Advertisement

Meccanica

, Volume 48, Issue 2, pp 307–321 | Cite as

Magnetohydrodynamic effects on natural convection flow of a nanofluid in the presence of heat source due to solar energy

  • N. Anbuchezhian
  • K. Srinivasan
  • K. Chandrasekaran
  • R. Kandasamy
Article

Abstract

The objective of the present work is to investigate theoretically the MHD convective flow and heat transfer of an incompressible viscous nanofluid past a porous vertical stretching sheet in the presence of variable stream condition due to solar radiation (incident radiation). The governing equations are derived using the usual boundary-layer and Boussinesq approximations and accounting for the presence of an applied magnetic field and incident radiation flux. The absorbed radiation acts as a distributed source which initiates buoyancy-driven flow and convection in the absorbed layer. The partial differential equations governing the problem under consideration are transformed by a special form of Lie symmetry group transformations viz. one-parameter group of transformation into a system of ordinary differential equations which are solved numerically using Runge Kutta Gill based shooting method. The conclusion is drawn that the flow field and temperature are significantly influenced by radiation, heat source and magnetic field.

Keywords

Lie symmetry group transformation Nanofluids Porous media Magnetic field Convective radiation Heat source 

Notes

Acknowledgements

The authors wish to express their cordial thanks to our beloved The Vice Chancellor and The Dean, FSTPi, UTHM, Malaysia, Head of the department of Mechanical Engineering, Anna University and The Chairman of RMK Engineering College and Sri Guru Institute of Technology, Anna University, India for their encouragements.

