Abstract
In this work, an exact analysis on the effects of heat generation and nanoparticle volume concentration on an unsteady free convective flow of a nanofluid past an impulsively started infinite vertical plate is presented. Nanofluids containing nanoparticles of aluminum oxide, copper, titanium oxide, and silver with a nanoparticle volume concentration range smaller than or equal to 0.04 are considered. The governing dimensionless partial differential equations are solved by using the Laplace transform technique. The effects of heat generation and nanoparticle volume concentration on the velocity and temperature profiles are represented graphically. The expressions for the skin friction coefficient and Nusselt number are derived. The effect of heat transfer is found to be more pronounced in a silver–water nanofluid than in the other nanofluids. Comparisons with other published results are found to be in excellent agreement.
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References
S. U. S. Choi, “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” in Developments and Applications of non-Newtonian Flows (Amer. Soc. Mech. Eng., New York, 1995), Vol. 231, pp. 99–105.
G. G. Stokes, “On the Effects of Internal Friction of Fluids on the Motion of Pendulums,” Cambridge Philos. Trans. 9, 8–106 (1851).
V. M. Soundalgekar, “Free Convection Effects on the Stokes Problem for an Infinite Vertical Plate,” Trans. ASME, J. Heat Transfer 99 (3), 499–501 (1977).
A. A. Raptis and G. J. Tzivanidis, “Effects of Mass Transfer, Free-Convection Currents and Heat Sources on the Stokes Problem for an Infinite Vertical Plate,” Astrophys. Space Sci. 78 (2), 351–357 (1981).
H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles. Dispersion of C-Al2O3, SiO2 and TiO2 Ultra-Fine Particles,” Netsu Bussei 7 (4), 227–233 (1993).
S. Lee, S. U. S. Choi, S. Li, and J. A. Eastman, “Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles,” Trans. ASME, J. Heat Transfer 121 (2), 280–289 (1999).
Y. Xuan and Q. Li, “Heat Transfer Enhancement of Nanofluids,” Int. J. Heat Fluid Flow 21, 58–64 (2000).
Y. Xuan and W. Roetzel, “Conceptions for Heat Transfer Correlation of Nanofluids,” Int. J. Heat Mass Transfer 43 (19), 3701–3707 (2000).
J. A. Eastman, S. U. S. Choi, S. Li, et al., “Anomalously Increased Effective Thermal Conductivity of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles,” Appl. Phys. Lett. 78 (6), 718–720 (2001).
B. C. Pak and Y. I. Cho, “Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particles,” Exp. Heat Transfer 11 (2), 151–170 (1998).
J. Buongiorno, “Convective Transport in Nanofluids,” Trans. ASME, J. Heat Transfer 128 (3), 240–250 (2006).
D. Wen and Y. Ding, “Natural Convective Heat Transfer of Suspensions of Titanium Dioxide Nanoparticles (Nanofluids),” IEEE Trans. Nanotechnol. 5 (3), 220–227 (2006).
L. Gosselin and A. K. Da Silva, “Combined Heat Transfer and Power Dissipation Optimization of Nanofluid Flows,” Appl. Phys. Lett. 85 (18), 4160–4162 (2004).
S. P. Jang and S. U. S. Choi, “Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids,” Appl. Phys. Lett. 84 (21), 4316–4318 (2004).
A. V. Kuznetsov and D. A. Nield, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate,” Int. J. Thermal. Sci. 49 (2), 243–247 (2010).
A. J. Chamkha and A. M. Aly, “MHD Free Convection Flow of a Nanofluid Past a Vertical Plate in the Presence of Heat Generation or Absorption Effects,” Chem. Eng. Comm. 198, 425–441 (2011).
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,” Int. J. Heat Mass Transfer 52 (25/26), 5792–5795 (2009).
W. A. Khan and I. Pop, “Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet,” Int. J. Heat Mass Transfer 53 (11/12), 2477–2483 (2010).
M. A. A. Hamad, I. Pop, and A. I. Md. Ismail, “Magnetic Field Effects on Free Convection Flow of a Nanofluid Past a Vertical Semi-Infinite Flat Plate,” Nonlinear Anal. Real World Appl. 12 (3), 1338–1346 (2010).
N. Bachok, A. Ishak, and I. Pop, “Unsteady Boundary-Layer Flow and Heat Transfer of a Nanofluid Over a Permeable Stretching/Shrinking Sheet,” Int. J. Heat Mass Transfer 55 (7/8), 2102–2109 (2012).
S. Ahmed and I. Pop, “Mixed Convective Boundary Layer Flow from a Vertical Flat Plate Embedded in a Porous Medium Filled with Nanofluids,” Int. Comm. Heat Mass Transfer 37 (8), 987–991 (2010).
K. C. Lin and A. Violi, “Natural Convection Heat Transfer of Nanofluids in a Vertical Cavity: Effects of Non-Uniform Particle Diameter and Temperature on Thermal Conductivity,” Int. J. Heat Fluid Flow 31 (2), 236–245 (2010).
H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” Int. J. Heat Fluid Flow 29 (5), 1326–1336 (2008).
R. K. Tiwari and M. K. Das, “Heat Transfer Augment in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” Int. J. Heat Mass Transfer 50 (9/10), 2002–2018 (2007).
H. Schlichting and K. Gersten, Boundary Layer Theory (Springer-Verlag, Berlin, 2001).
R. L. Hamilton and O. K. Crosser, “Thermal Conductivity of Heterogeneous Two-Component Systems,” Indust. Eng. Chem. Fundament. 1 (3), 187–191 (1962).
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Original Russian Text © P. Loganathan, P. Nirmal Chand, P. Ganesan.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 3, pp. 105–115, May–June, 2015.
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Loganathan, P., Nirmal Chand, P. & Ganesan, P. Transient natural convective flow of a nanofluid past a vertical plate in the presence of heat generation. J Appl Mech Tech Phy 56, 433–442 (2015). https://doi.org/10.1134/S002189441503013X
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DOI: https://doi.org/10.1134/S002189441503013X