Forced Convection Flow of Nanofluids Past Power Law Stretching Horizontal Plates

Author(s)
Fekry Mohamed Hady^{*},
Fouad Sayed Ibrahim,
Hassan Mohammed Hassan El-Hawary,
Ahmed Mostafa Abdelhady

ABSTRACT

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of AL_{2}O_{3} as a nanoparticles and water as a base fluid. The volume fraction of nanoparticles is considered in the range 0 ≤ * ?* ≤ 0.2. with prandtl number *pr* = 6.2 for the water working as a regular fluid. The parameters which governing the solution are volume fraction of nanoparticles , stretching plate parameter *ξ* and power law index *N*. We investigated the effect of these parameters on the skin friction coefficient, Nusselt number, velocity and temperature profiles. We found that heat transfer rate and skin fraction increased when * ?* increased. On the other hand, we concluded that the increase in *ξ* and *N* made heat transfer rate increases and skin fraction decreases.

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of AL

Cite this paper

F. Hady, F. Ibrahim, H. El-Hawary and A. Abdelhady, "Forced Convection Flow of Nanofluids Past Power Law Stretching Horizontal Plates,"*Applied Mathematics*, Vol. 3 No. 2, 2012, pp. 121-126. doi: 10.4236/am.2012.32019.

F. Hady, F. Ibrahim, H. El-Hawary and A. Abdelhady, "Forced Convection Flow of Nanofluids Past Power Law Stretching Horizontal Plates,"

References

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[2] S. Lee, S. U. S. Choi, S. Li and J. A. Eastman, “Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles,” Journal of Heat Transfer, Vol. 121, No. 2, 1999, pp. 280-289. doi:10.1115/1.2825978

[3] J. A. Estman, S. U. S. Choi, S. Li, W. Yu and L. J. Thomson, “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol Based Nanofluid Containing Copper Nanoparticles,” Applied Physics Letters, Vol. 78, No. 6, 2001, pp. 718-720. doi:10.1063/1.1341218

[4] M. Shahi, A. H. Mahmoudi and F. Talebi, “Numerical Study of Mixed Convective Cooling in a Square Cavity Ventilated and Partially Heated from the Below Utilizing Nanofluid,” International Communications in Heat and Mass Transfer, Vol. 37, No. 2, 2010, pp. 201-213. doi:10.1016/j.icheatmasstransfer.2009.10.002

[5] J. Buongiorno, “Convective Transport in Nanofluids,” Journal of Heat Transfer, Vol. 128, No. 3, 2006, pp. 240-250. doi:10.1115/1.2150834

[6] A. Mahdy and F. M. Hady, “Effect of Thermophoretic Particle Deposition in Non-Newtonian Free Convection Flow over a Vertical Plate with Magnetic Field Effect,” Journal of Non-Newtonian Fluid Mechanics, Vol. 161, No. 1-3, 2009, pp. 37-41. doi:10.1016/j.jnnfm.2009.04.00

[7] D. A. Nield and A. V. Kuznetsov, “The Cheng-Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, Vol. 52, No. 25-26, 2009, pp. 5792-5795. doi:10.1016/j.ijheatmasstransfer.2009.07.024

[8] A. V. Kuznetsov and D. A. Nield, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate,” International Journal of Thermal Sciences, Vol. No. 2, 49, 2010, pp. 243-247. doi:10.1016/j.ijthermalsci.2009.07.015

[9] S. Ahmed, A. M. Rohni and I. Pop, “Blasius and Sakiadis Problems in Nanofluids,” Acta Mechanica, Vol. 218, No. 3-4, 2011, pp. 195-204. doi:10.1007/s00707-010-0414-6

[10] H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International Journal of Heat and Fluid Flow, Vol. 29, No. 5, 2008, pp. 13261336. doi:10.1016/j.ijheatfluidflow.2008.04.009

[11] R. K. Tiwari and M. K. Das, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 50, No. 9-10, 2007, pp. 2002-2018. doi:10.1016/j.ijheatmasstransfer.2006.09.034

[12] H. C. Brinkman, “The Viscosity of Concentrated Suspensions and Solutions,” Journal of Chemical Physics, Vol. 20, No. 4, 1952, pp. 571-581. doi:10.1063/1.1700493

[13] S. E. B. Maiga, S. J. Palm, C. T. Nguyen, G. Roy and N. Galanis, “Heat Transfer Enhancement by Using Nanofluids in Forced Convection Flows,” International Journal of Heat and Fluid Flow, Vol. 26, No. 4, 2005, pp. 530546. doi:10.1016/j.ijheatfluidflow.2005.02.004

[14] E. Abu-Nada, “Application of Nanofluids for Heat Transfer Enhancement of Separated Flows Encountered in a Backward Facing Step,” International Journal of Heat and Fluid Flow, Vol. 29, No. 1, 2008, pp. 242-249. doi:10.1016/j.ijheatfluidflow.2007.07.001

[15] V. Pereyra, “An Adaptive Finite-Difference Fortran Program for First Order Nonlinear, ordinary boundary Problems Codes for Boundary Value Problems in Ordinary Differential Equations,” Codes for Boundary-Value Problems in Ordinary Differential Equations, Lecture Notes in Computer Science, Vol. 76, 1979, pp. 67-88.

