Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid

ABSTRACT

A boundary layer analysis is presented for the natural convection past a horizontal plate in a porous medium saturated with a nano fluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

A boundary layer analysis is presented for the natural convection past a horizontal plate in a porous medium saturated with a nano fluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

Cite this paper

nullR. Gorla and A. Chamkha, "Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid,"*Journal of Modern Physics*, Vol. 2 No. 2, 2011, pp. 62-71. doi: 10.4236/jmp.2011.22011.

nullR. Gorla and A. Chamkha, "Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid,"

References

[1] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu and L. J. Thompson, “Anomalously Increased Effective Thermal Conductivities Containing Copper Nanoparticles,” Applied Physics Letters, Vol. 78, No. 6, 2001, pp. 718-720. doi:10.1063/1.1341218

[2] S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood and E. A. Grulke, “Anomalous Thermal Conductivity Enhancement on Nanotube Suspensions,” Applied Physics Letters, Vol. 79, No. 14, 2001, pp. 2252-2254. doi:10.1063/1.1408272

[3] H. E. Patel, S. K. Das, T. Sundararajan, A. Sreekumaran, B. George and T. Pradeep, “Thermal Conductivities of Naked and Monolayer Protected Metal Nanoparticle Based Nanofluids: Manifestation of Anomalous Enhancement and Chemical Effects,” Applied Physics Letters, Vol. 14, No. 83, 2003, pp. 2931-2933. doi:10.1063/1.1602578

[4] S. M. You, J. H. Kim and K. H. Kim, “Effect of Nanoparticles on Critical Heat Flux of Water in Pool Boiling Heat Transfer,” Applied Physics Letters, Vol. 83, No. 16, 2003, pp. 3374-3376. doi:10.1063/1.1619206

[5] P. Vassallo, R. Kumar and S. D’Amico, “Pool Boiling Heat Transfer Experiments in Silica-Water Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 47, No. 2, 2004, pp. 407-411. doi:10.1016/S0017-9310(03)00361-2

[6] P. Cheng and W. J. Minkowycz, “Free Convection about a Vertical Flat Plate Embedded in a Saturated Porous Medium with Applications to Heat Transfer from a Dike,” Journal of Geophysics Res., Vol. 82, 1977, pp. 2040-2044. doi:10.1029/JB082i014p02040

[7] R. S. R. Gorla and R. Tornabene, “Free Convection from a Vertical Plate with Nonuniform Surface Heat Flux and Embedded in a Porous Medium,” Transport in Porous Media Journal, Vol. 3, 1988, pp. 95-106. doi:10.1007/BF00222688

[8] R. S. R. Gorla and A. Zinolabedini, “Free Convection From a Vertical Plate With Nonuniform Surface Temperature and Embedded in a Porous Medium,” Journal of Energy Resources Technology, Vol. 109, 1987, pp. 26-30. doi:10.1115/1.3231319

[9] H. T. Chen and C. K. Chen, “Natural Convection of Non-Newtonian Fluids about a Horizontal Surface in a Porous Medium,” Journal of Energy Resources Technology, Vol. 109, 1987, pp. 119-123. doi:10.1115/1.3231336

[10] K. N. Mehta and K. N. Rao, “Buoyancy-Induced Flow of Non-Newtonian Fluids in a Porous Medium Past a Horizontal Plate with Nonuniform Surface Heat Flux,” International Journal of Engineering Science, Vol. 32, 1994, pp. 297-302.

[11] A. Nakayama and H. Koyama, “Buoyancy-Induced Flow of Non-Newtonian Fluids Over a Non-Isothermal Body of Arbitrary Shape in a Fluid-Saturated Porous Medium,” Applied Scientific Research, Vol. 48, 1991, pp. 55-70. doi:10.1007/BF01998665

[12] 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, 2009, pp. 5792-5795. doi:10.1016/j.ijheatmasstransfer.2009.07.024

[13] D. A. Nield and A. V. Kuznetsov, “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, Vol. 52, No. 25-26, 2009, pp. 5796-5801. doi:10.1016/j.ijheatmasstransfer.2009.07.023

[14] F. G. Blottner, “Finite-Difference Methods of Solution of the Boundary-Layer Equations,” Journal of AIAA, Vol. 8, 1970, pp. 193-205. doi:10.2514/3.5642

