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Double Dispersion for Double Diffusive Boundary Layer in Non-Darcy Saturated Porous Medium Filled by a Nanofluid

Published online by Cambridge University Press:  14 April 2016

A. M. Bouaziz  and
S. Hanini
A. M. Bouaziz*
Affiliation:
Biomaterials and Transport Phenomena Laboratory University of Medea Quartier Ain d'Heb, Algeria
S. Hanini
Affiliation:
Biomaterials and Transport Phenomena Laboratory University of Medea Quartier Ain d'Heb, Algeria
*
*Corresponding author (manalbouaziz@yahoo.fr)
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Abstract

This work investigates mainly the double dispersion on the double diffusive convective boundary layer between a vertical plate immersed into a non-Darcy saturated porous medium with a nanofluid. The similarity transformations are involved and the governing system of nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations. Results are displayed graphically to illustrate the influence of δ, and ξ on the velocity, the temperature and concentration of the species profiles. Two interesting cases are treated, isothermal and non-isothermal wall plate. For a nanofluid, the rate of mass transfer is affected strongly by the double dispersion while the rate of heat transfer coefficient is less sensitive to it.

Keywords

Double dispersionNanofluidDouble diffusiveNon-Darcy porous medium
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 4 , August 2016 , pp. 441 - 451
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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References

