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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 (Al2O3)-water and Titanium Oxide (TiO2)-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.

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*Corresponding author. Email:shafqat.hussain@cust.edu.pk (S. Hussain)
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[1] B. C. Sakiadis , 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] B. C. Sakiadis , Boundary-layer behavior on continuous solid surfaces: II. the boundary layer on a continuous flat surface, AIChE J., 7(2) (1961), pp. 221225.

[3] B. C. Sakiadis , Boundary-layer behavior on continuous solid surfaces: III. the boundary layer on a continuous cylindrical surface, AIChE J., 7(3) (1961), pp. 467472.

[4] F. Tsou , E. Sparrow and R. Goldstein , Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. Heat Mass Transfer, 10(2) (1967), pp. 219235.

[5] L. Crane , Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, 21(4) (1970) pp. 645647.

[6] A. Chakrabarti and A. S. Gupta , Hydromagnetic flow and heat transfer over a stretching sheet, Quarterly Appl. Math., 37 (1979), pp. 7378.

[7] L. J. Grubka and K. M. Bobba , Heat transfer characteristics of a continuous, stretching surface with variable temperature, J. Heat Transfer, 107 (1985), pp. 248250.

[8] H. Andersson , K. Bech and B. Dandapat , Magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Int. J. Nonlinear Mech., 27(6) (1992), pp. 929936.

[9] C. H. Chen , Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat Mass Transfer, 33(5-6) (1998), pp. 471476.

[12] M. S. Abel and N. Mahesha , 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] A. Aziz , 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.

[16] H. U. Kang , S. H. Kim and J. M. Oh , Estimation of thermal conductivity of nanofluid using experimental effective particle volume, Exp. Heat Transfer, 19(3) (2006), pp. 181191.

[18] V. Rudyak , A. Belkin and E. Tomilina , On the thermal conductivity of nanofluids, Tech. Phys. Lett., 36(7) (2010), pp. 660662.

[19] A. Aziz , W. Khan and I. Pop , 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] X.-Q. Wang and A. S. Mujumdar , Heat transfer characteristics of nanofluids: a review, Int. J. Thermal Sci., 46(1) (2007), pp. 119.

[21] D. Wen and Y. Ding , 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] Y. Xuan and Q. Li , Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Flow, 21(1) (2000), pp. 5864.

[23] J. Albadr , S. Tayal and M. Alasadi , Heat transfer through heat exchanger using al2o3 nanofluid at different concentrations, Case Studies Thermal Eng., 1(1) (2013), pp. 3844.

[24] S. Abbasbandy , 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] N. S. Elgazery , Numerical solution for the falknerskan equation, Chaos, Solitons & Fractals, 35(4) (2008), pp. 738746.

[26] B. L. Kuo , Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method, Int. J. Heat Mass Transfer, 48(2324) (2005), pp. 50365046.

[34] F. Schieweck , A-stable discontinuous Galerkin-Petrov time discretization of higher order, J. Numer. Math., 18 (2010), pp. 2557.

[36] S. Hussain , F. Schieweck and S. Turek , Higher order Galerkin time discretizations and fast multigrid solvers for the heat equation, J. Numer. Math., 19(1) (2011), pp. 4161.

[37] E. Haile and B. Shankar , 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] M. Hamad , 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] P. Kameswaran , M. Narayana , P. Sibanda and P. Murthy , 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.

[41] R. Cess , The interaction of thermal radiation with free convection heat transfer, Int. J. Heat Mass Transfer, 9(11) (1966), pp. 12691277.

[42] V. S. Arpaci , 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] E. Cheng and M. Özişik , Radiation with free convection in an absorbing, emitting and scattering medium, Int. J. Heat Mass Transfer, 15(6) (1972), pp. 12431252.

[44] M. Hossain and H. Takhar , Radiation effect on mixed convection along a vertical plate with uniform surface temperature, Heat Mass Transfer, 31(4) (1996), pp. 243248.

[45] S. Siddiqa , M. Hossain and S. C. Saha , 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.

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Advances in Applied Mathematics and Mechanics
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