[15] P. A. L. Narayana, P. V. S. N. Murthy and R. S. R. Gorla, “Soret-Driven Thermosolutal Convection Induced by Inclined Thermal and Solutal Gradients in a Shallow Horizontal Layer of a Porous Medium,” Journal of Fluid Mechanics, Vol. 612, 2008, pp. 1-19. doi:10.1017/S0022112008002619

[1] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu and L. J. Thompson, “Anomalously Increased Effective Thermal Conductivities Containing Copper Nanoparticles,” Applied Physics Letters, Vol. 78, No. 6, 2001, pp. 718-720. doi:10.1063/1.1341218

[2] S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood and E. A. Grulke, “Anomalous Thermal Conductivity Enhancement on Nanotube Suspensions,” Applied Physics Letters, Vol. 79, No. 14, 2001, pp. 2252-2254. doi:10.1063/1.1408272

[3] H. E. Patel, S. K. Das, T. Sundararajan, A. Sreekumaran, B. George and T. Pradeep, “Thermal Conductivities of Naked and Monolayer Protected Metal Nanoparticle Based Nanofluids: Manifestation of Anomalous Enhancement and Chemical Effects,” Applied Physics Letters, Vol. 14, No. 83, 2003, pp. 2931-2933. doi:10.1063/1.1602578

[4] S. M. You, J. H. Kim and K. H. Kim, “Effect of Nanoparticles on Critical Heat Flux of Water in Pool Boiling Heat Transfer,” Applied Physics Letters, Vol. 83, No. 16, 2003, pp. 3374-3376. doi:10.1063/1.1619206

[5] P. Vassallo, R. Kumar and S. D’Amico, “Pool Boiling Heat Transfer Experiments in Silica-Water Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 47, No. 2, 2004, pp. 407-411. doi:10.1016/S0017-9310(03)00361-2

[6] P. Cheng and W. J. Minkowycz, “Free Convection about a Vertical Flat Plate Embedded in a Saturated Porous Medium with Applications to Heat Transfer from a Dike,” Journal of Geophysics Res., Vol. 82, 1977, pp. 2040-2044. doi:10.1029/JB082i014p02040

[7] R. S. R. Gorla and R. Tornabene, “Free Convection from a Vertical Plate with Nonuniform Surface Heat Flux and Embedded in a Porous Medium,” Transport in Porous Media Journal, Vol. 3, 1988, pp. 95-106. doi:10.1007/BF00222688

[8] R. S. R. Gorla and A. Zinolabedini, “Free Convection From a Vertical Plate With Nonuniform Surface Temperature and Embedded in a Porous Medium,” Journal of Energy Resources Technology, Vol. 109, 1987, pp. 26-30. doi:10.1115/1.3231319

[9] H. T. Chen and C. K. Chen, “Natural Convection of Non-Newtonian Fluids about a Horizontal Surface in a Porous Medium,” Journal of Energy Resources Technology, Vol. 109, 1987, pp. 119-123. doi:10.1115/1.3231336

[10] K. N. Mehta and K. N. Rao, “Buoyancy-Induced Flow of Non-Newtonian Fluids in a Porous Medium Past a Horizontal Plate with Nonuniform Surface Heat Flux,” International Journal of Engineering Science, Vol. 32, 1994, pp. 297-302.

[11] A. Nakayama and H. Koyama, “Buoyancy-Induced Flow of Non-Newtonian Fluids Over a Non-Isothermal Body of Arbitrary Shape in a Fluid-Saturated Porous Medium,” Applied Scientific Research, Vol. 48, 1991, pp. 55-70. doi:10.1007/BF01998665

[12] 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, 2009, pp. 5792-5795. doi:10.1016/j.ijheatmasstransfer.2009.07.024

[13] D. A. Nield and A. V. Kuznetsov, “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, Vol. 52, No. 25-26, 2009, pp. 5796-5801. doi:10.1016/j.ijheatmasstransfer.2009.07.023

[14] F. G. Blottner, “Finite-Difference Methods of Solution of the Boundary-Layer Equations,” Journal of AIAA, Vol. 8, 1970, pp. 193-205. doi:10.2514/3.5642

[15] P. A. L. Narayana, P. V. S. N. Murthy and R. S. R. Gorla, “Soret-Driven Thermosolutal Convection Induced by Inclined Thermal and Solutal Gradients in a Shallow Horizontal Layer of a Porous Medium,” Journal of Fluid Mechanics, Vol. 612, 2008, pp. 1-19. doi:10.1017/S0022112008002619