Unsteady Heat and Mass Transfer in MHD Flow of Nanofluids over Stretching Sheet with a Non-Uniform Heat Source/Sink

Authors: Bandaris Shankar, Yohannes Yirga

Abstract:

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.

Keywords: Manetohydrodynamics, nanofluid, non-uniform heat source/sink, unsteady.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336496

References:

[1] C. D. S. Devi, H. S. Takhar, G. Nath, "Unsteady mixed convection flow in stagnation region adjacent to a vertical surface,” Heat Mass Transfer, 26(1991) 71-79.
[2] E. M. A. Elbashbeshy, M. A. A. Bazid, "Heat transfer over an unsteady stretching surface,” Heat Mass Transfer, 41(2004) 1-4.
[3] R. Tsai, K. H. Huang, J. S. Huang, "Flow and heat transfer over an unsteady stretching surface with non-uniform heat source,” Int. Commun. Heat Mass Transfer, 35(2008) 1340-1343.
[4] A. Ishak, Unsteady, "MHD flow and heat transfer over a stretching plate,” J. Appied Sci. 10(18)(2010) 2127-2131.
[5] K. Sarit, Das SUSC, Yu. Wenhua, T. Pradeep, "Nanofluids Science and Technology,” 1 edition, Honboken, NJ, John Wiley & Sons, Inc, 2007.
[6] 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 Engineering, 29(5) (2008) 432-460 (1).
[7] 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)181–191.
[8] 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) 27–37.
[9] V.Y. Rudyak, A.A. Belkin, E.A. Tomilina, "On the thermal conductivity of nanofluids,” Tech. Phys. Lett. 36 (7) (2010) 660–662.
[10] 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) 227–233.
[11] 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.
[12] J. Buongiorno, "Convective transport in nanofluids,” ASME J Heat Transf, 128(2006)240-250.
[13] W. A. Khan, Pop I., "Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid,” Journal of Heat Transfer, vol. 133(2011)9.
[14] O.D. Makinde, Aziz A., "MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition,” International Journal of Thermal Sciences 49(2010)1813-1820.
[15] P. Ganesan, G. Palani, "Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux,” International Journal of Heat and Mass Transfer, 47(19-20)(2004) 4449–4457.
[16] 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) 1–11.
[17] 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.
[18] 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.
[19] A. Ishak, "Unsteady MHD flow and heat transfer over a stretching plate,” J.Applied sci. 10(18)(2010) 2127-2130.
[20] T. Fang, J. Zhang, S. Yao, "Slip MHD viscous flow over a stretching sheet – an exact solution,” Commun. Nonlinear Sci. Numer. Simul. 14 (11) (2009) 3731– 3737.
[21] T. Fang, J. Zhang, S. Yao, "Slip magnetohydrodynamic viscous flow over a permeable shrinking sheet,” Chin. Phys. Lett. 27 (12) (2010)124702.
[22] O. D. Makinde, "Entropy analysis for MHD boundary layer flow and heat transfer over a flat plate with a convective surface boundary condition,” Int. Journal of Exergy, 10(2)(2012)142-154.
[23] 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)327–350.
[24] 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) 1326–1336.
[25] R.K. Tiwari, M.N. Das, "Heat tranfer augmentation in a two – sided lid – driven diffrentially heated square cavity utilizing nanofluids,” Int. J. Heat Mass Transfer 50 (2007) 2002–2018.
[26] S. Ahmad, A. M. Rohni, I. Pop, 2011, "Blasius and Sakiadis problems in nanofluids,” Acta Mech. 218 (2011) 195–204.
[27] Abo-Eldahab EM, Aziz MAE, "Blowing/suction effect on hydromagnetic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation/absorption,” Intl J. Thermal Sci. 43 (7)(2004)709-719.
[28] T. Cebeci, P.Pradshaw, "Physical and Computational Aspects of Convective Heat Transfer,” New York:Springer, 1988.
[29] Hayat T, Hussain Q, Javed T. "The modified decomposition method and pade approximation for the MHD flow over a non-linear stretching sheet,” Nonlinear Anal: Real World Applications, 10(2)(2009) 966-973.
[30] Vajravelu K, Roper T , "Flow and heat transfer in a second grade fluid over a stretching sheet,” Intl J. Non-Linear Mech. 34 (6)(1999)1031-1036.