[16] M. Muthtamilselvan, P. Kandaswamy and J. Lee, “Heat Transfer Enhancement of Copper-Water Nanofluids in a Lid-Driven Enclosure,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 6, 2010, pp. 1501-1510. doi:10.1016/j.cnsns.2009.06.015

[17] B. Pak and Y. I. Cho, “Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particle,” Experimental Heat Transfer, Vol. 11, No. 2, 1998, pp. 151-170. doi:10.1080/08916159808946559

[1] J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 3rd Edition, Oxford University Press, London, 1892.

[2] S. Lee, S. U. S. Choi, S. Li and J. A. Eastman, “Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles,” Journal of Heat Transfer, Vol. 121, No. 2, 1999, pp. 280-289. doi:10.1115/1.2825978

[3] J. A. Estman, S. U. S. Choi, S. Li, W. Yu and L. J. Thomson, “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol Based Nanofluid Containing Copper Nanoparticles,” Applied Physics Letters, Vol. 78, No. 6, 2001, pp. 718-720. doi:10.1063/1.1341218

[4] M. Shahi, A. H. Mahmoudi and F. Talebi, “Numerical Study of Mixed Convective Cooling in a Square Cavity Ventilated and Partially Heated from the Below Utilizing Nanofluid,” International Communications in Heat and Mass Transfer, Vol. 37, No. 2, 2010, pp. 201-213. doi:10.1016/j.icheatmasstransfer.2009.10.002

[5] J. Buongiorno, “Convective Transport in Nanofluids,” Journal of Heat Transfer, Vol. 128, No. 3, 2006, pp. 240-250. doi:10.1115/1.2150834

[6] A. Mahdy and F. M. Hady, “Effect of Thermophoretic Particle Deposition in Non-Newtonian Free Convection Flow over a Vertical Plate with Magnetic Field Effect,” Journal of Non-Newtonian Fluid Mechanics, Vol. 161, No. 1-3, 2009, pp. 37-41. doi:10.1016/j.jnnfm.2009.04.00

[7] D. A. Nield and A. V. Kuznetsov, “The Cheng-Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, Vol. 52, No. 25-26, 2009, pp. 5792-5795. doi:10.1016/j.ijheatmasstransfer.2009.07.024

[8] A. V. Kuznetsov and D. A. Nield, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate,” International Journal of Thermal Sciences, Vol. No. 2, 49, 2010, pp. 243-247. doi:10.1016/j.ijthermalsci.2009.07.015

[9] S. Ahmed, A. M. Rohni and I. Pop, “Blasius and Sakiadis Problems in Nanofluids,” Acta Mechanica, Vol. 218, No. 3-4, 2011, pp. 195-204. doi:10.1007/s00707-010-0414-6

[10] H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International Journal of Heat and Fluid Flow, Vol. 29, No. 5, 2008, pp. 13261336. doi:10.1016/j.ijheatfluidflow.2008.04.009

[11] R. K. Tiwari and M. K. Das, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 50, No. 9-10, 2007, pp. 2002-2018. doi:10.1016/j.ijheatmasstransfer.2006.09.034

[12] H. C. Brinkman, “The Viscosity of Concentrated Suspensions and Solutions,” Journal of Chemical Physics, Vol. 20, No. 4, 1952, pp. 571-581. doi:10.1063/1.1700493

[13] S. E. B. Maiga, S. J. Palm, C. T. Nguyen, G. Roy and N. Galanis, “Heat Transfer Enhancement by Using Nanofluids in Forced Convection Flows,” International Journal of Heat and Fluid Flow, Vol. 26, No. 4, 2005, pp. 530546. doi:10.1016/j.ijheatfluidflow.2005.02.004

[14] E. Abu-Nada, “Application of Nanofluids for Heat Transfer Enhancement of Separated Flows Encountered in a Backward Facing Step,” International Journal of Heat and Fluid Flow, Vol. 29, No. 1, 2008, pp. 242-249. doi:10.1016/j.ijheatfluidflow.2007.07.001

[15] V. Pereyra, “An Adaptive Finite-Difference Fortran Program for First Order Nonlinear, ordinary boundary Problems Codes for Boundary Value Problems in Ordinary Differential Equations,” Codes for Boundary-Value Problems in Ordinary Differential Equations, Lecture Notes in Computer Science, Vol. 76, 1979, pp. 67-88.

[16] M. Muthtamilselvan, P. Kandaswamy and J. Lee, “Heat Transfer Enhancement of Copper-Water Nanofluids in a Lid-Driven Enclosure,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 6, 2010, pp. 1501-1510. doi:10.1016/j.cnsns.2009.06.015

[17] B. Pak and Y. I. Cho, “Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particle,” Experimental Heat Transfer, Vol. 11, No. 2, 1998, pp. 151-170. doi:10.1080/08916159808946559