Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30673
Heat and Mass Transfer in MHD Flow of Nanofluids through a Porous Media Due to a Permeable Stretching Sheet with Viscous Dissipation and Chemical Reaction Effects

Authors: Yohannes Yirga, Daniel Tesfay


The convective heat and mass transfer in nanofluid flow through a porous media due to a permeable stretching sheet with magnetic field, viscous dissipation, chemical reaction and Soret effects are numerically investigated. Two types of nanofluids, namely Cu-water and Ag-water were studied. The governing boundary layer equations are formulated and reduced to a set of ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier linearly stretching sheet problems in the literature.

Keywords: Nanofluid, Heat and Mass Transfer, Magnetohydrodynamics

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3283


[1] L. J. Crane, Flow past a stretching plate, Z Angew. Math. Phys. (ZAMP) 21(1970) 645 -647.
[2] L. E. Erickson, L. T. Fan and V. G. Fox, Heat and mass transfer on a moving continuous flat plate with suction or injection, Ind. Eng. Chem. Fundam. 5(1966)19 - 25.
[3] L. G. Grubka, K.M. Bobba, Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J. Heat Transfer 107 (1985) 248250.
[4] C.-H. Chen, Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat Mass Transfer 33(1998)471 - 476.
[5] E. M. Abo-Eldahab, M.A. El-Aziz, Blowing/suction effect on hydromagnetic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation/absorption, Int. J. Therm. Sci. 43(2004)709 - 719.
[6] P. Ganesan, G. Palani, Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux, Int. J. of Heat and Mass Transfer, 47(19-20)(2004) 4449- 4457.
[7] K. Jafar, R. Nazar, A. Ishak, I. Pop, MHD flow and heat transfer over stretching/shrinking sheets with external magnetic field, viscous dissipation and Joule Effects, Can. J. Chem. Eng. 9999 (2011) 111.
[8] M.A.A. Hamada, I. Pop, A.I. Md Ismail, Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate, Nonlinear Anal. Real World Appl. 12 (2011) 1338-1346.
[9] K.V. Prasad, D. Pal, V. Umesh, N.S. Prasanna Rao, The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet, Commun. Nonlinear Sci. Numer. Simul. 15 (2) (2010) 331-334.
[10] A. Beg, A.Y. Bakier, V.R. Prasad, Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects, Comput. Mater. Sci. 46 (2009) 57-65.
[11] T. Fang, J. Zhang, S. Yao, SlipMHD viscous flow over a stretching sheet an exact solution, Commun. Nonlinear Sci. Numer. Simul. 14 (11) (2009) 3731- 3737.
[12] T. Fang, J. Zhang, S. Yao, Slip magnetohydrodynamic viscous flow over a permeable shrinking sheet, Chin. Phys. Lett. 27 (12) (2010)124702.
[13] Einstein, A., Ann. phys., 19, 286(1906); Ann. Phys., 34, 591(1911).
[14] K. Vajravelu, A. Hadjinicolaou, Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation, Int. Commun. in Heat and Mass Transfer, 20(3) (1993)417-430.
[15] T. G.Motsumi, O. D.Makinde, Effects of thermal radiation and viscous dissipation on boundary layer flow of nanofluids over a permeable moving flat plate, Phys. Scr. 86 (2012) 045003 (8pp).
[16] B. Gebhart, Effect of viscous dissipation in natural convection, J. Fluid Mech. 14 (1962) 225232.
[17] B. Gebhart, J. Mollendorf, Viscous dissipation in external natural convection flows, J. Fluid Mech. 38(1969) 97107.
[18] A. Javad, S. Sina, viscous flow over nonlinearly stretching sheet with effects of viscous dissipation, J. Appl. Math. (2012)110. ID 587834.
[19] M. Habibi Matin, M. Dehsara, A. Abbassi, 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) (2012) 415-423.
[20] F. Khani, A. Farmany, M. Ahmadzadeh Raji, Abdul Aziz, F. Samadi, Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects,Commun Nonlinear Sci Numer Simulat 14(2009) 38673878.
[21] M. H. Yazdi, S. Abdullah, I. Hashim, A. Zaharim, K. Sopian, Entropy Generation Analysis of the MHD Flow over Nonlinear Permeable Stretching Sheet with Partial Slip, IASME/WSEAS Energy & environment (6)(2011) 292-297.
