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Effects of Thermal Radiation on Mixed Convection in a MHD Nanofluid Flow over a Stretching Sheet Using a Spectral Relaxation Method

Authors: Precious Sibanda, Sabyasachi Mondal, Nageeb A. H. Haroun


The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: Nanofluid, Thermal radiation, Magnetic Field, non-isothermal wedge, soret and dufour effects

Digital Object Identifier (DOI):

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[1] A. Subhas, P. H. Veena, “Visco-elastic fluid flow and heat transfer in porous medium over a stretching sheet”, Int. J. Non-linear Mech. vol. 33, pp, 531–540, 1998.
[2] K. V. Prasad, M. S. Abel, A. Joshi, “Oscillatory motion of a visco-elastic liquid over a stretching sheet in porous media”, J. Porous Media, vol. 3, PP. 61–68, 2000.
[3] H. Blasius, “Grenzschichten in Flussigkeiten Mit Kleiner Reibung”, Zeitschrift f¨ur Angewandte Mathematik und Physik, vol. 56, pp. 1–37, 1908.
[4] L. Howarth, “On the solution of the laminar boundary layer equations”, Proceedings of the Society of London, Mathematical and Physical Sciences, vol. 919, pp. 547–579, 1938.
[5] L. J. Crane, “Flow past a stretching plate”, Zeitschrift f¨ur Angewandte Mathematik und Physik, ZAMP vol. 21, pp. 645–647, 1970.
[6] P. S. Gupta, A. S. Gupta, “Heat and mass transfer on a stretching sheet with suction or blowing”, Can. J. Chem. Eng., vol. 55, pp. 744–746, 1977.
[7] Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo, “The analysis of hydromagnetic free convection heat and mass transfer flow over a stretching vertical plate with suction”, Amer. J. Comput. Appl. Math., vol. 1, pp. 20–26, 2011.
[8] S. J. Liao, “Series solutions of unsteady boundary layer flows over a stretching flat plate”, Studies Applied Mathematics, vol. 117, pp. 239–263, 2006.
[9] H. Xu, S. J. Liao, I. Pop, “Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate”, Eur. J. Mech. B/Fluids, vol. 26, pp. 15–27, 2007.
[10] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, “Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of − Al2O3, SiO2 and TiO2 ultra-fine particles)”, Netsu. Bussei., vol. 7, pp. 227–233, 1993.
[11] J. Buongiorno, W. Hu, “Nanofluid coolants for advanced nuclear power plants”, Proceedings of ICAPP05, Seoul, 15-19 May 2005, vol. 5, pp. 15–15.
[12] S. Choi, Z. Zhang, W. Yu, F. Lockwood, E. Grulke, “Anomalously thermal conductivity enhancement in nanotube suspensions”, Appl. Phys. Letters, vol. 79, pp. 2252–2254, 2001.
[13] N. A. H. Haroun, S. Mondal, P. Sibanda, S. S. Motsa, M. M. Rashidi, “Heat and mass transfer of nanouid through an impulsively vertical stretching surface using the spectral relaxation method”, Boundary Value Problems vol. 2015, no. 161, pp. 1-16, 2015.
[14] N. A. H. Haroun, S. Mondal, P. Sibanda,“The effects of thermal radiation on an unsteady MHD axisymmetric stagnation- point flow over a shrinking sheet in presence of temperature dependent thermal conductivity with Navier slip”, PLoS One, vol. 10, no. 9: e0138355. doi:10.1371/journal.pone.0138355, 2015.
[15] N. A. H. Haroun, S. Mondal, P. Sibanda, “Unsteady natural convective boundary-layer flow of MHD nanofluid over a stretching surfaces with chemical reaction using the spectral relaxation method: A revised model”, Procedia Engineering, vol. 127, pp. 18 - 24, 2015.
[16] I. S. Oyelakin, S. Mondal, P. Sibanda, “Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions”, Alexandria Engineering Journal, vol. 55, no. 2, pp. 10251035, 2016.
[17] T. M. Agbaje, S. Mondal, Z. G. Makukula, S. S. Motsa, P. Sibanda, “A new numerical approach to MHD stagnation point flow and heat transfer towards a stretching Sheet”,Ain Shams Engineering Journal doi:10.1016/j.asej.2015.10.015, 2016.
