Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-29T08:22:00.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of Variable Viscosity and Thermal conductivity on Natural-Convection of Nanofluids Past a Vertical Plate in Porous Media

Published online by Cambridge University Press:  02 December 2013

A. Noghrehabadi ,
M. Ghalambaz  and
A. Ghanbarzadeh
A. Noghrehabadi*
Affiliation:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz Ahvaz, Iran
M. Ghalambaz
Affiliation:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz Ahvaz, Iran
A. Ghanbarzadeh
Affiliation:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz Ahvaz, Iran
*
[email protected]
Get access

Abstract

The effects of variable viscosity and thermal conductivity on the natural convection heat transfer over a vertical plate embedded in a porous medium saturated by a nanofluid are investigated. In the nanofluid model, a gradient of nanoparticles concentration because of Brownian motion and thermophoresis forces is taken into account. The nanofluid viscosity and the thermal conductivity are assumed as a function of local nanoparticles volume fraction. The appropriate similarity variables are used to convert the governing partial differential equations into a set of highly coupled nonlinear ordinary differential equations, and then, they numerically solved using the Runge-Kutta-Fehlberg method. The practical range of non- dimensional parameters is discussed. The results show that the range of Lewis number as well as Brownian motion and thermophoresis parameters which were used in previous studies should be reconsidered. The effect of non-dimensional parameters on the boundary layer is examined. The results show that the reduced Nusselt number would increase with increase of viscosity parameter and would decrease with increase of thermal conductivity parameter.

