Effects of Thermal Radiation on Mixed Convection in a MHD Nanofluid Flow over a Stretching Sheet Using a Spectral Relaxation Method
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.
[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, http://dx.doi.org/10.1063/1.2977868, 2008.
[27] J. Philip, P. D. Shima, B. Raj, “Nanofluid with tunable
thermal properties”, Appl. Phys. Lett., vol. 92, pp. 043108,
http://dx.doi.org/10.1063/1.2838304, 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.
[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, http://dx.doi.org/10.1063/1.2977868, 2008.
[27] J. Philip, P. D. Shima, B. Raj, “Nanofluid with tunable
thermal properties”, Appl. Phys. Lett., vol. 92, pp. 043108,
http://dx.doi.org/10.1063/1.2838304, 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:74732", author = "Nageeb A. H. Haroun and Sabyasachi Mondal and Precious Sibanda", title = "Effects of Thermal Radiation on Mixed Convection in a MHD Nanofluid Flow over a Stretching Sheet Using a Spectral Relaxation Method", abstract = "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 = "Non-isothermal wedge, thermal radiation, nanofluid,
magnetic field, Soret and Dufour effects.", volume = "11", number = "2", pages = "56-10", }