[18] J. A. Gbadeyan, A. S. Idowu, A. W. Ogunsola, O. O. Agboola, P. O. Olanrewaju, “Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid in the presence of magnetic field”, Global J. Sci. Front. Res., vol. 11, pp. 1–19, 2011.
[19] M. J. Subhakar, K. Gangadhar, “Soret and Dufour effects on MHD free convection heat and mass transfer flow over a stretching vertical plate with suction and heat source/sink”, Int. J. Modern Eng. Res., vol. 2, pp. 3458–3468, 2012.
[20] T. R. Mahapatra, S. Mondal, D. Pal, “Heat transfer due to magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface in the presence of thermal radiation and suction/injection”, ISRN Thermodynamics vol. 9, pp. 1–9, 2012.
[21] Md. S. Khan, Md. M. Alam, M. Ferdows, “Effects of magnetic field on radiative flow of a nanofluid past a stretching sheet”, Procedia Engineering vol. 56, pp. 316–322, 2013.
[22] P. Singh, D. Sinha, N. S. Tomer, “Oblique stagnation-point Darcy flow towards a stretching sheet”, J. Appl. Fluid Mech., vol. 5, pp. 29–37, 2012.
[23] A. M. Rohni, S. Ahmad, Md. I. A. Ismail, I. Pop, “Flow and heat transfer over an unsteady shrinking sheet with suction in a nanofluid using Buongiorno’s model”, Int. Commu. Heat Mass Trans., vol. 43, pp. 75–80, 2013.
[24] J. Buongiorno, “Convective transport in nanofluids”, ASME Journal of Heat Transfer, vol. 128, pp. 240–250, 2006.
[25] H. F. Oztop, E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids”, Int. J. Heat Fluid Flow, vol 29 pp. 1326–1336, 2008.
[26] P.E. Gharagozloo,J. K. Eaton, K. E. Goodson, “Diffusion, aggregation, and the thermal conductivity of nanofluids”,Appl. Phys. Lett. vol. 93, pp. 103110,, 2008.
[27] J. Philip, P. D. Shima, B. Raj, “Nanofluid with tunable thermal properties”, Appl. Phys. Lett., vol. 92, pp. 043108,, 2008.
[28] N. A. H. Haroun, P. Sibanda, S. Mondal, S. S. Motsa, “On unsteady MHD mixed convection in a nanofluid due to a stretching/shrinking surface with suction/injection using the spectral relaxation method”, Boundary Value Problems, vol. 15, pp. 1–17, 2015.
[29] S. S. Motsa, “A new spectral relaxation method for similarity variable nonlinear boundary layer flow systems”, Chem. Eng. Commu., vol. 16, pp. 23–57, 2013.
[30] K. A. Yih, “MHD forced convection flow adjacennt to a non-isothermal wedge”, Int. Commun. Heat Mass Trans., vol. 26, pp. 819–827, 1999.
[31] R. K. Tiwari, M. K. Das, “Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids”, Int. J. Heat Mass Trans., vol. 50, pp. 2002–2018, 2007.
[32] H. C. Brinkman, “The viscosity of concentrated suspensions and solution”, J. Chem. Phys. vol. 20, pp. 571–581, 1952.
[33] E. Abu-Nada, “Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step”, Int. J. Heat Fluid Flow, vol. 29, pp. 242–249, 2008.
[34] M. Sheikholeslami, M. G. Bandpy, D. D. Ganji, S. Soleimani, S. M. Seyyedi, “Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field”, Int. Commun. Heat Mass Trans., vol. 39, pp. 1435–1443, 2012.
[35] S. S. Motsa, P. G. Dlamini, M. Khumalo, “Spectral relaxation method and spectral quasilinearization method for solving unsteady boundary layer flow problems”, Adv. Math. Phys., vol. 12, Article ID 341964, doi 10.1155/2014/341964, 2014.
[36] S. S. Motsa, Z. G. Makukula, “On spectral relaxation method approach for steady von Karman flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation”, Cent. Eur. J. Phys., vol. 11, pp. 363–374, 2013.
[37] P. K. Kameswaran, M. Narayana, P. Sibanda, P. V. S. N. Murthy, “Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects”, Int. J. Heat Mass Trans., vol. 55, pp. 7587–7595, 2012.
[38] P. K. Kameswaran, P. Sibanda, “Thermal dispersion effects on convective heat and mass transfer in an Ostwald de Waele nanofluid flow in porous media”, Boundary Value Problems, vol. 10, pp. 1–12, 2013.