1. Das, S. K., Choi, S. U. S. and Patel, H. E., “Heat Transfer in Nanofluids-A Review,” Heat Transfer Engineering, 27, pp. 3–19 (2006).CrossRefGoogle Scholar
2. Chen, H. and Ding, S. Y., “Heat Transfer and Rheological Behavior of Nanofluids — A Review,” Advances in Transport Phenomena, pp. 135–177 (2009).CrossRefGoogle Scholar
3. Wen, D., Lin, G., Vafaei, S. and Zhang, K., “Review of Nanofluids for Heat Transfer Applications,” Particuology, 7, pp. 141–150 (2009).CrossRefGoogle Scholar
4. Kakaç, S. and Pramuanjaroenkij, A., “Review of Convective Heat Transfer Enhancement with Nanofluids,” International Journal of Heat and Mass Transfer, 52, pp. 3187–3196 (2009).CrossRefGoogle Scholar
5. Godson, L., Raja, B., Mohan lal, D. and Wongwises, S., “Enhancement of Heat Transfer Using Nanofluids — An Overview,” Renewable and Sustainable Energy Reviews, 14, pp. 629–641 (2010).CrossRefGoogle Scholar
6. Saidur, R., Leong, K. Y. and Mohammad, H. A., “A Review on Applications and Challenges of Nanofluids,” Renewable and Sustainable Energy Reviews, 15, pp. 1646–1668 (2011).CrossRefGoogle Scholar
7. Sarkar, J., “A Critical Review on Convective Heat Transfer Correlations of Nanofluids,” Renewable and Sustainable Energy Reviews, 15, pp. 3271–3277 (2011).CrossRefGoogle Scholar
8. Kleinstreur, C. and Feng, Y., “Experimental and Theoretical Studies of Nanofluid Thermal Conductivity Enhancement: A Review,” Nanoscale Research Letters, 6, pp. 229–241 (2011).CrossRefGoogle Scholar
9. Chandrasekar, M., Suresh, S. and Senthilkumar, T., “Mechanisms Proposed Through Experimental Investigations on Thermophysical Properties and Forced Convective Heat Transfer Characteristics of Various Nanofluids — A Review,” Renewable and Sustainable Energy Reviews, 16, pp. 3917–3938 (2012).CrossRefGoogle Scholar
10. Huminic, G. and Huminic, A., “Application of Nanofluids in Heat Exchangers: A Review,” Renewable and Sustainable Energy Reviews, 16, pp. 5625–5638 (2012).CrossRefGoogle Scholar
11. Pang, C., Won Lee, J. and Kang, Y. T., “Review on Combined Heat and Mass Transfer Characteristics in Nanofluids,” International Journal of Thermal Sciences, 87, pp. 49–67 (2015).CrossRefGoogle Scholar
12. Mahdi, R. A., Mohammed, H. A., Munisamy, K. M. and Saeid, N. H., “Review of Convection Heat Transfer and Fluid Flow in Porous Media with Nanofluid,” Renewable and Sustainable Energy Reviews, 41, pp. 715–734 (2015).CrossRefGoogle Scholar
13. Keblinski, P. A., Phillipot, S. R., Choi, S. U. S. and Eastman, J. A., “Mechanisms of Heat Flow in Suspensions of Nano-Sized Particles (Nanofluid),” International Journal of Heat and Mass Transfer, 45, pp. 855–863 (2002).CrossRefGoogle Scholar
14. Buongiorno, J., “Convective Transport in Nanofluids,” Journal of Heat Transfer, 128, pp. 240–250 (2006).CrossRefGoogle Scholar
15. Vafai, K., Handbook of Porous Media, 2nd Ed., Taylor & Francis, CRC Press, Boca Raton, pp. 81–140 (2005).CrossRefGoogle Scholar
16. Kumar, S., Prasad, S. K. and Banerjee, J., “Analysis of Flow and Thermal Field in Nanofluid Using a Single Phase Thermal Dispersion Model,” Applied Mathematical Modelling, 34, pp. 573–592 (2010).CrossRefGoogle Scholar
17. Michaelides, E. E., Nanofluidics, Thermodynamics and Transport Properties, Springer International Publishing AG, Cham, pp. 54–76 (2014).CrossRefGoogle Scholar
18. Cheng, P., “Thermal Dispersion Effects on Non-Darcy Convection Flows in a Saturated Porous Medium,” Letters in Heat and Mass Transfer, 8, pp. 267–270 (1981).CrossRefGoogle Scholar
19. Hong, J. T. and Tien, C. L., “Analysis of Thermal Dispersion Effect on Vertical Plate Natural Convection in Porous Media,” International Journal of Heat and Mass Transfer, 30, pp. 143–150 (1987).CrossRefGoogle Scholar
20. Mokmeli, A. and Saffar-Awal, M., “Prediction of Nanofluid Convective Heat Transfer Using the Dispersion Model,” International Journal of Thermal Sciences, 49, pp. 471–478 (2010).CrossRefGoogle Scholar
21. Lai, F. C. and Kulacki, F. A., “Thermal Dispersion Effect on Non-Darcy Convection from Horizontal Surface in Saturated Porous Media,” International Journal of Heat and Mass Transfer, 32, pp. 971–976 (1989).CrossRefGoogle Scholar
22. Telles, R. S. and Trevisan, O. V., “Dispersion in Heat and Mass Transfer Natural Convection Along Vertical Boundaries in Porous Media,” International Journal of Heat and Mass Transfer, 36, pp. 1357–1365 (1993).CrossRefGoogle Scholar
23. Pedras, M. H. J. and de Lemos, M. J. S., “Thermal Dispersion in Porous Media as a Function of the Solid-Fluid Conductivity,” International Journal of Heat and Mass Transfer, 51, pp. 5359–5367 (2008).CrossRefGoogle Scholar
24. Murthy, P.V.S.N., “Effect of Double Dispersion on Mixed Convection Heat and Mass Transfer in Non-Darcy Porous Medium,” Journal of Heat Transfer, 122, pp. 476–483 (2000).CrossRefGoogle Scholar
