Chandra A. K. S., Empirical correlations to predict thermophysical and heat transfer characteristics of nanofluids, Thermal Sci., 12 (2008), pp. 2737.
[18] Rudyak V., Belkin A. and Tomilina E., On the thermal conductivity of nanofluids, Tech. Phys. Lett., 36(7) (2010), pp. 660662.
[19] Aziz A., Khan W. and Pop I., Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms, Int. J. Thermal Sci., 56(0) (2012), pp. 4857.
[20] Wang X.-Q. and Mujumdar A. S., Heat transfer characteristics of nanofluids: a review, Int. J. Thermal Sci., 46(1) (2007), pp. 119.
[21] Wen D. and Ding Y., Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions, Int. J. Heat Mass Transfer, 47(24) (2004), pp. 51815188.
[22] Xuan Y. and Li Q., Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Flow, 21(1) (2000), pp. 5864.
[23] Albadr J., Tayal S. and Alasadi M., Heat transfer through heat exchanger using al2o3 nanofluid at different concentrations, Case Studies Thermal Eng., 1(1) (2013), pp. 3844.
[24] Abbasbandy S., A numerical solution of blasius equation by adomian's decomposition method and comparison with homotopy perturbation method, Chaos, Solitons & Fractals, 31(1) (2007), pp. 257260.
[25] Elgazery N. S., Numerical solution for the falknerskan equation, Chaos, Solitons & Fractals, 35(4) (2008), pp. 738746.
[26] Kuo B. L., Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method, Int. J. Heat Mass Transfer, 48(2324) (2005), pp. 50365046.
[27] Wazwaz A. M., The variational iteration method for solving two forms of blasius equation on a half-infinite domain, Appl. Math. Comput., 188(1) (2007), pp. 485491.
[28] Liao S., Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Series–Modern Mechanics and Mathematics, Chapman & Hall/CRC Press, 2004.
[29] Yao B. and Chen J., A new analytical solution branch for the blasius equation with a shrinking sheet, Appl. Math. Comput., 215(3) (2009), pp. 11461153.
[30] Yao B. and Chen J., Series solution to the falknerskan equation with stretching boundary, Appl. Math. Comput., 208(1) (2009), pp. 156164.
[31] Noiey A. R., Haghparast N., Miansari M. and Ganji D. D., Application of homotopy perturbation method to the mhd pipe flow of a fourth grade fluid, J. Physics: Conference Series, 96(1) (2008), 012079.
[32] Motsa S. S. and Shateyi S., A new approach for the solution of three-dimensional magnetohydrodynamic rotating flow over a shrinking sheet, Math. Problems Eng., 2010 (2010), 15 pages.
[33] Makukula Z. G., Sibanda P., Motsa S. S. and Shateyi S., On new numerical techniques for the mhd flow past a shrinking sheet with heat and mass transfer in the presence of a chemical reaction, Math. Problems Eng., 2011 (2011), 19 pages.
[34] Schieweck F., A-stable discontinuous Galerkin-Petrov time discretization of higher order, J. Numer. Math., 18 (2010), pp. 2557.
[35] Matthies G. and Schieweck F., Higher order variational time discretizations for nonlinear systems of ordinary differential equations, Preprint 23/2011, Otto-von-Guericke Universität Magdeburg, Fakultät für Mathematik (2011).
[36] Hussain S., Schieweck F. and Turek S., Higher order Galerkin time discretizations and fast multigrid solvers for the heat equation, J. Numer. Math., 19(1) (2011), pp. 4161.
[37] Haile E. and Shankar B., Heat and mass transfer through a porous media of MHD flow of nanofluids with thermal radiation, viscous dissipation and chemical reaction effects, American Chemical Science J., 4 (2014), pp. 828846.
[38] Hamad M., Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field, Int. Commun. Heat Mass Transfer, 38(4) (2011), pp. 487492.
[39] Kameswaran P., Narayana M., Sibanda P. and Murthy P., Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects, Int. J. Heat Mass Transfer, 55 (2526) (2012), pp. 75877595.
[40] Rosseland S., Theoretical Astrophysics: Atomic Theory and the Analysis of Stellar Atmosphere and Envelopes, The International Series of Monographs on Nuclear Energy: Reactor Design Physics, At the Clarendon Press, 1936.
[41] Cess R., The interaction of thermal radiation with free convection heat transfer, Int. J. Heat Mass Transfer, 9(11) (1966), pp. 12691277.
[42] Arpaci V. S., Effect of thermal radiation on the laminar free convection from a heated vertical plate, Int. J. Heat Mass Transfer, 11(5) (1968), pp. 871881.
[43] Cheng E. and Özişik M., Radiation with free convection in an absorbing, emitting and scattering medium, Int. J. Heat Mass Transfer, 15(6) (1972), pp. 12431252.
[44] Hossain M. and Takhar H., Radiation effect on mixed convection along a vertical plate with uniform surface temperature, Heat Mass Transfer, 31(4) (1996), pp. 243248.
[45] Siddiqa S., Hossain M. and Saha S. C., The effect of thermal radiation on the natural convection boundary layer flow over a wavy horizontal surface, Int. J. Thermal Sci., 84 (2014), pp. 143150.
[46] Srivastava A. C. and Hazarika G. C., Shooting method for third order simultaneous ordinary differential equations with application to magnetohydrodynamic boundary layer, Math. Problems Eng., 40 (1990), pp. 263273.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 56 *
Loading metrics...

Abstract views

Total abstract views: 332 *
Loading metrics...

* Views captured on Cambridge Core between 18th January 2017 - 25th November 2017. This data will be updated every 24 hours.