RADIATION EFFECTS ON AN UNSTEADY MHD NATURAL CONVECTIVE FLOW OF A NANOFLUID PAST A VERTICAL PLATE

Abstract

Numerical analysis is carried out on an unsteady MHD natural convective boundary layer flow of a nanofluid past an isothermal vertical plate in the presence of thermal radiation. The governing partial differential equations are solved numerically by an efficient, iterative, tri-diagonal, semi-implicit finite-difference method. In particular, we investigate the effects of radiation, magnetic field and nanoparticle volume fraction on the flow and heat transfer characteristics. The nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. The numerical results indicate that in the presence of radiation and magnetic field, an increase in the nanoparticle volume fraction will decrease the velocity boundary layer thickness while increasing the thickness of the thermal boundary layer. Meanwhile, an increase in the magnetic field or nanoparticle volume fraction decreases the average skin-friction at the plate. Excellent validation of the present results has been achieved with the published results in the literature in the absence of the nanoparticle volume fraction.

Keywords

Dates

  • Submission Date2012-12-08
  • Revision Date2013-09-07
  • Acceptance Date2013-11-07
  • Online Date2013-12-22

DOI Reference

10.2298/TSCI121208155P

References

  1. Ostrach, S., An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force, NACA Report, 1111 (1953), pp. 63-79
  2. Pohlhausen, E., Der Warmeaustausch zwichen festen korpen und Flussingkeiten mit kleiner Reibung und kleiner Warmeleitung, Z. Angew. Math. Mech., 1(1921), pp. 115-121
  3. Siegel, R. Transient free convection from a vertical flat plate. Transactions of American Society of Mech. Eng., 80 (1958), pp. 347-359
  4. Gebhart, B., Pera, L., The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat Mass Transf., 14 (1971), 12, pp. 2025-2050
  5. Hellums, J. D., Churchill, S.W., Transient and steady state, free and natural convection, numerical solutions. Part 1. The isothermal vertical plate, American Institute of Chem. Engineers Journal, 8 (1962) , 5, pp. 690-692
  6. Takhar, H. S., Ganesan, P., Ekambavanan, V., Soundalgekar, V. M., Transient free convection past a semi-infinite vertical plate with variable surface temperature, Int. J. Numerical Methods for Heat and Fluid Flow, 7 (1996), 4, pp. 280-296
  7. Soundalgekar, V.M., Ganesan, P., The finite difference analysis of transient free convection with mass transfer of an isothermal vertical flat plate, Int. J. Engineering Sciences, 19 (1981), 6, pp.757-770
  8. England, W. G., Emery, A. F., Thermal radiation effects on the laminar free convection boundary layer of an absorbing gas, J. Heat Transf., 91 (1969), 1, pp. 37-44
  9. Soundalgekar, V. M., Takhar, H. S., Radiation Effects on Free Convection Flow past a Semi-Infinite Vertical Plate, Modelling, Measurement and Control, B51 (1993), pp. 31-40
  10. Hossain, M. A., Takhar, H. S., Radiation effect on mixed convection along a vertical plate with uniform surface temperature, J. Heat and Mass transf., 31 (1996), pp. 243-248
  11. Das, U. N., Deka, R. K., Soundalgekar, V. M., Radiation effects on flow past an impulsively started vertical infinite plate, J. Theoretical Mech., 1 (1996), pp. 111-115
  12. Choi, S. U. S., Enhancing thermal conductivity of fluids with nano- particles, ASME Fluids Engineering Division, 231 (1995), pp. 99-105
  13. Buongiorno, J., Convective transport in nanofluids, J. Heat Transf., 128 (2006), pp. 240- 250
  14. Kuznetsov, A. V., Nield, D. A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci., 49 (2010), 2, pp. 243-247
  15. Nield, D. A., Kuznetsov, A. V., The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, Int. J. Heat and Mass Transf., 52 (2009), 25-26, pp. 5792-5795
  16. Khan, W. A., Pop, I., Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat and Mass Transf., 53 (2010), 11-12, pp. 2477-2483
  17. HabibiMatin, M., Dehsara, M., Abbasi, A., Mixed convection MHD flow of nanofluid over a non-linear stretching sheet with effects of viscous dissipation and variable magnetic field, MECHANIKA, 18 (2012), 4, pp. 415-423
  18. Hamad, M. A. A., Pop, I., Ismail, A. I. Md., Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate, Nonlinear Analysis.: Real World Applications, 12 (2011), pp. 1338-1346
  19. Chamkha, A. J., Aly, A. M., MHD free convection flow of a nanofluid past a vertical plate in the presence of heat generation or absorption effects, Chem. Eng. Comm., 198 (2011), pp. 425-441
  20. Dehsara, M., HabibiMatin, M., Dalir, N., Entropy analysis for MHD flow over a non-linear stretching inclined transparent plate embedded in a porous medium due to solar radiation, MECHANIKA, 18 (2012), 5, pp. 524-533
  21. Ferdows, M., Shakhaoath Khan, M., Alam, M., Shuyu, S., MHD Mixed convective boundary layer flow of a nanofluid through a porous medium due to an Exponentially Stretching sheet, Mathematical problems in Eng., 3 (2012),7, pp. 2551-1557
  22. Ahmed, S., Pop, I., Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids, Int. Comm. Heat and Mass Transf., 37 (2010), 8, pp. 987-991
  23. Hady, F. M., Ibrahim, F. S., Abdel-Gaied, S. M., Eid, Md. R., Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet, Nanoscale Res. Lett., 7 (2012), pp. 229-241
  24. Shakhaoath Khan, M., Alam, M., Ferdows, M., Effects of Magnetic field on Radiative flow of a Nanofluid past a Stretching Sheet, Procedia Engineering, 56 (2013), pp. 316-322
  25. Loganathan, P., Nirmal Chand, P., Ganesan, P., Radiation effects on an unsteady natural convective flow of a nanofluid past an infinite vertical plate, NANO, 8(2013), 1, pp.1350001-1350010
  26. Oztop, H. F., Abu - Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid flow, 29 (2008), pp. 1326-1336
  27. Tiwari, R. K., Das, M. K., Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids, Int. J. Heat and Mass Transf., 50 (2007), 9-10, pp. 2002-2018
  28. Schlichting, H., Gersten, K., Boundary layer theory, Springer-Verlag, New York, USA, 2001
  29. Hamilton, R. L., Crosser, O. K., Thermal conductivity of Heterogeneous two component system, I&Ec. Fundamental,1 (1962), pp.187-191
  30. Brewster, M. Q., Thermal Radiative Transfer and Properties, Wiley, New York, USA,1992
  31. Smith, G.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Oxford University press, USA, 1986