25. Wang, C., Liao, J. and Zhu, M., “An Explicit Analytic Solution for Non-Darcy Natural Convection Over Horizontal Plate with Surface Mass Flux and Thermal Dispersion Effects,” Acta Mechanica, 165, pp. 139–150 (2003).CrossRefGoogle Scholar
26. Chamkha, A. J. and Quadri, M. M. A., “Simultaneous Heat and Mass Transfer by Natural Convection from a Plate Embedded in a Porous Medium with Thermal Dispersion Effects,” Heat and Mass Transfer, 39, pp. 561–569 (2003).CrossRefGoogle Scholar
27. El-Amin, M. K., “Double Dispersion Effects on Natural Convection Heat and Mass Transfer in Non-Darcy Porous Medium,” Applied Mathematics and Computation, 156, pp. 1–17 (2004).CrossRefGoogle Scholar
28. Gorla, R. S. R. and Chamkha, A. J., “Natural Convective Boundary Layer Flow Over a Nonisothermal Vertical Plate Embedded in a Porous Medium Saturated with a Nanofluid,” Nanoscale and Microscale Thermophysical Engineering, 15, pp. 81–94 (2011).CrossRefGoogle Scholar
29. Pal, D. and Mondal, H., “Hydromagnetic Convective Diffusion of Species in Darcy-Forchheimer Porous Medium with Non-Uniform Heat Source/Sink and Variable Viscosity,” International Communications in Heat and Mass Transfer, 39, pp. 913–917 (2012).CrossRefGoogle Scholar
30. Hamad, M. A. A. and Ferdows, M., “Similarity Solution of Boundary Layer Stagnation-Point Flow Towards a Heated Porous Stretching Sheet Saturated with a Nanofluid with Heat Absorption/Generation and Suction/Blowing: A Lie Group Analysis,” Communications in Nonlinear Science and Numerical Simulation, 17, pp. 132–140 (2012).CrossRefGoogle Scholar
31. Rashad, A. M., Chamkha, A. J. and Modather, M., “Mixed Convection Boundary-Layer Flow Past a Horizontal Circular Cylinder Embedded in a Porous Medium Filled with a Nanofluid Under Convective Boundary Condition,” Computers & Fluids, 86, pp. 380–388 (2013).CrossRefGoogle Scholar
32. Rana, P., Bhargava, R. and Beg, O. A., “Numerical Solution for Mixed Convection Boundary Layer Flow of a Nanofluid Along an Inclined Plate Embedded in a Porous Medium,” Computers and Mathematics with Applications, 64, pp. 2816–2832 (2012).CrossRefGoogle Scholar
33. Murthy, P. V. S. N., Sutradhar, A. and RamReddy, Ch., “Double Diffusive Free Convection Flow Past an Inclined Plate Embedded in a Non-Darcy Porous Medium Saturated with a Nanofluid,” Transport Porous Media, 98, pp. 553–564 (2013).CrossRefGoogle Scholar
34. Srinivasacharya, D. and Surender, O., “Non-Similar Solution for Natural Convective Boundary Layer Flow of a Nanofluid Past a Vertical Plate Embedded in a Doubly Stratified Porous Medium,” International Journal of Heat and Mass Transfer, 71, pp. 431–438 (2014).CrossRefGoogle Scholar
35. Kuznetsov, A. V. and Nield, D. A., “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate,” International Journal of Thermal Sciences, 49, pp. 243–247 (2010).CrossRefGoogle Scholar
36. Kuznetsov, A. V. and Nield, D. A., “Double-Diffusive Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate,” International Journal of Thermal Sciences, 50, pp. 712–717 (2011).CrossRefGoogle Scholar
37. Kuznetsov, A. V. and Nield, D. A., “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate: A Revised Model,” International Journal of Thermal Sciences, 77, pp. 126–129 (2014).CrossRefGoogle Scholar
38. 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
39. Nield, D. A. and Kuznetsov, A. V., “The Cheng-Minkowycz Problem for the Double-Diffusive Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, 54, pp. 374–378 (2011).CrossRefGoogle Scholar
40. Nield, D. A. and Kuznetsov, A. V., “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model,” International Journal of Heat and Mass Transfer, 68, pp. 211–214 (2014).CrossRefGoogle Scholar
41. Kuznetsov, A. V. and Nield, D. A., “The Cheng-Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid: A Revised Model,” International Journal of Heat and Mass Transfer, 65, pp. 682–685 (2013).CrossRefGoogle Scholar
42. Makinde, O. D. and Aziz, A., “MHD Mixed Convection from a Vertical Plate Embedded in Porous Medium with a Convective Boundary Condition,” International Journal of Thermal Sciences, 49, pp. 1813–1820 (2010).CrossRefGoogle Scholar
43. Jaluria, Y., Design and Optimization of Thermal Systems, CRC press, Taylor & Francis group, Boca Raton, pp. 104–112 (2008).Google Scholar
44. Rubinstein, J., “Effective Equations for Flow in Random Porous Media with a Large Number of Scales,” Journal of Fluid Mechanics, 170, pp. 379–383 (1986).CrossRefGoogle Scholar
45. Kaviany, M., Principles of Heat Transfer in Porous Media, Springer-Verlag, New York, p. 66 (1991).CrossRefGoogle Scholar
46. Leont'ev, N. E., “Flow Past a Cylinder and a Sphere in a Porous Medium within the Framework of the Brinkman Equation with the Navier Boundary Condition,” Fluid Dynamics, 49, pp. 232–237 (2014).CrossRefGoogle Scholar