Boundary layer flow of a nanofluid in an inclined wavy wall with convective boundary condition

Abstract

This problem focuses on the laminar flow of a nanofluid in an inclined permeable parallel walls. We assume that the lower wall is wavy while the upper wall is flat with Dufour effects, Soret effects, and a magnetic field effect with boundary conditions been convective. The rectangular coordinate system has been used to present the model for this problem. It also incorporates the effect of thermophoresis parameter and Brownian motion. The obtained similarity solution is dependent on the thermophoresis number (Nt ), Darcy number (Da), Magnetic parameter (M), Dufour (DU) number, Soret (Sr) number, Brownian motion (Nb), Lewis number (Le), Prandtl number (Pr). It is found that at the wavy wall, the fluid flow back.

Keywords

• Thermophoresis,nanofluid,nano particles,boundary layer,thermo-difussion,difussion thermo,channel flow

References

1. [1] Y. M. Aiyesimi, A. Yusuf, M. Jiya, “Hydromagnetic Boudary-Layer Flow of a Nanofluid Past a Stretching Sheet Embedded in a Darcian Porous Medium with Radiation”. Nigerian Journal of Mathematics and Applications, 24, (2015a). 13-29.
2. [2] Y. M. Aiyesimi, A. Yusuf, & M. Jiya, “An Analytic Investigation of Convective Boundary-Layer Flow Of A Nanofluid Past A Stretching Sheet With Radiation”. Journal of Nigerian Association of Mathematical Physics. 29 1, (2015b). 477-490.
3. [3] A. Ebaid, & N. Al-Armani, “A new Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method “. Abstract and Applied Analysis, the Scientific World Journal, 2013.
4. [4] B. J. Gireesha , & B. Mahanthesh, “Perturbation solution for radiating viscoelastic fluid flow and heat transfer with convective boundary condition in nonuniform channel with hall current and chemical reaction”. ISRN Thermodynamics, (2013). Article ID 935481, 14. http://dx.doi.org/10.1155/2013/935481.
5. [5] W. A. Khan, & I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet”, Int. J. HeatMass Transf. 53, 2477-2483 (2010).
6. [6] A. S. Kherbeet, H. A. Mohammed, & B. H. Salman, “The effect of nanofluids flow on mixed convection heat transfer over microscale backward-facing step”, Int. J. Heat Mass Transfer 55, (2012). 5870–5881.
7. [7] J. P. Kumar, & J. C. Umavathi, “Free convective flow in an open-ended vertical porous wavy channel with a perfectly conductive thin baffle”. Heat Transfer—Asian Research, (2013). DOI: 10.1002/htj.21118. http://dx.doi.org/10.1002/htj.21118.
8. [8] S. G. Lekoudis, A. H. Nayfeh, , & W. S. Saric, “Compressible boundary layers over wavy walls”. Physics of Fluids, 19, (1976). 514–519. http://dx.doi.org/10.1063/1.861507.

9. [9] M. Lessen, M & S. T. Gangwani, “Effects of small amplitude wall waviness upon the stability of the laminar boundary layer”. Physics of Fluids, 19, (1976).510–513. http://dx.doi.org/10.1063/1.861515.
10. [10] R. Muthuraj, & S. Srinivas, “Mixed convective heat and mass transfer in a vertical wavy channel with traveling thermal waves and porous medium”. Computers & Mathematics with Applications, 59, (2010).3516–3528. http://dx.doi.org/10.1016/j.camwa.2010.03.045.
11. [11] D. A. S. Rees, & I. Pop, “Free convection induced by a horizontal wavy surface in a porous medium”. Fluid Dynamics Research, 14, (1994). 151–66. http://dx.doi.org/10.1016/0169-5983 94, 90026-4.
12. [12] P. N. Shankar, &U. N. Sinha, “The Rayleigh problem for a wavy wall”. Journal of Fluid Mechanics, 77, (1976). 243–256. http://dx.doi.org/10.1017/S0022112076002097.
13. [13] M. Sheikholeslami, M. Gorji-Bandpy, R. Ellahi, & A. Zeeshan, “ Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces”, J. Mag. Magn. Mater. 369,(2014) 69–80.
14. [14] J. C. Umavathi, & M. Shekar, “Mixed convection flow and heat transfer in a vertical wavy channel containing porous and fluid layer with traveling thermal waves”. International Journal of Engineering, Science and Technology, 197 3 , (2011). 196-219.
15. [15] J. C. Umavathi, & M. Shekar, “!Mixed convective flow of immiscible fluids in a vertical corrugated channel with traveling thermal waves”. Journal of King Saud University – Engineering Sciences, 26, (2014). 49–68. http://dx.doi.org/10.1016/j.jksues.2012.11.002.