Keywords

Natural-convectionVariable viscosityVariable thermal conductivityNanofluidsPorous media
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 3 , June 2014 , pp. 265 - 275
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Das, S. K., Choi, S. U. S., Yu, W. and Pradeep, T., Nanofluids — Science and Technology, John Wiley & Sons Publishers, Hoboken (2007).Google Scholar
2.Khanafer, K., Vafai, K. and Lightstone, M., “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids,” International Journal of Heat and Mass Transfer, 46, pp. 3639–3653 (2003).CrossRefGoogle Scholar
3.Hwang, K. S., Jang, S. P. and Choi, S. U. S., “Flow and Convective Heat Transfer Characteristics of Water-Based Al2O3 Nanofluids in Fully Developed Laminar Flow Regime,” International Journal of Heat and Mass Transfer, 52, pp. 193–199 (2009).Google Scholar
4.Yu, W., France, D. M. and Routbort, J. L., “Review and Comparison of Nanofluid Thermal Conductivity and Heat Transfer Enhancements,” Heat Transfer Engineering, 29, pp. 432–460 (2008).Google Scholar
5.Daungthongsuk, W. and Wongwises, S., “A Critical Review of Convective Heat Transfer of Nanofluids,” Renewable and Sustainable Energy Reviews, 11, pp. 797–817 (2007).Google Scholar
6.Wang, X-Q. and Mujumdar, A. S., “A Review on Nanofluids — Part I: Theoretical and Numerical Investigations,” Brazilian Journal of Chemical Engineering, 25, pp. 613–630 (2008).Google Scholar
7.Wang, X-Q, and Mujumdar, A. S., “A Review on Nanofluids — Part II: Experiments and Applications,” Brazilian Journal of Chemical Engineering, 25, pp. 631–648 (2008).Google Scholar
8.Kakac, S. and Pramuanjaroenkij, A., “Review of Convective Heat Transfer Enhancement with Nanofluids,” International Journal of Heat and Mass Transfer, 52, pp. 3187–3196 (2009).Google Scholar
9.Nield, D. A. and Bejan, A., Convection in Porous Media, 3rd Edition, Springer, New York (2006).Google Scholar
10.Ingham, D. B. and Pop, I., Transport Phenomena in Porous Media, Elsevier, Oxford (2005).Google Scholar
11.Vafai, K., Handbook of Porous Media, 2nd Edition, Taylor & Francis, New York (2005).CrossRefGoogle Scholar
12.Vadasz, P., Emerging Topics in Heat and Mass Transfer in Porous Media, Springer, New York (2008).Google Scholar
13.Gorla, R. S. R., Chamkha, A. J. and Rashad, A. M., “Mixed Convective Boundary Layer Flow over a Vertical Wedge Embedded in a Porous Medium Saturated with a Nanofluid-Natural Convection Dominated Regime,” Nanoscale Research Letters, 6, pp. 1–9 (2011).CrossRefGoogle Scholar
14.Cheng, P. and Minkowycz, W. J., “Free Convection About a Vertical Flat Plate Embedded in a Saturated Porous Medium with Applications to Heat Transfer from a Dike,” Journal of Geophysical Research, 82, pp. 2040–2044 (1977).CrossRefGoogle Scholar
15.Gorla, R. S. R. and Zinolabedini, , “Free Convection from a Vertical Plate with Non Uniform Surface Temperature and Embedded in a Porous Medium,” Journal of Energy Resources Technology, 109, pp. 26–30 (1987).Google Scholar
16.Joshi, Y. and Gebhart, B., “Mixed Convection in Porous Media Adjacent to a Vertical Uniform Heat Flux Surface,” International Journal of Heat and Mass Transfer, 28, pp. 1783–1786 (1985).Google Scholar
17.Belhachmi, Z., Brighi, B., Sac-Epee, J. M. and Taous, K., “Numerical Simulations of Free Convection About a Vertical Flat Plate Embedded in a Porous Medium,” Computational Geosciences, 7, pp. 137–166 (2003).CrossRefGoogle Scholar
18.Buongiorno, J., “Convective Transport in Nanofluids,” Journal of Heat Transfer, 128, pp. 240–250 (2006).Google Scholar
19.Nield, D. A. and Kuznetsov, A. V., “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, 52, pp. 5792–5795 (2009).CrossRefGoogle Scholar
20.Chamkha, A., Gorla, R. S. R. and Ghodeswar, K., “Non-Similar Solution for Natural Convective Boundary Layer Flow over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid,” Transport in Porous Media, 86, pp. 13–22 (2011).Google Scholar
21.Rashad, A. M., El-Hakiem, M. A. and Abdou, M. M. M., “Natural Convection Boundary Layer of a Non-Newtonian Fluid About a Permeable Vertical Cone Embedded in a Porous Medium Saturated with a Nanofluid,” Computers & Mathematics with Applications, 62, pp. 3140–3151 (2011).CrossRefGoogle Scholar
22.Gorla, R. S. R. and Chamkha, A., “Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid,” Journal of Modern Physics, 2, pp. 62–71 (2011).Google Scholar
23.Khanafer, K. and Vafai, K., “A Critical Synthesis of Thermophysical Characteristics of Nanofluids,” International Journal of Heat and Mass Transfer, 54, pp. 4410–4428 (2011).Google Scholar
24.Chandrasekar, M. and Suresh, S., “A Review on the Mechanisms of Heat Transport in Nanofluids,” Heat Transfer Engineering, 30, pp. 1136–1150 (2009).CrossRefGoogle Scholar
25.Chin, K. E., Nazar, R., Arifin, N. M. and Pop, I., “Effect of Variable Viscosity on Mixed Convection Boundary Layer Flow over a Vertical Surface Embedded in a Porous Medium,” International communications in Heat and Mass Transfer, 34, pp. 464–473 (2007).CrossRefGoogle Scholar
26.Kumari, M, “Effect of Variable Viscosity on Non-Darcy Free or Mixed Convection Flow on a Horizontal Surface in a Saturated Porous Medium,” International Communications in Heat and Mass Transfer, 28, pp. 723–732 (2001).Google Scholar
27.Hossain, M. A., Munir, M. S. and Pop, I., “Natural Convection Flow of Viscous Fluid with Viscosity Inversely Proportional to Linear Function of Temperature from a Vertical Cone,” International Journal of Thermal Sciences, 40, pp. 366–371 (2001).Google Scholar
28.Shit, G. C. and Haldar, R., “Effects of Thermal Radiation on MHD Viscous Fluid Flow and Heat Transfer over Nonlinear Shrinking Porous Sheet,” Applied Mathematics and Mechanics, 32, pp. 677–688 (2011).Google Scholar
29.Prasad, K. V., Dulal Pal, V., Umesh, N. S. and Rao, P., “The Effect of Variable Viscosity on MHD Vis-coelastic Fluid Flow and Heat Transfer over a Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 331–344 (2010).Google Scholar
30.Chaim, T. C., “Heat Transfer with Variable Thermal Conductivity in a Stagnation-Point Flow Towards a Stretching Sheet,” International Communications in Heat and Mass Transfer, 23, pp. 239–248 (1996).Google Scholar
31.Hwang, K. S., Jang, S. P. and Choi, S. U. S., “Flow and Convective Heat Transfer Characteristics of Water-Based Al2O3 Nanofluids in Fully Developed Laminar Flow Regime,” International Journal of Heat and Mass Transfer, 52, pp. 193–199 (2009).CrossRefGoogle Scholar
32.Oztop, H. F. and Abu-Nada, E., “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International Journal of Heat and Mass Transfer, 29, pp. 1326–1336 (2008).Google Scholar
33.Ma, K.-Q. and Liu, J., “Nano Liquid-Metal Fluid as Ultimate Coolant,” Physics Letters, 361, pp. 252–256 (2007).Google Scholar
34.Nassan, T. H., Zeinali Heris, S. and Noie, S. H., “A Comparison of Experimental Heat Transfer Characteristics for Al2O3/Water and Cuo/Water Nanofluids in Square Cross-Section Duct,” International Communications in Heat and Mass Transfer, 37, pp. 924–928 (2010).Google Scholar