References

  1. 1.
    Hunt AJ (1978) Small particle heat exchangers. Report LBL-7841 for the U.S. Department of Energy, Lawrence Berkeley Laboratory Google Scholar
  2. 2.
    Choi S (1995) Enhancing thermal conductivity of fluids with nanoparticle in: Siginer DA, Wang HP (Eds), Developments and applications of non-Newtonian flows, ASME, vol. 231/FED, vol. 66, pp 99–105 Google Scholar
  3. 3.
    Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7:227–233 CrossRefGoogle Scholar
  4. 4.
    Buongiorno J, Hu W (2005) Nanofluid coolants for advanced nuclear power plants. In: Proceedings of ICAPP ’05, Seoul, May 15–19. Paper no. 5705 Google Scholar
  5. 5.
    Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250 CrossRefGoogle Scholar
  6. 6.
    Kuznetsov AV, Nield DA (2011) Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 50:712–717 CrossRefGoogle Scholar
  7. 7.
    Nield DA, Kuznetsov AV (2011) The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 54:374–378 MATHCrossRefGoogle Scholar
  8. 8.
    Cheng P, Minkowycz WJ (1977) Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J Geophys Res 82:2040–2044 ADSCrossRefGoogle Scholar
  9. 9.
    Birkoff G (1948) Mathematics for engineers. Electr Eng 67:1185 Google Scholar
  10. 10.
    Birkoff G (1960) Hydrodynamics. Princeton University Press, Princeton Google Scholar
  11. 11.
    Moran MJ, Gaggioli RA (1968) Similarity analysis via group theory. AIAA J 6:2014–2016 ADSCrossRefGoogle Scholar
  12. 12.
    Moran MJ, Gaggioli RA (1968) Reduction of the number of variables in systems of partial differential equations with auxiliary conditions. SIAM J Appl Math 16:202–215 MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Ibrahim FS, Hamad MAA (2006) Group method analysis of mixed convection boundary layer flow of a micropolar fluid near a stagnation point on a horizontal cylinder. Acta Mech 181:65–81 MATHCrossRefGoogle Scholar
  14. 14.
    Yurusoy M, Pakdemirli M (1997) Symmetry reductions of unsteady three-dimensional boundary layers of some non-Newtonian fluids. Int J Eng Sci 35(2):731–740 MathSciNetCrossRefGoogle Scholar
  15. 15.
    Yurusoy M, Pakdemirli M (1999) Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet. Mech Res Commun 26(1):171–175 MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yurusoy M, Pakdemirli M, Noyan OF (2001) Lie group analysis of creeping flow of a second grade fluid. Int J Non-Linear Mech 36(8):955–960 MathSciNetCrossRefGoogle Scholar
  17. 17.
    Avramenko AA, Kobzar SG, Shevchuk IV, Kuznetsov AV, Iwanisov LT (2001) Symmetry of turbulent boundary-layer flows: Investigation of different eddy viscosity models. Acta Mech 151:1–14 MATHCrossRefGoogle Scholar
  18. 18.
    Mirmasoumi S, Behzadmehr A (2008) Effect of nanoparticles mean diameter on mixed convection heat transfer of a nanofluid in a horizontal tube. Int J Heat Fluid Flow 29:557–566 CrossRefGoogle Scholar
  19. 19.
    Kalteh M, Abbassi A, Saffar-Avval M, Harting J (2011) Eulerian–Eulerian two-phase numerical simulation of nanofluid “laminar” forced convection in a microchannel. Int J Heat Fluid Flow 32:107–116 CrossRefGoogle Scholar
  20. 20.
    He Y, Men Y, Zhao Y, Lu H, Ding Y (2009) Numerical investigation into the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions. Appl Therm Eng 29:1965–1972 CrossRefGoogle Scholar
  21. 21.
    Rosmila A-K, Kandasamy R, Muhaimin I (2011) Scaling group transformation for boundary-layer flow of a nanofluid past a porous vertical stretching surface in the presence of chemical reaction with heat radiation. Comput Fluids 52:15–21 MathSciNetCrossRefGoogle Scholar
  22. 22.
    Loganathan R, Kandasamy P, Puvi Arasu P (2011) Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection. Nucl Eng Des 241:2053–2059 CrossRefGoogle Scholar
  23. 23.
    Vajravelu K, Prasad KV, Lee J, Lee C, Pop I, Van Gorder RA (2011) Convective heat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface. Int J Therm Sci 50:843–851 CrossRefGoogle Scholar
  24. 24.
    Rana R, Bhargava R (2011) Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids. Commun Nonlinear Sci Numer Simul 16:4318–4334 MathSciNetADSMATHCrossRefGoogle Scholar
  25. 25.
    Trieb F, Nitsch J (1998) Recommendations for the market introduction of solar thermal power stations. Renew Energy 14:17–22 CrossRefGoogle Scholar
  26. 26.
    Richard KS, Lee SM (1999) 800 hours of operational experience from a 2 kW solar dynamic system. In: El-Genk MS (ed.) Space technology and application international forum, pp 426–1431 Google Scholar
  27. 27.
    Odeh SD, Behnia M, Morrison GL (2003) Performance evaluation of solar thermal electric generation systems. Energy Convers Manag 44:2425–2443 CrossRefGoogle Scholar
  28. 28.
    Clausing A (1981) Analysis of convective losses from cavity solar central receivers. Sol Energy 27:295–300 ADSCrossRefGoogle Scholar
  29. 29.
    Dehghan AA, Behnia M (1996) Combined natural convection conduction and radiation heat transfer in a discretely heated open cavity. ASME J Heat Transf 118:54–56 CrossRefGoogle Scholar
  30. 30.
    Muftuoglu A, Bilgen E (2008) Heat transfer in inclined rectangular receivers for concentrated solar radiation. Int Commun Heat Mass Transf 35:551–556 CrossRefGoogle Scholar
  31. 31.
    Kennedy CE (2002) Review of mid- to high-temperature solar selective absorber materials. NREL/TP-520-31267 Google Scholar
  32. 32.
    Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336 CrossRefGoogle Scholar
  33. 33.
    Brewster MQ (1972) Thermal radiative transfer properties. Wiley, New York Google Scholar
  34. 34.
    Sparrow EM, Cess RD (1978) Radiation heat transfer. Hemisphere, Washington Google Scholar
  35. 35.
    Raptis A (1998) Radiation and free convection flow through a porous medium. Int Commun Heat Mass Transf 25:289–295 CrossRefGoogle Scholar
  36. 36.
    Aminossadati SM, Ghasemi B (2009) Natural convection cooling of a localized heat source at the bottom of a nanofluid-filled enclosure. Eur J Mech B, Fluids 28:630–640 MATHCrossRefGoogle Scholar
  37. 37.
    Makinde OD, Olanrewaju PO (2010) Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition. Trans ASME J Fluids Eng 132:044502 CrossRefGoogle Scholar
  38. 38.
    Wang CY (1989) Free convection on a vertical stretching surface. J Appl Math Mech 69:418–420 MATHGoogle Scholar
  39. 39.
    Gorla RSR, Sidawi I (1994) Free convection on a vertical stretching surface with suction and blowing. Appl Sci Res 52:247–257 MATHCrossRefGoogle Scholar
  40. 40.
    Mukhopadhyay S, Layek GC (2008) Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface. Int J Heat Mass Transf 51:2167–2178 MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • N. Anbuchezhian
    • 2
  • K. Srinivasan
    • 3
  • K. Chandrasekaran
    • 4
  • R. Kandasamy
    • 1
  1. 1.Computational Fluid DynamicsFSTPi Universiti Tun Hussein Onn MalaysiaBatu PahatMalaysia
  2. 2.Department of Mechanical EngineeringSri Guru Institute of TechnologyCoimbatoreIndia
  3. 3.Department of Mechanical EngineeringAnna UniversityChennaiIndia
  4. 4.Department of Mechanical EngineeringR.M.K. Engineering CollegeChennaiIndia

Personalised recommendations