[22] Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. Can J.Chem Eng. 1977;55:7446.
[23] Vajravelu K. Hydromagnetic flow and heat transfer over a continuous, moving, porous, flat surface. Acta Math 1986;64:17985.
[24] Chen C.K, Char M. Heat transfer of a continuous stretching surface with suction or blowing, J. Math. Anal Appl. 1988;135:56880.
[25] Chaudhary MA, Merkin JH, Pop I. Similarity solutions in the free convection boundary layer flows adjacent to vertical permeable surface in porous media. Eur J Mech B/Fluids 1995; 14:21737.
[26] Magyar E, Keller B. Exact solutions for self-similar boundary layer flows induced by permeable stretching wall. Eur J Mech BFluids 2000; 19:10922.
[27] A.J. Chamka, MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction, Int. Commun. Heat Mass Transfer 30 (2003) 413-422.
[28] A. Afifi, MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, J. Heat and Mass Transfer 40 (2004) 495500.
[29] A. Postelnicu, Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects, J. Heat and Mass Transfer 43(2007) 595602.
[30] R. Kandasamy, P.G. Palanimani, Effects of chemical reactions, heat, and mass transfer on nonlinear magnetohydrodynamic boundary layer flow over a wedge with a porous medium in the presence of ohmic heating and viscous dissipation, J. Porous Media 10 (2007) 489502.
[31] K. Sarit, Das SUSC, Yu. Wenhua, T. Pradeep, Nanofluids Science and Technology. 1 edition, Hon-boken, NJ, John Wiley & Sons, Inc, 2007.
[32] J. Buongiorno, (March 2006), Convective Transport in Nanofluids, Journal of Heat Transfer (ASME) 128 (3) (2010) 240.
[33] W. Yu, D.M. France, J. L. Routbort, and S. U. S. Choi, Review and Comparison of Nanofluid Thermal Conductivity and Heat Transfer Enhancements, Heat Transfer Eng., 29(5) (2008) 432-460 (1).
[34] H.U. Kang, S.H. Kim, J.M. Oh, Estimation of thermal conductivity of nanofluid using experimental effective particle volume, Exp. Heat Transfer 19 (3) (2006)181191.
[35] V. Velagapudi, R.K. Konijeti, C.S.K. Aduru, Empirical correlation to predict thermophysical and heat transfer characteristics of nanofluids, Therm. Sci. 12 (2) (2008) 2737.
[36] V.Y. Rudyak, A.A. Belkin, E.A. Tomilina, On the thermal conductivity of nanofluids, Tech. Phys.Lett. 36(7) (2010) 660662.
[37] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu Bussei 7 (1993) 227233.
[38] J. Buongiorno, W. Hu, Nanofluid coolants for advanced nuclear power plants. Proceedings of ICAPP 05: May 2005 Seoul. Sydney: Curran Associates, Inc, (2005)15-19.
[39] J. Buongiorno, Convective transport in nanofluids. ASME J Heat Transf, 128(2006)240-250.
[40] W. A. Khan, Pop I., Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid, J. Heat Transfer, vol. 133(2011)9.
[41] O.D. Makinde, Aziz A., MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition, Int. J. of Thermal Sci., 49(2010)1813-1820.
[42] H. B. Keller, A new difference scheme for parabolic problems: Numerical solutions of partial differential equations, II (Hubbard, B. ed.), New York: Academic Press, (1971)327350.
[43] H.F. Oztop, E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow 29 (2008) 13261336.
[44] P.K. Kameswaran, S. Shaw, P. Sibanda, P.V.S.N. Murthy, Homogeneous- heterogeneous reactions in a nanofluid flow due to a porous stretching sheet, Int. J. of Heat and Mass Transfer 57 (2013) 465- 472.
[45] R.K. Tiwari, M.N. Das, Heat tranfer augmentation in a two sided lid driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer 50 (2007) 2002-2018.
[46] S. Ahmad, A. M. Rohni, I. Pop, 2011, Blasius and Sakiadis problems in nanofluids, Acta Mech. 218(2011) 195204.
[47] T. Cebeci, P.Pradshaw, Physical and Computational Aspects of Convective Heat Transfer, New York:Springer, 1988.
[48] M.A.A. 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 (2011) 487492.